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Relationships among the schemata of perceptual-motor behavior: Input patterns, system dynamics, and movement patterns
Hah, Sehchang, Ph.D.
The Ohio State University, 1989
Copyright ©1089 by Hah, Sehchang. All rights reserved.
UMI 300 N. Zeeb Rd. Ann Arbor, MI 48106 Relationships Among the Schemata of
Perceptual-Motor Behavior:
Input Patterns, System Dynamics, and Movement Patterns
DISSERTATION
Presented In Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate School
of The Ohio State University
By
Sehchang Hah, B.A., M.A.
* * * * *
The Ohio State University
1989
Dissertation Committee: Approved by
R. J. Jagacinski
H. G. Shulman
T . E. Nygren of Psychology Copyright by Sehchang Hah 1989 To My Parents, and
Children, Hina and Sehjung ACKNOWLEDGEMENTS
I would like to thank Dr. Richard J. Jagacinski for his advice, guidance, and support while I was at The Ohio
State University. I also thank Dr. Harvey Shulman for his constant support of my studies and for his participation in my various committee meetings. Thanks also go to Dr.
Thomas E. Nygren who served on my dissertation committee. I wish to express appreciation to Drs.
Jacqueline Herkowitz, F. Gregory Ashby, and Barbara
Forsyth for their support. I also thank my family for their understanding and encouragement. VITA
February 12, 1948 ..... Born, Seoul, Korea.
1970-1973 ...... Military service (Army), Korea.
1975 ...... B.A., Department of Psychology, Seoul National University, Seoul, Korea.
1975-1978 ...... Machinist, Chicago, Illinois.
1978-1979 ...... Graduate Teaching Assistant, Department of Psychology, Oklahoma State University, Stillwater, Oklahoma.
1980 & 1981 ...... Graduate Research Associate, Department of Psychology, The Ohio State University, Columbus, Ohio.
1982-1988 ...... Research Assistant, OCLC Online Computer Library Center, Dublin, Ohio.
1984 ...... M.A., Human Performance in Experimental Psychology, Department of Psychology, The Ohio State University, Columbus, Ohio. PAPERS
Hah, S. (1984). Progression and regression effects in tracking behavior. Unpublished master's thesis, The Ohio State University, Columbus.
Tolle, J. E. & Hah, S. (1985). Online search patterns: NLM CATLINE Database. Journal of the American Society for Information Science. 36. (2), 82-93.
Jagacinski, R. J. & Hah, S. (1988). Progression - regression effects in tracking repeated patterns. Journal of Experimental Psychology; Human Perception and Performance. 14 (1), 77-88.
Hah, S. & Hickey, B. T. (1989). Document display with gray levels incorporating psychophysical characteristics of brightness. OCLC Online Computer Library Center Technical Report (in press). Dublin, OH.
FIELDS OF STUDY
Major field: Human Performance in Experimental Psychology.
Studies in Human Performance: Professors R. J. Jagacinski & H. Shulman.
Studies in Mathematical Psychology: Professor F. G. Ashby.
Studies in Physiological Psychology: Professor D. R. Meyer.
Studies in Motor Learning: Professor J . Herkowitz.
v TABLE OF CONTENTS
ACKNOWLEDGEMENT...... ii
VITA ...... iv
LIST OF TABLES ...... ix
LIST OF FIGURES ...... X
LIST OF SYMBOLS, ACRONYMS, AND ABBREVIATIONS .... xii
CHAPTER PAGE
I. INTRODUCTION ...... 1
What is a Schema? Different Views ...... 4
The Successive Organization of Perception (SOP) Model ...... 7
A Comparison of Position and Rate Control Systems ...... 14
The Possible Relationships Among the Schemata of the Input Pattern, the System Dynamics, and the Movement Pattern ...... 17
Experimental Design ...... 22
Predicted Error Patterns ...... 26
Constraints of the Experiment ...... 28
Weak and Strong Hypotheses Concerning the Three Schemata ...... 29 Weak Hypothesis ...... 30
Strong Hypothesis ...... 34
Performance Measures ...... 37
II. METHOD
Subjects ...... 40
Apparatus ...... 40
Procedure ...... 42
III. RESULTS
Screening Trials ...... 45
Learning ...... 45
Initial Transfer ...... 57
Weak and Strong Hypotheses ...... 64
Weak Hypothesis ...... 65
Strong Hypothesis ...... 70
The Summary of the Results of the Weak and Strong Hypotheses ...... 75
Comparisons of Movement Patterns on Block 12 . 76
Movement Pattern as a Variable in the Model instead of the Input Pattern ...... 78
Comparison between the Experimental Conditions and Control Condition on T r a n s f e r ...... 82
Summary ...... 84
IV. DISCUSSION
Input Reconstruction Model Revisited ...... 86
vii Learning ...... 87
Experimental Evidence for the Dominance of the Schema of the Movement Pattern over Other Schemata on Transfer ...... 88
Supporting Evidence for the Schema of the Movement Pattern from Other Research ...... 90
The Schema of the System Dynamics ...... 93
Theoretical Implications of the Current Experimental Results ...... 94
Conclusion ...... 100
APPENDIX
INSTRUCTIONS TO SUBJECTS ...... 103
LIST OF REFERENCES ...... 108
viii LIST OF TABLES
TABLES PAGE
1. t-values to show the learning effect from Block 1 to Block 12 and Block 13 to Block 16 ...... 46
2. Weights on variables of the Input Reconstruction Model (Bg: offset, B ^ : weight on position of input, B2 : wexght on velocity of input) and the proportion of the variance accounted for by the model for the ensemble-averaged trajectory for each group of subjects ...... 49
3. Mean absolute error (ABS) and mean absolute deviation error (DABS) in degrees of visual angle on Block 13 ...... 66
4. Weak hypothesis, transfer performance, and t-values for each hypothesis ...... 67
5. Strong hypothesis, transfer performance, and t-values for each sub-hypothesis ...... 71
6. Weights on variables of the movement model (Bg: offset, B ^ : weight on position of movement, B2 : weight on velocity of movement) and the proportion of the variance accounted for by the model for the ensemble-averaged trajectory for each group of subjects ..... 80
7. Group performance differences of mean absolute error in degrees of visual angle on transfer ...... 83
ix LIST OF FIGURES
FIGURES PAGE
1. A weak hypothesis regarding a position control system ...... 9
2. A weak hypothesis regarding a rate control system ...... 11
3. The schemata and the predicted error patterns ...... 24
4. Characteristics of the five conditions concerning the input patterns, the system dynamics, and the movement patterns and the transfer conditions of the experiment ...... 27
5. A strong hypothesis regarding a position control system ...... 31
6. A strong hypothesis regarding a rate control system ...... 32
7. Ensemble-averaged movement pattern on Block 12 ...... 47
8. Weights on the input velocity ...... 50
9. Ensemble-averaged tracking error and the model fit for Condition A ...... 52
10. Ensemble-averaged tracking error and the model fit for Condition B ...... 53
11. Ensemble-averaged tracking error
x and the model fit for Condition C ...... 54
12. Ensemble-averaged tracking error and the model fit for Condition D ...... 55
13. Ensemble-averaged tracking error and the model fit for Condition E ...... 56
14. Ensemble-averaged tracking error on Block 16 ...... 58
15. Ensemble-averaged tracking error on Block 13 with Block 1 of Condition A .... 59
16. Ensemble-averaged tracking error and the model fit on Block 13...... 62
17. Ensemble-averaged movement pattern on Block 12 ...... 77
18. Ensemble-averaged movement pattern on Blocks 1 and 12 for Conditions B and D and the model fit when the movement pattern was used instead of the input pattern ...... 81
xi Te efrac lvlo CniinA A group Condition level of performance The A E The performance level of Condition E E group Condition level of performance The Exponential E € e Estimate of error velocity error of Estimate velocity Error error of Estimate D group Condition Error level of e C group performance Condition The level of e performance The movement hand of e velocity of Estimate movement e hand of Velocity position D hand of Estimate C B group position Condition Hand level of c performance The c c Amplitude c B a i Input position Input i F-»> F-» F -> LIST OF SYMBOLS, ACRONYMS, AND ABBREVIATIONS AND ACRONYMS, SYMBOLS, OF LIST Estimate of input velocity input of Estimate position input of Estimate Input velocity Input xii
I Input pattern of Condition A
Ke Human operator's gain for error nulling
K System dynamics of Condition A (position
control)
Kc Control system gain /*> Kc Estimate of control system gam m System output m Estimate of system output m Rate of system output m Estimate of rate of system output
M Movement pattern of Condition A o System output s Laplace operator
S The schema of the system dynamics
SOP Successive Organization of Perception t Time in seconds
0(theta) Phase lag in radians
T(tau) Effective time lag o»(omega) Frequency in radians
xiii CHAPTER I
INTRODUCTION
Motor behavior is not controlled by a strictly hierarchical system. The system is an interactive hierarchical system. It has been called hierarchically organized (Pew, 1974), heterarchical (Green, 1975), or lattice hierarchical (termed by Gallistel (1980) for the principle of the common path of Sherrington (1947)) . It is also interactive because the lower levels send feedback or information to the higher levels to guide motor behavior.
The central nervous system sends signals downward and also interprets signals sent upward. If corrections are needed, a new command to adjust motor behavior is sent downward. However, it is assumed that the central nervous system does not send specific signals to muscles
(Schmidt, 1982; Pew, 1984). Rather it sends parameter values for specific movements, and the lower levels take over the next step of motor processes (Arbib, 1980) .
Similarly, Gallistel (1980) thought the hierarchical
1 structure of motor behavior to be based on three principles for movement: the hierarchical organization, the lattice hierarchy principle, and the principle of selective potentiation and depotentiation. He presented
Weiss' (1941) six levels of hierarchy as a good motor control system: motor units, whole muscle, simple reflex, an entire limb, coupling circuitry, and taxes in ascending order. He argued that beyond the sixth level the problem is about motivation, not about motor coordination. Still it has been widely acknowledged that the lower levels can have autonomous processes to cope with the constantly changing environment (Pew, 1984? Gallistel, 1980).
Usually whenever a movement is executed, a person has some criteria or goals, and the movement is monitored to reach those goals. The main study of motor behavior has been the interaction between cognition and movement (Printz and Sanders, 1984). Goals and monitoring are two relevant components of motor behavior
(Krendel and McRuer, 1968). This relationship between two components was described mathematically in Krendel and McRuer's (1968) model. In the process of achieving a goal, a person builds a certain memory-based structure which will relate his/her cognition to the environment. This structure can be called a schema.
The main construct to describe what is learned in motor behavior is the schema (Pew, 1984; Schmidt, 1975).
When a person practices a certain motor task, he/she tries to learn what the input pattern, the system dynamics, and the movement pattern are like. The input pattern is the recognizable pattern that an operator must follow or duplicate using the control system. The system dynamics are the inherent characteristics of the system an operator must manipulate. The movement pattern is the pattern of movements an operator must execute in space and time to track the ever changing displayed cues. From his/her experience in the task, he/she develops schemata corresponding to these three components. The focus of the present study was to find out which schemata among the three were more influential when the task was compensatory tracking of a repeated input pattern. A transfer paradigm was used to make the inference. The findings can be important because they will indicate what aspects of motor behavior are most crucial in such motor skill. 4
What is a Schema? Different Views
Bartlett (1932) considered a schema as a core of memory. He thought people resolve the schemata into elements and rearrange the sequencing of them, which is manifested as a novel reaction. Guiding this process are images, which are details of the schemata. Bartlett (1932) thought schemata to be plastic and changing with the influx of sensory impulses. Any response is always new because it is created based on schemata and the constantly changing environment.
Schmidt (1975) proposed a schema theory of motor behavior. He considered that the formation of a schema involves rule learning, a product of practice. This rule is the relationship between the person's experience and its outcome. Schmidt (1982) proposed that a schema is a generalized motor program. A motor program is an abstract structure in memory that provides preparation for movement. The execution of a motor program may not require feedback. A motor program does not specify any particular muscles to be used. In general, a motor program is considered as a rather specific motor memory having parameter values. It seems that a motor schema originates from a motor program. The memory of a motor program fades and remains as a more abstract image (Bartlett, 1932). This image is actually a generalized motor program (Schmidt,
1982), and can be called a schema. It is understandable that, in general, motor programs and schemata are not differentiated by all students of motor behavior. To
Schmidt (1982), parameters must be supplied to execute movement: the parameters of duration, force, direction, and amplitude. To him, there was no specific differentiation between the upper-level and the lower-level schemata.
Neisser (1976) considered schema formation as a process undergoing accommodation, that is, it is built upon the past experience and also constantly changes with the present circumstances. To him, a schema is not a format or just a plan (Miller, Galanter, and Pribram,
1960). It is more open and flexible. He thought of it as a genotype which develops and changes with information from the environment. He said, "The schema picks it
(information) up, is altered by it, uses it (p. 61)." He claimed a schema develops from the general to the particular. Schemata interact with each other in complex ways and some are embedded in others. He also considered motives as general schemata. However, including motives as schemata is beyond the realm of most theories of movement (Gallistel, 1980).
Arbib (1980) considered four levels of locomotion control: the goal, its path, the actual pattern, and the detailed pattern of locomotion. He proposed motor schemata as motor processes which receive a plan as the input and deliver the output to the lower levels. He considered the lowest level, that is, the detailed pattern of locomotion to be insignificant in determining motor coordination. Pew (1984) , citing Bernstein's (1967) studies, claimed a schema is encoded as spatio-temporal geometry of movement. Arbib (1980) also considered this characteristic as the main core of schema, as did others
(Neisser, 1976; MacKay, 1982).
To conclude, a motor schema can be considered as a core of memory which has spatio-temporal characteristics and may develop from specific motor programs. Schemata are interactively hierarchical and can be executed together or separately. 7
The Successive Organization of Perception (SOP) Model
As is evident in many experimental results, perceptual-motor skill cannot be explained by only feedback theory or schema theory (for a discussion, see
Hah, 1984) . It is likely that both schema and feedback mechanisms must be incorporated to explain any complex perceptual-motor skill. As Pew (1984) thought, feedback consists of signals to higher levels to create and change schemata. This is well described mathematically by the
Successive Organization of Perception (SOP) model
(Krendel and McRuer, 1968), even though the model describes a closed feedback loop having the operator inside of the loop. This model assumes that the operator tries to distinguish the effects of control dynamics from the input trajectory conceptually. In the process the operator is assumed to develop tracking skills and progress from an error nulling mode to a pursuit mode and finally to an open-loop mode. For instance, in the error nulling mode, the operator attends to the displayed error signal and relies mostly on closed-loop feedback. In the pursuit mode, the operator is able to estimate the input and the controlled element dynamics from the displayed error and his/her own movement. The operator can then more directly respond to the input. In the last stage of learning, the open-loop or "precognitive" mode, the operator can learn a coherent input pattern and store it in long-term memory. This stored pattern can be used to generate the corresponding movement pattern with little feedback information. In this mode the operator can duplicate the input without lag or even lead the input.
As Jagacinski and Hah (1988) mentioned, operator's tracking skill can be explained by what signal sources or derivatives of signals are attended to by the operator with practice. Jagacinski and Hah (1988) assumed subjects tracking a repeated pattern focus mainly on the origin of the constantly changing error trajectory, that is, the input. Their experiments used a position control, so that the input and the movement patterns of the well-practiced subjects were nearly identical. The relative influence of input, system dynamics, and movement pattern can be investigated in the proposed experiment via the same general approach by using both position and rate control systems.
One version of the SOP model is described in Figure
1, which is based on the experimental results for compensatory tracking tasks of repeated inputs with a Proprtoceptlan
Cantral stick m •a trist
* 1 Errar
Errar
rigara I. Nivai ilt n |« n M | a Mtltlaa caatral tgtlam 10 position control system (Jagacinski and Hah, 1988). In this version, subjects are assumed to use the error-nulling mode, the pursuit mode, and the precognitive mode of the SOP model. With a rate control
A A system Kc and Kc should be changed to Kq/s and K q / s as shown in Figure 2. s is a complex Laplace operator.
For the position control system (Figure 1), subjects would develop three schemata from the visual display of error and proprioception of the control stick. Kc is subjects' internal estimate of the system dynamics (Kc). It is assumed subjects would perceive error (e) and error velocity (e) from the display of error
(e) . From proprioception, the hand position (c) and the velocity of the hand position (c) will be internally represented as c and c. The internal estimate of
A the system dynamics (Kc) can be inferred from the relation
Kc* = (i - e) / c, (1)
A A where i is an estimate of an input position. Kc* is an instantaneous estimate of Kc, and is averaged over time
A to arrive at Kc . Subjects can estimate output (m) and its
a ^ A A <£» velocity (m) as Kcc and Kcc, and these are K,/t
-K •
-xt •aH i I lapat
(I
Flgara 2. I walk fe|aalhatlt ragarflag a rata caatral agttam 12 represented in Figure 1 as m and m. From the estimates of the output and error, subjects can estimate the input
(i) and the input velocity (i) as i* and i*, respectively.
These estimates are refined by the memory of the input ys <• to become i and i, which is possible by the repeated presentation of the same input across trials. For a rate control system (Figure 2),
K c * = (i - e) / c, (2)
and the internal representation of the system dynamics is A assumed to be Kc/s. The error-nulling transfer function is assumed to be K^£_Cs/s for the position control system and
Ke £ "rs for the rate control system consistent with the
McRuer Crossover Model (McRuer & Jex, 1967), where € is the base of natural logarithms. The McRuer model assumed that subjects would make their hand movement proportional to the integral of error with the position control, and proportional to error with the rate control. Subjects were assumed to use this error-nulling function to fine-tune their movements. Dashed lines with arrows in the figures are the paths to form the hypothetical schemata: the input pattern, the system dynamics, and the movement pattern. 13
The pursuit transfer function of a person using a position control system (middle of Figure 1) Is
(1 + Bi) / Kc ,
where B is a weight for the input velocity which changes with practice. The weight of the input position was close to unity for all days of practice in previous studies (Hah, 1984; Jagacinski and Hah, 1988). For a rate control system, the pursuit transfer function
(middle of Figure 2) is
(i + Bi) / (Kc/ s ) .
As shown in the equation for the schema of the system dynamics, the schema of the input must be well established to obtain a good schema of the system dynamics. A similar dependency also exists for the schema of the input, because it is established by the knowledge of the output based on the estimates of the system dynamics and the displayed error. It is another matter, though, how well a subject could develop a specific schema because there should be some intentional action like rehearsal to form the schema 14 efficiently.
Using the schema of the movement pattern, or
"precognitive mode", is the ultimate level of skill
(Krendel and McRuer, 1968) . In this mode subjects were assumed to use a memorized movement pattern. It might not be possible for subjects to reach this mode with only three days of practice in the proposed experiment.
However, since the inputs were simple, subjects might reach this level of skill.
A Comparison of Position and Rate Control Systems.
Researchers have been interested in the different effects of the system dynamics. Especially the differences between the position and the rate control systems have been studied actively. The prime example is the McRuer Crossover Model (McRuer & Jex, 1967). They showed that when the tracking task was compensatory and the inputs were random appearing, operators' performance was such that the overall effects of the operator and the system dynamics resembled a gain, integrator, and time-delay whether the system dynamics were a position control or a rate control. 15
Subjects trained with one system may show no detrimental effects when they perform with a different dynamic system. When the transfer is performed in the reversed direction, however, the transfer effect might be negative. Such a phenomenon is called asymmetrical transfer. Lincoln (1953, quoted by Poulton, 1974) reported such asymmetrical transfer using a position control system and a rate or a rate-aided control system on a pursuit tracking task. Subjects' transfer performance from a position control system to a rate control system or a rate-aided control system revealed some benefits from the practice with a position control system. However, transfer from a rate control or a rate-aided control system to a position control system was negative. Poulton (1974) assumed that practice with a rate control system tended to make subjects lead the target in a manner that was inappropriate for a position control. In Gibbs' (1962) target-acquisition experiment subjects' performance was more sensitive to gain if the control system was a rate control instead of a position control. Subjects showed a more distinct U-shaped relationship in gain versus mean time on a target with a rate control than with a position control system. The above result implies that there are different 16 performance characteristics between rate and position control systems.
Poulton (1974) cited some experimental results showing the superiority of a position control system over a rate or a rate-aided control system in tracking sine wave inputs. He also cited the opposite results and concluded a rate or a rate-aided control system was not worse than a position control system for sine wave inputs.
Also in Jagacinski, Repperger, Ward, and Moran's
(1980) experiments, subjects' performance in acquiring a stationary target was better with a position control than with a rate control system. For small, fast-moving targets, a rate control system was better. This result implies that most efficient system dynamics may depend on the tracking task.
From the above experimental results, it seems subjects could develop different schemata for different control systems when the same input is repeated. If subjects develop a schema of the system dynamics with one system, this schema may be beneficial for certain systems and not beneficial for other systems in a transfer situation. 17
The Possible Relationships Among the Schemata of the
Input Pattern, the System Dynamics, and the Movement
Pattern
In the current experiment, the relationship of the three schemata in their degree of dominance on transfer was investigated. Subjects transferred from one input pattern, control system, and movement pattern to a combination of these where two of them changed. The movement pattern was dictated by the combination of input and system dynamics. The major question of interest was whether the input pattern, the system dynamics, or the movement pattern was most influential in transferring from one situation to another.
There is uncertainty about the relative dominance among the three components. As proposed in Krendel and
McRuer's (1968) pursuit mode, an operator may attend to the invariant input trajectory with practice when the same input is presented repeatedly (Hah, 1984;
Jagacinski & Hah, 1988) . Then the operator will learn mostly the overall input trajectory, and the input will be the most dominant factor in the transfer. In the present experiment, the internal representation of 18 input can be represented as a higher level schema. For instance, in an automobile driving situation, the schema of the input consists of road geometry and other vehicles and obstacles (McRuer, Allen, Weir, and Klein,
1977). Marteniuk and Romanow (1983) reported that subjects lessened variability of memorized irregular movement patterns with practice and overall trajectory rather than specific parts of the trajectory changed with practice.
It can also be argued that a change of the system dynamics would be more detrimental in transfer performance than the change of the input, as implied by
McRuer and Jex (1967) who used a random-appearing sum of sine wave inputs. They found that the crossover frequency was strongly dependent on the form of the controlled element, but less dependent on input bandwidth (p. 2 36). In the current experiment an input was presented repeatedly, which enabled subjects to anticipate. This situation is quite different from that of random appearing inputs. However, in certain situations, the control system dynamics may be more crucial than the input pattern. In the present experiment, the schema of the system dynamics was assumed to develop from the relationships among 19 proprioception of the hand position, the estimated input, and the visually perceived error.
It can also be hypothesized that the higher level of motor behavior, which is assumed to include the schema of the input pattern, is easier to change than the lower levels, which are assumed to include the schema of the movement pattern. This is based on the fact that the central nervous system must interpret the environmental change and deliver commands to the lower levels and change the learned pattern of the lower level systems. It implies that the higher level system is more flexible than the lower level system. Cigar wrapping behavior reported by Crossman (1959) may be a good example. The performance improvement of cigar wrapping over seven years may be due to efficient coordination of the lower level system, rather than the higher level system. If we generalize Arbib's (1980) proposal of four control-levels of motor behavior, it might be that the third (the actual pattern of limb movements) and fourth
(the detailed pattern of motor-unit movements) levels became more efficient in cigar wrapping rather than the first and the second which were goal and its path, respectively. Once a movement pattern is learned, it is presumed that the corresponding command pathways are well established. For instance, a skillful typist does not spend much time to look down at the keyboard, measure the distance, and control the strength of striking.
What the typist needs to know is the words to type. The necessary movements would be executed rather automatically. The skillful typist does not need to calculate the necessary parameter values for movements.
These parameter values are already built into the skilled movements. If movement change is needed, a new appropriate command structure must be built on the lower peripheral level which is assumed to be less cognitive than the higher level system. Presumably this will be hard to adjust.
Another example is that if your new car has a gear shift at the right side of the steering wheel instead of the right side of your seat like in your old car, sometimes you would tend to stretch your arm to the right side of your seat to shift the gear like a reflex.
In this example it could be assumed that the connection between the higher level and the lower levels was not properly interwoven. Or it could be that the higher center gave a general global command, "Shift gear!" and the lower levels were not practiced enough to move in the right direction. In either case the higher level sends a correct message, which is not executed properly at the lower levels. So we might say that the schema of the movement pattern would be a more dominant component in this transfer condition.
Or, as reported by Briggs, Fitts, and Bahrick
(1957) who compared force and amplitude cues in tracking tasks, there might be no differential effects of input, system dynamics, and movement pattern changes on transfer. Assuming there is an interaction between force and amplitude cues on tracking tasks (Bahrick,
Bennett, and Fitts, 1955), Briggs et al. (1957) tried to find which was more the dominant factor between force and amplitude cues in a transfer task. Each group of subjects had a different combination of force and amplitude cues. In the transfer condition all subjects had the same force and amplitude cues as the control condition. The performance measure was the accumulated time on target. Training performance showed a main effect of amplitude and an interaction effect between force and amplitude cues. The main effect of force was not significant. Multiple comparison tests showed that amplitude cues were the more dominant factor only when 22 force was high. There was a significant positive effect of practice for all groups except the control group.
There was, however, no significant difference on transfer conditions between groups. This indicated that there was no especially favorable learning condition to improve transfer performance. Briggs et al. (1957) argued that if there is no apparent system transformation, or if no qualitatively different responses were involved in the transfer condition, there would be no performance level difference in the transfer condition between groups. If similar results would be obtained with the three schemata in the current experiment, it could be concluded that they do not have different effects in a transfer situation.
Experimental Design
The current experiment involved five training conditions in order to test the relative dominance of schemata of input patterns, system dynamics, and movement patterns when two of these components changed in a transfer condition. It was not possible to change only one of these components at a time. The inputs, system dynamics, movement patterns, and proposed error 23 profiles of each condition for practice are shown in
Figure 3. s is a complex Laplace operator used to convert time functions to complex variable functions, that is, f (t) -> F(s) . Multiplication by s denotes differentiation, s2 a second derivative, and 1/s integration. For the convenience of notation, it was assumed that Condition A had I, K, M for the input pattern, the system dynamics, and the movement pattern, respectively. Then, Condition B had I/s, K/s, and M.
Condition C had si, K, and sM. Condition D had I, K/s, and sM. Condition E had I/s, K, and M/s.
The input for Condition A (I, K, M) (control condition) was
i(t) = d(a x arctangent(wt-0) )/dt (3) or I.
i was the input position in degrees of visual angle, a was an amplitude, t was the time in seconds,w was a frequency in rad/s, and 6 was a phase lag in radians. The input for Condition B (I/s, K/s, M) was
i (t) = a x arctangent(wt-®) (4) or I/s (the integral of the input for Condition A). 24
Id eal Predicted Input pottern System movement pattern error pattern dynamics f
0 2 I « 4 10 12 It
fO I K /s i|
0 I 4 I I 10 II l« 0 2 • • 10 II it
* sM 9? 1
e i 0 2 4 6 8 10 12 14
a q sM r v sI K /s 3 i e i s 0 2 4 6 8 10 12 14
a 97 .5 M/s 3 1 i I • « 10 II I* e z 0 2 « 10 II It T V n o { » ) TVne Figure 3. The input patterns, system dynamics, ideal movement patterns, and the predicted error patterns The horizontal axis is time in seconds, and the vertical axis is tracking input, movement, and error. 25 The input for Condition C (si, K, sM) was i(t) = d2 (ax arctangent(wt-fi)/dt2 (5) or si (the derivative of the input for Condition A). The input for Condition D (I, K/s, sM) was the same as the control condition (A), and the input for Condition E (I/s, K, M/s) was same as Condition B (I/s, K/s, M). Conditions A, C, and E were position control systems and Conditions B and D were rate control systems. Since Conditions A, C, and E were position control systems, the input and the ideal movement patterns were same. Because Conditions B and D were rate control systems which integrate, subjects must produce a movement trajectory resembling input velocity to make the output of the system match the input pattern. Subjects' performance on the transfer task was expected to depend on what kind of practice they had before the transfer. The performance difference between experimental groups and also between the control group and the experimental group would reveal how the change of the three components influenced transfer. In Figure 4, the transitions occurring on transfer are described. When subjects in Condition B (I/s, K/s, M) transferred to the control condition (A (I, K, M)), they had the same required movement pattern as they had prior to transfer. However, the input pattern and the system dynamics in the control condition were different from their practice condition. Likewise, subjects in Condition C (si, K, sM) transferred to the same system dynamics, but the input pattern and the movement pattern were the temporal integrals of those they had practiced. Subjects in Condition D (I, K/s, sM) transferred to the same input pattern, but the system dynamics and the movement pattern were different. Subjects in Condition E (I/s, K, M/s) transferred to the same system dynamics, but the input and the movement patterns were the temporal derivatives of the patterns they had practiced. Predicted Error Patterns The predicted error patterns (Figure 3) resemble the velocity patterns of the inputs for a position control system (Hah, 1984). For a rate control system it was assumed that subjects' error profile would resemble the acceleration pattern of the input based on Input patterns I/s si SK M/s Required K/s SK movement B p attern s * K/sK/s sM Figure 4. Characteristics of the five conditions concerning the input patterns, the system dynamics, and the movement patterns and the transfer conditions ( — ) of the experiment. ► denotes the comparisons on transfer. and ------denote the axes of the system dynamics and the movement patterns, respectively. For the input patterns, no axis is denoted. For them the left side of the figure is I/s, the middle is I, and the right side is si. s is a complex Laplace operator. 28 the previous reports by Phatak and Kessler (1977) and Garvey (1960). In Phatak and Kessler's (1977) report subjects' error profile resembled the acceleration pattern of the input when subjects used a rate-aided control system. Garvey (1960) also found a similar error pattern with a rate control system. Constraints of the Experiment The present experiments had a constraint in manipulating three variables corresponding to three schemata. If two variables were fixed, the other was automatically determined (Figure 3). This made it impossible to isolate each variable, which posed a problem for analyzing interactions between variables. However, as noted in Krendel and McRuer (1968) and Jagacinski and Hah (1988), subjects seemed to be able to isolate the input pattern from the controlled dynamics elements. Also what concerned the author here was whether any component was more dominant than others in transferring tracking tasks. It was assumed that main effects were much larger than the interaction effects. It was also assumed the effects of differentiation and integration between the practice and transfer conditions 29 would not differ in performance difficulty much. In other words, transferring from Conditions C (si, K, sM) and E (I/s, K, M/s) should be about equally difficult. Also, another concern regarding the transfer task was the possible positive or negative transfer effects like the negative transfer from a rate to a position control system reported by Poulton (1974). In the proposed experiment, however, those effects were the very effects of interest. Weak and Strong Hypotheses Concerning the Three Schemata Two hypotheses, a strong and a weak one, concerned how much influence the three schemata had in tracking skill. The weak hypothesis assumed that all three schemata were always used by subjects even at the later stage of practice. Only the degree to which subjects used a particular schema relative to other schemata mattered (Figures 1 and 2) . The strong hypothesis assumed subjects would use only one or two schemata in tracking at the later stage of practice. This behavior was described by switches which could connect or disconnect paths from particular schemata (arrow 30 switches at numbers 1, 2, 3, and 4 in Figures 5 and 6). These hypotheses are described in terms of comparisons between conditions as follows. Capital letters A, B, C, D, and E were the five conditions, and JJ, £, fi, and £ were the transfer performance levels of these conditions. All of these hypotheses also assume that error nulling may be used secondarily for small corrections. Weak Hypothesis The weak hypothesis about the relative dominance of three schemata was tested with the following three comparisons of transfer performance. The comparison of the performance levels of Conditions C (si, K, sM) and D (I, K/s, sM) would reveal the relative dominance between the schemata for the input pattern and the system dynamics (Figures 3 and 4) . Both Conditions C (si, K, sM) and D (I, K/s, sM) had the same movement pattern, which was different from the control condition, A (I, K, M) ; however, Condition C (si, K, sM) had a different input and Condition D (I, K/s, sM) had different system dynamics from the control condition. For example, if the transfer performance for c, c PraprtoctpU** Palpal -HD" M lh n li ____ x_____ 1- • ^ litkaata at Haaiarg at —f - “ Kt* Spstaai Maaamaat rn c i|iltln Bgaaatks Pattara * Caatral •tick * 4 ,-Vv* i 1.1 I» “FT •ati al I °TfI Paiitlaa »|wn— |-^-^ Maaiarg ml Part all lapal 'Errar lapat Pattara lirar NaMag . . f m i a . . Flgara s. I »trMg kypathatl* ragaraiag a paiitlaa caatral syitaai u> H waitfi* iu i m n u • Iw j i Iu lmj|« «•* uali j VII* |W|M] u*im ■■nliiMui 33 Condition C (si, K, sM) were better than Condition D (I, K/s, sM), it meant the schema for the system dynamics was more dominant than the schema for the input pattern (C > D => S > I) . The comparison of the performance levels of Conditions B (I/s, K/s, M) and D (I, K/s, sM) would show the relative dominance between the schemata for the input pattern and the movement pattern. Both Conditions B (I/s, K/s, M) and D (I, K/s, sM) had the same system dynamics, which was different from the control condition, A (I, K, M) ; however, Condition B (I/s, K/s, M) had a different input pattern and Condition D (I, K/s, sM) had a different movement pattern from the control condition (A (I, K, M)) . For example, if Condition B (I/s, K/s, M) were better than Condition D (I, K/s, sM), the schema for the movement pattern would be more dominant than that of the input pattern in the transfer condition (B > D => M > I). The comparison of the performance levels of Conditions B (I/s, K/s, M) and E (I/s, K, M/s) would reveal whether the schema of the system dynamics or the movement pattern was more influential in the transfer condition. Conditions B (I/s, K/s, M) and E (I/s, K, M/s) had the same input, which was different from the 34 control condition, A (I, K, M) . However, Condition B (I/s, K/s, M) had different system dynamics, and Condition E (I/s, K, M/s) had a different movement pattern from the control condition (Condition A (I, K, M)) . For example, if Condition B (I/s, K/s, M) were better than Condition E (I/s, K, M/s), it would mean the schema for the movement pattern would be more dominant than that of the system dynamics (B > E => M > S). The above three comparisons were tested with a priori two-tailed t-test because the directions of the effects could be in either direction. Also equal performance effects by the schemata of components on transfer were not ruled out. The assumption of equivalence of integration vs. differentiation was also tested with Conditions C (si, K, sM) and E (I/s, K, M/s) . Strong Hypothesis Memorized movement. If subjects would have memorized the movement pattern and used this schema exclusively, the second switch would be connected to 4 (Figures 5 & 6) . The first switch would not matter. This would predict B > (C = D = E), because Condition B 35 (I/s, K/s, M) had the same movement pattern as Condition A (I, K, M). It was assumed that error nulling would not be a dominant movement strategy if subjects were relying on a memorized movement pattern. The transfer performance of Conditions C (si, K, sM) and D (I, K/s, sM) should be equivalent (Figures 3 & 4) because they have the same movement pattern, which was different from the control condition, A (I, K, M) . Condition E (I/s, K, M/s) might also be equivalent to Conditions C and D if M/s and sM were equally different from M and had a similar effect on transfer. (Figures 3 & 4) . Memorized input, calculated movement. If subjects had used the memory of the input to calculate the movement pattern they would generate, switches would be connected to positions 2 and 3 in Figures 5 and 6 . Subjects would use the schemata of the input pattern and the system dynamics. The predicted pattern of results would be D > (C = E) > B or (C = E) > D > B. If the input schema were more important than the schema of the system dynamics, D might be superior, because Condition D (I, K/s, sM) had the same input as Condition A (I, K, M) . However, if the schema of the system dynamics were 36 more influential than the schema of the input pattern, then Conditions C (si, K, sM) and E (I/s, K, M/s) might be superior, because Conditions C (si, K, sM) and E (I/s, K, M/s) had the same system dynamics as Condition A (I, K, M) . Since the input pattern also mattered, fi would be the next best because Condition D (I, K/s, sM) had the same input as the control condition (A (I, K, M)) . B would be the worst in both predictions because Condition B (I/s, K/s, M) had a different input pattern and different system dynamics from Condition A (I, K, M). (Figures 3 & 4). Calculated input, calculated movement. If subjects used only the memory of the system dynamics, switches would be connected to 1 and 3 in Figures 5 and 6 . According to this hypothesis, the input pattern would be calculated from the perceived visual error and proprioception of hand position. The movement pattern would be calculated from the input and the schema of the system dynamics. The schemata of the input pattern and the movement pattern would not be used. The expected performance levels would be (C = E) > (B = D) because Conditions C (si, K, sM) and E (I/s, K, M/s) had the same system dynamics as Condition A (I, K, M), 37 unlike Conditions B (I/s, K/s, M) and D (I, K/s, sM) . (Figures 3 & 4). Performance Measures Mean absolute error was used as a summary performance measure. This measure would not reveal much about the shape of the subjects' tracking error trajectory. Therefore, performance was also interpreted in terms of the Input Reconstruction Model (Hah, 1984; Jagacinski and Hah, 1988) which used the weight on the input velocity as a performance measure. The Input Reconstruction Model for both a position control system and a rate control system was m(t) = B 0 + Bx i( t - 0.150 ) + B2 i( t - 0.150 ), (6 ) where m is system output, i is input, i is input velocity, and 0.150 is an inherent effective time delay in seconds. This measure, weight on the input velocity in the input reconstruction model (B2), conveyed information about the shape of error trajectory and was part of a linear approximation to subjects' overall trajectory pattern. It was hoped that this measure would 38 accurately reflect the subjects' tracking behavior in the time dimension. However, this measure would not be very sensitive to any nonlinear and random behavior which was included in the mean absolute error score, the first measure. In previous experiments (Hah, 1984; Jagacinski & Hah, 1988) the weight on the input velocity increased with practice. The weight on the input was approximately unity and did not change with practice. The weight on the input velocity was basically the same as (0.150-1) of the simplified Input Reconstruction Model, which was m(t) = B 0 + E x i(t-x), (7) where B 0 and were constant, t was time in seconds, and x was an effective time delay that varied with practice. 0.150 s was assumed to be the inherent fixed time delay. With practice, (0.150 -t) would get larger. This means subjects are shortening their effective time delay. This improvement of skill is described as a lead, manifested as a weight on the input velocity in the Input Reconstruction Model (for a detailed discussion, see Jagacinski & Hah, 1988) . The usefulness of an effective time delay as a performance measure is also 39 supported by Pew and Rupp (1971), who showed that it was a more sensitive measure than an error score for continuous tracking. The progression hypothesis of Fitts, Bahrick, Noble, and Briggs (1959) states that as subjects get more practice, they will put more relative weight on velocity cues. Fuchs (1962) also found in compensatory tracking experiments with an acceleration control system, subjects increased the weight on error acceleration and decreased it with a secondary concurrent tracking task. In the previous research by the author (Hah, 1984; Jagacinski & Hah, 1988) subjects put more weight on the input velocity cues with practice and decreased the trend with a secondary concurrent memory task. In the current experiment the same Input Reconstruction Model was used to test subjects' performance levels on transfer. If the error patterns do not correspond to the predictions of the model well, weight on the input velocity cue (B2 ) cannot be used as a performance measure to compare the three schemata in the current experiment. CHAPTER II METHOD Subi ects A total of 134 subjects participated in a pre-test, and 50 of them who performed better than a criterion were selected for the main experiment. There were ten subjects in each of five conditions. They received credit in an introductory psychology course for participating in the experiment. To motivate the subjects, they were told that the best subject would get a monetary reward of a $ 2 0 bonus. All subjects were right-handed and had 20/20 vision. Apparatus Subjects manipulated the control-stick that was six centimeters long and 0.4 millimeters in diameter. Its angular range was 30 degrees to the right and left from the vertical position. Subjects viewed a compensatory 40 41 error display on an oscilloscope screen (Tektronix 602) which was about 50 centimeters away at eye level height. Its center was marked with a vertical yellow stripe, which was 1 . 1 centimeters long and 0 . 1 centimeters wide. A 5.5 centimeter vertical green line moved horizontally over a 10 centimeter range (11.4 degrees of visual angle) to indicate tracking error. Tracking error was defined as the distance of the green line from the center yellow line. The position of the control-stick determined either the position (Conditions A, C, and E) or rate of the system output (Conditions B and D). The sensitivity of the position control-stick was set so that two degrees of displacement of the control-stick resulted in one-degree of visual angle displacement of the display. The sensitivity of the rate control-stick was set so that one degree of displacement of the control-stick corresponded to two degrees of visual angle/second velocity of the display. During the experiment subjects wore headphones through which they heard random-noise. This prevented them from hearing unnecessary external noises. Through the headphone the subjects also heard the error score from the experimenter after each trial. A Data General Nova 4X computer was used to conduct the experiment and to collect the data. It 42 refreshed the error display every 1 0 ms and recorded the data every 50 ms. Procedure All prospective subjects were tested on the transfer condition (Condition A) with screening trials. The subjects who were better than a criterion were selected to participate in the experiment during the next week. The criterion absolute error score was 0.31 degrees of visual angle. Briggs (1969) suggested such a screening procedure for transfer experiments. Based on the mean absolute error score for the last three trials of five screening trials, subjects were chosen if they were above a criterion score. These subjects were assigned to one of five groups randomly. The same procedure was used for other weeks. Because all subjects had the same transfer condition, the screening procedure should have affected subjects equally. Therefore, there was no grounds to expect that subjects' performance would be differentially biased by the initial administration of the transfer condition for screening. Subjects practiced for three days on one of five conditions (A - E) and on the fourth day they participated in the transfer condition, Condition A. Subjects had four blocks of trials per day for four days. Each block had two practice trials followed by ten data trials. Each block of trials lasted about seven minutes. After each block there was a two-minute break. Subjects had 10 data trials x 4 blocks x 3 days = 120 training trials and 10 data trials x 4 blocks = 40 transfer trials. Subjects were asked to minimize tracking error, which was the absolute distance of the target position from the center yellow stripe on the screen. They were instructed to put the control-stick about at the center before each trial for all conditions except Condition E. For Condition E subjects were instructed to put it about middle to the left from the center position. Such instructions were necessary to prevent the error display from jumping too far from the center of the screen when a trial began. Before each trial the vertical line stayed at the left-most side of the screen for 16 s, and then jumped to the center for two s before the next trial began. The green line then moved to the left or to the right near the center depending on how the subject placed the control-stick initially. This abrupt movement signaled the start of a trial. Each trial lasted 14 s. At the end of each trial the moving line jumped to the left-most side of the 44 screen and stayed there for 16 s. This occurrence signaled the end of the trial. During this interval, subjects were told their average absolute error for the middle 1 0 s of tracking on the previous trial. Subjects' instructions are in the Appendix. CHAPTER III RESULTS Screening Trials An analysis of variance was performed on mean absolute error of the last three of five screening trials to find out whether the five groups were homogeneous in tracking ability. As anticipated, the F-test turned out to be non-significant (F(4,45) = 1.00, p>0.05; Zdf=4,45^=0.05 = 2.59) . (Note: If any statistical value was significant, it will be denoted with * in this report.) Learning Mean absolute error of all groups decreased significantly with practice from Block 1 to Block 12 (Table 1 and Figure 7) . This measure was a summary performance measure and implied very little about the shape of the subjects' tracking error profile. It was 45 46 Table 1 t-values to show the learning effect from Block 1 to Block 12 and Block 13 to Block 16 (tone-tailed, df=9 =1 *8 3 f°r <*=0.05, tone-tailed, df= 9 = 2 -8 2 for *= 0 .0 1 ) Control and experimental conditions Performance A BC D E measure From Block 1 to Block 12 Mean absolute 5.19* 8.27* 7.64* 3.41* 6.82* error Weight on the input velocity 3.71* 0.30 8.97* 2.53* 2.67* (B2) From Block 13 to Block 16 Mean absolute 2.18* 3.01* 4.39* 5.33* 6.84* error Weight on the input velocity 1.55 2.83* 0.95 2.84* 4.68* (B2) *p<0.05 Tracking error (degrees of visual angle) 0.36 0.32 0.40 0.28 0.20 0.24 0.04 0.08 0.00 0 2 iue . en boue rcig error. tracking absolute Mean 7. Figure 4 Blocks ofTrials 6 ■A 8 a - 10 12 • ------ls, s, M) , /s K , (l/s B • ls, , s) /s M K, , (l/s E 14 16 48 calculated by averaging the instantaneous absolute errors sampled every 50 ms in a trial and averaged across trials in a block. For each block of trials there was one mean absolute error score for each subject. As shown in Figure 7, in terms of this measure subjects in Condition C (si, K, sM) performed worse than other groups during practice (Blocks 1-12). The second measure, weight on the input velocity in the Input Reconstruction Model (B2), conveys information about the shape of error trajectory and was part of a linear approximation to subjects' overall trajectory pattern. It was hoped that this measure would accurately reflect the subjects' tracking behavior in the time dimension. However, this measure would not be very sensitive to any nonlinear and/or random behavior which was included in the mean absolute error score, the first measure. As shown in Table 2 and Figure 8 , subjects put more weight on the input velocity with practice. In a comparison of Blocks 1 and 12 all conditions except Condition B (I/s, K/s, M) showed statistically significant increases in B2 (Table 1). However B2 must be interpreted with caution. If the value of B^ was close to 1.0 across the various inputs as in the previous experiments (Hah, 49 Table 2 Weights on variables of the Input Reconstruction Model (Bq(degrees of visual angle), offset; B^tunitless), weight on position of input; B 2 (seconds), weight on velocity of input); the proportion of the variance accounted for by the model for the ensemble-averaged error trajectory for each group of subjects Condition Block B0 Bl B 2 Variance of trials accounted for A 1 0.004 0.965 0.043 0.979 1 2 0.047 0.942 0.075 0.965 13 0.026 0.949 0.081 0.967 16 0.028 0.954 0.087 0.956 B 1 0.024 1.013 0.129 0.715 1 2 0.030 1.006 0.131 0 . 8 8 6 13 0.023 0.958 0.080 0.952 16 0.033 0.951 0.093 0.889 C 1 0.036 0.875 0.028 0.932 1 2 -0.000 0.878 0.090 0.683 13 0.111 0.926 0.085 0.853 16 0.055 0.964 0.090 0.907 D 1 -0.072 1.074 0.044 0.951 1 2 -0.023 1 . 0 1 0 0.098 0.907 13 0.083 0.938 0.078 0 . 8 8 6 16 0.053 0.944 0.090 0.900 E 1 -0.017 0.997 0.087 0.900 1 2 - 0 . 0 0 1 1.000 0 . 1 0 2 0.927 13 0.056 0.959 0.060 0.932 16 0.046 0.952 0.084 0.935 0.14 — o o — 0.12 B(l/s, K/s, M) ♦ — ♦ D(l, K/s, sM) • — • E (l/s , K, M /s ) 0.10 &— 0.08 (0 0.04 0.02 0.00 0 2 4 6 8 10 12 14 16 Blocks of trials Figure 8. Weight on the input velocity. 1984; Jagacinski & Hah, 1988) and if the variance accounted for by the model was high (Table 2) , there would be no problem in comparing B2 's. The variances accounted for by the model were relatively low for Blocks 1, 12, and 16 of Condition B (I/s, K/s, M), Blocks 12, 13, and 16 of Condition C (si, K, sM), and Blocks 12, 13, and 16 of Condition D (I, K/s, sM) and Block 1 of Condition E (I/s, K, M/s). Large discrepancies between the model and the data for the above blocks of trials are clearly shown in Figures 9 to 13. In Jagacinski and Hah (1988), B2, the weight on the input velocity of the Input Reconstruction Model, m(t) = 6 0 + 6 ! i(t-0.150) + B 2 i(t-0.150), was more sensitive than the mean absolute error. Since both B^ and B2 changed their values in the current experiment, it is hard to draw conclusions solely based on B 2 values. This is because the Input Reconstruction Model was based on the assumption of the weight on the input position to be close to 1.0 (see Jagacinski & Hah, 1988). Some B^'s were not close to 1.0 (Table 2). Given this problem, B2 was not as sensitive a measure of performance as in the previous experiments. Subjects' performance also improved after transfer (Blocks 13 -16) as shown in Figures 7 and 8 . Conditions Tracking error (degrees of visual angle) Tracking error (degrees of visual angle) 4 1 - - 2 0 - - 0.4 02 .6 0 .0 0 1 0.4 2 0 .6 0 4 0 .6 0 00 0.4 j O 4 4 Figure 9. Ensem ble-averaged tracking error (dots) and the model fit (solid Hne) for Condition A. Condition for Hne) (solid fit model the and (dots) error tracking ble-averaged Ensem 9. Figure S 6 6 0 Time (s) 7 7 6 8 lc 1 Block lc 13 Block 0 9 10 10 4 0 - 6 0 - 4 0 - •U> 6 0 02 4 0 6 0 00 04 2 0 4 0 6 0 4 0 4 S 0 6 6 Time(s) 7 7 6 8 lc 12 Block lc 1$ Block 9 94 10 10 to U1 Tracking error (degrees of visual angle) Tracking error (degrees of visual angle) 3 0 - 06 03 o a 02 06 Oft 04 14 14 4 4 iue 0 Esmbeaeae rcig ro dt) n h oe ft(oi ie o odto B ^ B. Condition for line) (solid fit model the and (dots) error tracking ble-averaged Ensem 10. Figure S 6 ie a Tm (a) Time (a) Time 7 7 8 lc 1 Block lc 13 Block to 10 -Of I - -04 •14 o a 02 06 04 2 0 14 14 j O 4 4 S 0 6 6 7 7 a a lc 16 Block lc 2 1 Block 9 10 9 10 u> Tracking error (degrees of visual angle) Tracking error (degrees of visual angle) - .5 -1 - 3.0 -3 .5 -2 0. 0.2 -0 .4 -0 .2 -0 1.0 -1 .8 -0 .6 -0 1.2 -1 0.5 2.5 3.0 2.0 0.0 2.0 0.6 8 0 0.0 1.0 0.4 0.2 1.0 1.2 1.0 4 579 10 10456789 456789 - - - - - iue 1 Ensmbeaeae takn err dos od h mdl i (oi ln) o Cniin C. Condition for line) (solid fit model the ond ots) (d error tracking ble-averaged sem n E 11. Figure -- . ------\ 1 1 1 1 1 \ . v j y _ 6 s \ ie s Tm (s) Time (s) Time 7 ______9 lc 1 Block lc 13 Block 9 105 0 3 - .5 -2 -20 -1.5 -10 5 0 - 1.0 -1 0.8 -0 4 0 - -1.2 -0.6 00 5 0 20 2.5 3.0 0.8 1.0 4 0 6 0 0.0 2 0 12 10 4 - - - - 5 1 ------1 1 1 1 e \ f 7 4r lc 16 Block 8 ------lc 12 Block 9 . L 10 tfl Tracking error (degrees of visual angle) Tracking error (degrees of visual angle) - 4 0 - -ae 4 0 02 04 4 0 4 0 oe 1.0 4 4 iue 2 nebeaeae rcigerr(os n h oe i sldln)frCniin0 ^ 0. Condition for line) (solid fit model the and (dots) error tracking Ensemble-averaged 12. Figure S 9 6 () (s) e m i T (s) e m i T 7 7 Block 1 Block lc 13 Block 8 9 10 10 2 0 - 4 0 4 4 4 s 6 6 6 7 7 lc 12 Black i 8 lc 16 Block B 9 10 10 0* A and D did not exhibit significant learning effects (Table 1) when the performance measure was B 2 . In terms of mean absolute error all conditions showed significant improvement (Table 1) . Subjects' performance converged after three blocks of 12 trials of transfer (Figures 7, 8, 14 & 15) . When an ANOVA was performed to test if there were any group differences on Block 16 after transfer, the F value was nonsignificant for both mean absolute error (F(4,45) = 0.48; 4 5 . ^ 0 . 0 5 =2.59) and B2 (F(4,45) = 0.20). Initial Transfer Ensemble-averaged tracking error on initial transfer (Block 13) showed an asymmetrical error pattern (Figure 14) . Block 1 of Condition A (I, K, M) is also provided for comparison in Figure 14. The error trajectories for the first part of a trial, that is, from 4 s to 7 s, of all conditions were similar in shape. However the second part of the error trajectory from 7 s to 10 s was quite different in shape across conditions. All experimental groups showed larger mean absolute error scores than Condition A (I, K, M) (Figure 7). There was a significant difference among groups on initial transfer, Tracking error (degrees of visual angle) 0. - .3 -0 -0.9 - 0.0 0.3 0.6 0.9 0.6 iue 4 Esml—vrgd rcig ro o Bok 13 Block on error tracking Ensemble—averaged 14. Figure - - 5 7 9 8 7 6 5 4 ih lc 1 f odto A. Condition of 1 Block with ie (s) Time B(/ s M] /s, K , (l/s 'B , lc 1 Block A, (, , M) K, A(l, (l K sM’ K, C(sl, ls K M/ ’ /s M K, (l/s, E D(l, D(l, / K s , s M 10 Ul OJ Tracking error (degrees of visual angle) 0.4 -0 - - - 0.8 0.6 0.2 0.0 0.2 0.4 0.6 0.8 iue 5 Esml—vrgd rcig ro o Bok 16. Block on error tracking Ensemble—averaged 15. Figure 4 5 6 ie (s) Time 7 8 ° *Cs, , sM) K, *C(si, * — ------ls K/, M) /s, K (l/s, °B 9 10 U1 V£> 60 Block 13 ( F (4,45) = 2.66*, E <0.05) ^ 4 ,4 5 . ^ 0 . 0 5 = 2.59) . These error measures were also translated into relative improvement measures using a transformation recommended by Briggs (1969). Experimental Group - Control Group on Block 13 on Block 1 x 100(%) (8) Control Group - Control Group on Block 13 on Block 1 This formula reflected how much an experimental group gained with practice compared with the control group. The performance of the experimental group was described relative to the performance gain of the control group. If it were close to 100 %, it meant that there was no significant difference between the experimental group and the control group. If it were significantly less than 100 % or negative, it showed negative transfer for the experimental group. This meant that practice with the experimental condition was not as beneficial to transfer performance as practice with the control task. When Briggs' (1969) formula was used, the percentages of 61 transfer for Groups B, C, D, and E were 66%, 58%, 27%, and 56%, respectively. Condition B (I/s, K/s, M) showed the largest percentage of transfer. B2 was not as sensitive as the mean absolute error measure as evidenced by a non-significant difference among B2 /s on the first block of transfer trials, Block 13 (F (4,45) = 1.26, p > 0 .05). Also the variance accounted for by the model was low for some conditions (Table 2). The model had trouble in describing the oscillatory error pattern after the input and the movement changed direction at 7 s (Figures 9 to 13 & Figure 16) . This phenomenon was more evident on initial transfer performance on Block 13 (Figure 16) , especially for Conditions C (si, K, sM) and D (I, K/s, sM). This pattern was subdued with more practice as shown on Block 16 (Figures 14 & 15) . The pattern was similar to the oscillatory error pattern near the directional change of the input and the movement reported previously (Hah, 1984; Jagacinski & Hah, 1988). Given the lack of fit between the linear input reconstruction model and the empirical error trajectories, a different measure of trajectory shape was used. The difference between the shapes of the ensemble-averaged error trajectories for the control condition (A) and the Tracking •rror (d^nMi of vtauol arvgl.) Tracking error (degree* of vteuol onglo) .4 0 - -02 at -a - ao 02 at OJ t a t a t a 1.0 10 11 4 4 iue 6 Esmbeaeae takn err dt ad h mdl i (oi ln) n lc 1. 0* 13. Block on line) (solid fit model the and (dot) error tracking ble-averaged Ensem 16. Figure B 9 t ie() Time(*) Time (e) 7 7 odto D Condition odto B Condition t 10 10 t I r 1 2 § o ? t ? - - 00 4 0 0.4 4 5 Time(•) 7 Condition A Condition 10 •to ao 0.1 t a as 1.2 1.2 4 4 9 9 Time (s) Time 7 7 odto E Condition Condition C Condition 0 10 10 63 experimental conditions (B - E) was calculated. More specifically, the absolute difference of ensemble-averaged tracking error between an experimental condition and the control condition was calculated and averaged. This measure would hopefully capture the experimental effects of transfer. It was defined as ^lEjk(^i) “ EA(ti) I (9) N where t^ is time in seconds in a trial, Ejjc(ti) is the ensemble-averaged error in experimental condition j for a subject k at time t^ in a trial, and E^ft^) is the ensemble-averaged error at time t^ averaged across subjects in the control condition, Condition A (I, K, M) . N is the total number of analyzed data points in a trial. In the current experiment data were collected every 50 ms for 14 s, but only data between 4 s and 10 s were analyzed. So N was 120. For each subject there resulted one value to show how his/her ensemble-averaged error trajectory deviated from the trajectory of the control condition group. This mean absolute deviation error exhibited a significant difference among groups on Block 64 13 (F(3,36) = 6.28*, p<0.01; F3/36;ol=0.01 = 4.39). Weak and Strong Hypotheses As mentioned above, the weight on the input velocity of the model (B2 ) was not significant among different groups on Block 13. Due to the insensitivity of B2, it was not used to test the weak and the strong hypotheses. Mean absolute error and mean absolute deviation error were used. The weak hypotheses concerned the relative dominance of the three schemata. How much subjects used a particular schema relative to other schemata mattered (Figures 1 & 2). For the strong hypotheses it was assumed that subjects would use only one or two schemata in tracking at the later stage of learning. This was shown as switches to connect or disconnect paths for particular schemata (arrow switches 1, 2, 3, and 4 in Figures 5 & 6). The presumed adjustments of schemata during transfer are shown in Figure 4. These transitions were tested in the following hypotheses. 65 Weak Hypotheses Since there was no directional prediction concerning which schemata were more dominant, two-tailed a priori t-tests (Kirk, 1968, p. 74) were conducted on mean absolute error and mean absolute deviation error (Tables 3 & 4). Variances of all the experimental conditions were pooled to estimate the population error variance. Comparing the schemata of the system dynamics and the input pattern (Condition C fsl. K. sM) vs. Condition D (I, K/s. sM)) The difference between Conditions C and D on transfer was that subjects in Condition C (si, K, sM) must integrate the schema of the input pattern and subjects in Condition D (I, K/s, sM) must differentiate the schema of the system dynamics. Both mean absolute error (t(36) = 1.56, p>0.05) and mean absolute deviation error (t(36) = 1.96, p>0.05) were not significant (Tables 3 & 4). However, any non-significance could be either due to the effects of differential difficulties in integration and differentiation processes or the main treatment effects of the two schemata (Table 4). From the above result it was 66 Table 3 Mean absolute error (ABS) and mean absolute deviation error (DABS) in degrees of visual angle on Block 13 Condition ABS Condition DABS A 0.133 B 0.152 B - A 0.078 1 C 0.157 0 > 0.130 Q < D 0.179 i 0.106 E 0.155 E - A 0.104 67 Table 4 Weak hypothesis, transfer performance, and ^-values for each hypothesis (£df=36;two-tailed ato<=0.05 *2.03) Hypothesized movement Transfer i-value generation processes performance ABS DABS 1. System dynamics vs. £ vs. fi 1.56 1.96 input (S vs. I) 2. Movement pattern vs. fi vs. £ 1.94 2.37* input (M vs. I) 3. Movement pattern vs. B vs. £ 0.24 2.18* system dynamics (M vs. S) *p<0.05 Note: ABS is mean absolute error. DABS is mean absolute deviation of the error trajectory of the experimental group from the control group. 68 not clear whether there was any ordering in dominance on transfer for those schemata (Tables 3 & 4). Comparing the schemata of the movement pattern and the input pattern (Condition B (I/s. K/s. M) vs. Condition D (I. K/s. sM )) The difference between Conditions B (I/s, K/s, M) and D (I, K/s, sM) on transfer was that subjects in Condition B (I/s, K/s, M) must differentiate the schema of the input pattern and subjects in Condition D (I, K/s, sM) must integrate the schema of the movement pattern. Mean absolute error showed a non-significant difference (t(36) = 1.94, p>0.05) and mean absolute deviation error showed a significant difference (t(36) = 2.37*, £><0.05) (Table 4). This latter result could indicate the greater importance of the movement pattern in comparison with the input pattern. However, since the different processes of integration and differentiation were involved for these conditions, it was not clear whether even a significant difference between them could be due to the difference between the schemata on the transfer or the differential difficulties of differentiation and integration of the schemata (Tables 3 & 4). 69 Comparing the schemata of the movement pattern and the system dynamics (Condition B (1/s. K/s. M) vs. Condition E (1/s. K. M/s)) Here the only difference between the conditions on transfer was the main effects of the two schemata, that is, the schema of the system dynamics and the schema of the movement pattern, because subjects in both conditions must differentiate either the schema of the system dynamics for Condition B (I/s, K/s, M) or the schema of the movement pattern for Condition E (I/s, K, M/s) . Mean absolute error showed no significance (t(36) = 0.24, p>0.05). With the mean absolute deviation error measure, which was more sensitive to treatment effects than the mean absolute error measure, there was a significant difference (t(36) =2.18*, p<0.05). This result showed that the schema of the movement pattern was more influential than the schema of the system dynamics on transfer (Tables 3 & 4) . 70 Strong Hypotheses All the strong hypotheses were tested with a priori orthogonal t-tests on mean absolute error and on mean absolute deviation error (Kirk, 1968, p. Ill) (Table 5) . The first hypothesis was that subjects memorized the movement pattern and used this schema exclusively. It predicted B > (C = D = E). For mean absolute error, the three orthogonal t- tests of B > (C + D + E) / 3, C = D, and C = E gave t- values (df=36) of 1.02 (p>0.05), 1.56 (p>0.05), and 0.14 (p>0.05) , respectively. For mean absolute deviation error, t-values (df=36) of the above sub-hypotheses were 3.62* (p<0.05), 1.96 (p>0.05), and 2.15* (p<0.05), respectively. With the mean absolute error, the sub-hypotheses of C=D and C=E were supported. The sub-hypothesis of C=D assumed that there was no difference between Conditions C (si, K, sM) and D (I, K/s, sM) , which meant no differential effects on transfer in integrating the schema of the movement pattern even when the two conditions had different schemata of the input pattern and the system dynamics. Comparing C=E was actually testing the differential effects of differentiation and integration. Subjects in Condition C (si, K, sM) must integrate both 71 Table 5 Strong hypothesis, transfer performance, and t-values for each sub-hypothesis (^df»36;one-tailed at«*=0.05 3,1 •69'^df-36;two-tailed at <**0.05 “ 2.03) Hypothesized movement Transfer Test t-value generation processes performance ABS DABS Memorized movement fi>(£+fi+fi)/3 1.02, 3.62*1 (M only) fi> (£=E=E) £-12 1.56 * 1.961 £-E 0 .1 4 1 2.15* Memorized input, C>(C+£)/2 -1.84 1.02 calculated movement D> (£-E) >fi (£+E)/2>fi -0.35 -3.76 (S and I) £=E 0 .1 4 ! 2.15* or (£+E)/2>D 1.84* * -1.02 (£=E) >D>fi E>B -1.89 -2.37 £=E 0.14 * 2.15* Calculated input, (£+E)/2>(fi+E)/2 0.91 -2.93 calculated movement ( £ = £ ) > £=E 0.14 * 2.15* (S only) 1.89 2.37* *p<0.05 * means the t-value supports the sub-hypothesis. Note: ABS is mean absolute error. DABS is mean absolute deviation error of the experimental performance from the control performance. 72 the schemata of the input pattern and the movement pattern and subjects in Condition E (I/s, K, M/s) must differentiate the same schemata during transfer. Tests on the mean absolute error showed there were no differential effects of the differentiation and integration on transfer. With the mean absolute deviation error measure the hypothesis was supported even though the sub-hypothesis of (C = E) was rejected (t (36) = 2.15*, p<0.05), because the comparison of C and E was only testing the difference between differentiation and integration as mentioned above. B was superior to the other conditions, and C and D were not significantly different. It can be tentatively concluded that subjects used the memorized movement pattern exclusively later in practice. However, the nearly significant large difference between C and D does suggest that other schemata may be involved to some lesser degree. The second hypothesis was that subi ects would use the memory of the input and calculate the movement pattern. It predicted either D > (C = E) > B or (C = E) > D > B depending on whether or not the system dynamics were more important than the input pattern. For mean absolute error, the first case was tested with three orthogonal t-tests of D > (C + E) / 2 (t(36) = -1.84, £>0.05), (C + E) / 2 > S (t(36) = -0.35, E>0.05) , and C = E (t(36) = 0.14, £>0.05). For mean absolute deviation error, t-values (df=36) were 1.02 (e>0.05), -3.76 (e>0.05), and 2.15* (e<0.05) for the sub-hypotheses, respectively. With the mean absolute error, only one sub-hypothesis, that there were no differential effects of differentiation and integration on transfer, was supported. The sub hypothesis, (C + E) / 2 > B, was based on the assumption that as described above the schema of the movement pattern did not matter. The main concern was whether the average effects of the differentiation of the schema of the input pattern for subjects in Condition E (I/s, K, M/s) and the integration of that schema for subjects in Condition C (si, K, sM) were the same as the effects of the differentiation of both the schemata of the input pattern and the system dynamics for subjects in Condition B (I/s, K/s, M) . Since the sub-hypothesis was not supported, the effects of changes in the schema of the input pattern was not less detrimental than the effects of differentiation of the schema of the system dynamics if subjects memorized the input patterns and used them. The second case was tested on mean absolute error with (C + E) / 2 > D (t(36) = 1.84*, £<0.05), D > B (t (36) = -1.89, E> 0 -0 5 ), and C = E (t(36) = 0.14, E>0.05). For the mean absolute deviation error, t-values (df=36) for the three sub-hypotheses were -1.02, -2.37, 2.15*, respectively. With the mean absolute error measure one sub-hypothesis, (C + E) / 2 > D, was supported in addition to the sub-hypothesis of no differential effects of integration and differentiation. The sub-hypothesis, (C + E) / 2 > D, was about whether the average detrimental effects of the integration of the schema of the input pattern for subjects in Condition C (si, K, sM) and the differentiation of the schema of the input pattern for subjects in Condition E (I/s, K, M/s) were significantly less than the differentiation of the schema of the system dynamics for subjects in Condition D (I, K/s, sM). Since the sub-hypothesis was supported, the effects of changes of the input pattern might be less detrimental than the effects of differentiation of the schema of the system dynamics. For the mean absolute deviation error measure, no sub-hypothesis was supported. The third hypothesis was that subjects would use only the memory of the system dynamics and calculate the input and the movement patterns. The schemata for the input pattern and the movement pattern would not be used. It would predict (C = E) > (B = D), and was tested 75 with three orthogonal t-tests of (C + E) / 2 > (B + fi) / 2 (t(36) = 0.91) , C = E (£(36) = 0.14) , and £ = £ (£(36) = 1.89) for mean absolute error. For mean absolute deviation error, t-values (df=36) were -2.93, 2.15*, and 2.37*, respectively. For mean absolute error the sub hypothesis that there was no significant difference between differentiation and integration was supported. For mean absolute deviation error, no sub-hypothesis was supported. The Summary of the Results of the Weak and Strong Hypotheses With the mean absolute error neither weak nor strong hypotheses were supported. One weak hypothesis that the schema of the movement pattern was more dominant than the schema of the system dynamics was supported with the mean absolute deviation error. Results on another weak hypothesis concerning the dominance of the movement pattern over the input pattern were not clear because of the differential effects of integration and differentiation. With the same measure, one strong hypothesis that subjects memorized the movement pattern and used it exclusively was supported. It can be 76 concluded the schema of the movement pattern was most dominant on transfer. Comparisons of Movement Patterns on Block 12 As mentioned above the schema of the movement pattern was the most dominant one. This was verified by the tests of a weak hypothesis and a strong hypothesis in terms of the mean absolute deviation error measure, which supported the closeness of Condition B (I/s, K/s, M) to the control condition, A (I, K, M). This closeness of the two conditions may be because subjects in both conditions practiced very similar movement patterns (Figure 17). The actual movement patterns on Block 12 of all conditions (Figure 17) were similar to the ideal movement patterns shown in Figure 3. These patterns are similar before 7 s and dissimilar after 7 s. Also, as shown in Figure 15, error trajectories of all conditions during transfer were similar before 7 s in a trial and quite dissimilar after 7 s. Since the movement pattern was the dominant schema, it could be argued that the dissimilar movement patterns after 7 s during practice might be the D O O D > o cn cji o cji Movement pattern (degrees of control stick angle) ai ai o CO o 00 Timet(s) Figure 17. Ensemble—averaged movement pattern on Block 12. LL 78 main factor for the very different error trajectories across conditions (Figure 15). Also, the non-significant difference between Conditions C (si, K, sM) and D (I, K/s, sM) of a weak hypothesis comparing the schemata of the input pattern and the system dynamics might be due to the same movement pattern they had during practice (Figure 17). In Figure 17 the movement patterns could be grouped into three distinct patterns, that is, the movement patterns of Conditions C (si, K, sM) and D (I, K/s, sM), Conditions B (I/s, K/s, M) and A(I, K, M), and Condition E (I/s, K, M/s) . These data show empirically the three different types of movement patterns expected in the current experiment (Figure 4) . Movement Pattern as a Variable in the Model instead of the Input Pattern The movement pattern can be used as a variable replacing the input pattern in the Input Reconstruction Model. In this modeling the movement pattern (c(t)) was predicted instead of the system output (m(t)) (Figures 1, 2, 5, & 6) using ideal movement components. The following equations represent the movement pattern model 79 and movement errors (Table 6 and Figure 18). c(t) = Bq +B^ c ideal(t-0.15) + B2 cideal(t-!). 15). (10) ec(^*) = cideal(t-) - cactuai(t). (11) ec(^)= cideal(t*) ~ cpredicted(t ) • (12) Only Conditions B (I/s, K/s, M) and D (I, K/s, sM) had ideal movement patterns that were different from the input patterns because only these two conditions involved rate control systems (Figure 3) . The Input Reconstruction Model and the Ideal Movement Model were substantially identical for Conditions A(I, K, M), C(sl, K, sM), and E(I/s, K, M/s) which involved position control systems. For Conditions B (I/s, K/s, M) and D (I, K/s, sM), for both Blocks 1 and 12 the percent of variance in c(t) accounted for by the Ideal Movement Model was larger for Condition B (I/s, K/s, M) and less for Condition D (I, K/s, sM) than the percent of variance in e(t) accounted for by the Input Reconstruction Model (Tables 2 and 6 and Figure 18). In terms of the weights on the movement velocity of the Ideal Movement Model, subjects in Condition B (I/s, K/s, M) did not show significant learning from Block 1 to Block 12 (t=l.74, p>0.05), and subjects in Condition D 80 Table 6 Weights on variables of the movement model (Bg(degrees of control-stick), offset; Bi(unitless), weight on position of ideal movement; B 2 (seconds), weight on velocity of ideal movement); the proportion of the variance accounted for by the model for the ensemble-averaged movement error trajectory for each group of subjects Condition Block B0 Bl B2 Variance of trials accounted for A 1 0.009 0.965 0.043 0.979 12 0.094 0.942 0.075 0.965 B 1 -0.237 1.061 0.114 0.993 12 -0.074 1.020 0.125 0.997 C 1 0.072 0.875 0.028 0.932 12 -0.000 0.878 0.090 0.683 D 1 -0.031 1.081 0.023 0.941 12 -0.013 1.007 0.091 0.789 E 1 -0.034 0.997 0.087 0.900 12 -0.001 1.000 0.102 0.927 iue 8 Ensmbl- r d moe nt ro ( ) n moe ft sld) o Codtos ad D. and B onditions C for ) (solid fit odel m and t) o (d error t en ovem m ed g era v le-a b sem n E 18. Figure Movementerror (degrees of control-stfck angle) Movement error (degrees of control-stick ongle) -15 •10 -15 -5 5 - 4 5 6 7 » Tm (s) Time (») odto D Condition lc 1 Block 0 odto B Condition lc 1 Block 10 -3 4 - -2 -5 -2 4 4 5 0 I 7 7 odtn D Conditon lc 13 Block 8 9 ok 12 lock B B Condition 9 9 10 10 82 (I, K/s, sM) showed significant learning from Block 1 to Block 12 (t=3.95, p<0.01) (tone_tailed, df=9,ct=0.01 = 1 *8 3 • tone-tailed, df=9, ot=0.05 =2.82). These results parallel those obtained with the Input Reconstruction Model. Comparison between the Experimental Conditions and the Control Condition on Transfer. As a post hoc test, all experimental conditions were tested to determine whether any condition was significantly different from the control condition in terms of mean absolute error. This test would indicate what pair of schemata was more influential during transfer. Dunnett's test for comparisons involving a control mean (Kirk, 1968, p. 94) revealed that only Condition D (I, K/s, sM) was significantly different from the control condition in terms of mean absolute error (Table 7). From these results it could be concluded that when both the system dynamics and the movement pattern on the transfer task were different from those during practice trials, subjects' performance deteriorated significantly. 83 Table 7 Group performance differences of mean absolute error in degrees of visual angle on transfer Condition Condition Mean h fi £ ID A 0.1327 - 0.019 0.025 0.047 0.023 B 0.1520 0.005 0.027 0.003 C 0.1574 - 0.022 -0.002 D 0.1794 -0.024 E 0.1554 — Note: The critical difference (d') for Dunnett * a test (Kirk, 1968, p. 94) for five treatments including control and df*45 was 0.031 when ^*0.05, one-tailed. 0 84 Summary Overall, the Input Reconstruction Model could not explain subjects' tracking performance well, probably because it had problems in describing the oscillatory error patterns. This resulted in poor sensitivity of the weight on the input velocity to transfer effects. However, the increase of the weight on the input velocity with practice was consistent (Table 2). The error patterns on Block 12 of all conditions except Conditions C (si, K, sM) and D (I, K/s, sM) matched well to the expected error patterns before the movement changed direction at seven seconds in a trial (Figure 3 and Figures 9 to 13) . After the direction of the movement changed, the corresponding match was not good for all conditions. The weak hypothesis that the schema of the movement pattern was more dominant than the schema of the system dynamics, and the strong hypothesis that the schema of the movement pattern was the most dominant were supported with the mean absolute deviation error measure. Thus, the schema of the movement pattern was the most dominant schema. With a measure of the mean absolute deviation error there was no significant difference among experimental conditions for the first part of the error trajectories on Block 13 (F(3,36) = 2.86, p>0.05). For the second part, they were significantly different (E(3,36) = 4.24, p<0.05) (Fdf= 3 ^3 6 . =o.05 = 2.87). Such difference could be due to the different movement patterns after 7 s in a trial in contrast to the similar movement patterns before 7 s each group had practiced before transfer (Figure 17). With the mean absolute error measure, Condition D (I, K/s, sM) was significantly different from the control condition, A (I, S, M). This meant that when the schema of the movement pattern was changed along with the schema of the system dynamics on transfer, the detrimental effects were very pronounced. CHAPTER IV DISCUSSION Input Reconstruction Model Reconsidered The hypothesis that subjects rely on input reconstruction was supported by the previous experiments (Hah, 1984; Jagacinski and Hah, 1988), which showed that with practice subjects could extrapolate the input pattern when only error and proprioception of the control stick were available in a compensatory tracking task with a repeated input. However, in those experiments the system dynamics was a position control system, which made the input pattern and the ideal movement pattern the same. As shown in Conditions A(I, K, M), C (si, K, sM) , and E (I/s, K, M/s) in Figure 3, the input and the ideal movement patterns were the same if the system dynamics was a position control system. Due to this experimental setup, it was not clear whether the schema subjects formed was a schema of the input or a schema of the movement pattern. Since the present experimental results 86 87 supported the dominance of the movement pattern, it might have been that subjects used the schema of the movement pattern in the later stage of the practice in the previous experiments as well. In contrast to the previous experiments (Hah, 1984; Jagacinski & Hah, 1988) , B2 (weight on the input velocity of the model) was not a sensitive measure of transfer performance in the current experiment. It seemed the oscillatory error pattern was the main factor of the insensitivity (Table 2 and Figures 9 to 13). It might be that subjects might have used error nulling mode in addition to pursuit mode for that situation assuming a model with the error nulling mode could describe the oscillatory error pattern. Learning Subjects7 tracking performance improved from Blocks 1 to 12 and Blocks 13 to 16 in terms of the mean absolute error measure (Table 1) . After transfer, subjects seemed to learn the new tracking task so quickly that on Block 16 there was no significant difference among groups. This demonstrated that the human operator is very adaptive to changes in the tracking environment. 88 Experimental Evidence for the Dominance of the Schema of the Movement Pattern over Other Schemata on Transfer The weak hypothesis comparing the schemata of the movement pattern and the system dynamics was tested with mean absolute deviation error. The test showed that the schema of the movement pattern was more dominant than that of the system dynamics. With the same measure a strong hypothesis that subjects would memorize the movement pattern and use its schema exclusively was supported. From the above results it was clear that the schema of the movement pattern was the most dominant. The movement patterns of all experimental conditions showed similar patterns before 7 s in a trial (Figure 17) . After 7 s the movement patterns were dissimilar across conditions, which might have contributed to the dissimilar oscillatory error trajectories across conditions on Block 13 (Figures 14 & 16) . Only Condition D (I, K/s, sM) was significantly worse than the control condition on Block 13 in terms of the mean absolute error measure. The result demonstrated that when the movement pattern changed with the system 89 dynamics on transfer, the detrimental effects were more pronounced than when the movement and the input patterns changed as in Condition E(I/s, K, M/s) or in Condition C (si, K, sM) or when the input pattern and the system dynamics changed as in Condition B (I/s, K/s, M). One may argue that the current experiment did not test directly what component among the three subjects actually learned during practice. This argument is not valid because tests were done with the absolute deviation error of the experimental condition from the error of the control condition. This method tests what condition was close to the control condition, which in turn illuminated what component was most dominant in transfer situation. This method is similar to most cognitive tests which ask us directly what we have memorized. We must recall the correct item memorized. The method of testing was same in the present experiment even though the subjects were not asked to repeat the same task again. In the current experiment, they transferred to a task which had one common component used and memorized during practice. For instance, the current result that Condition B (I/s, K/s, M) was the closest to the control condition, Condition A (I, K, M), in terms of transfer performance means that the common component with the control 90 condition, that is, the movement pattern, was the component subjects memorized most even though other components were available during practice. The above argument might not be necessarily true. It could be possible that subjects built all three schemata to the same degree during practice and they might have problems in adjusting only certain schemata during transfer. That is, the schema of the movement pattern might happen to be less flexible than others. However, this argument can not be supported because we must assume that subjects must have utilized the most useful schema for the transfer task whatever schemata they memorized during practice. Obviously subjects in Condition B (I/s, K/s, M) were most successful in transferring, which verified that subjects had memorized the schema of the movement pattern mostly during practice. Supporting Evidence for the Schema of the Movement Pattern from Other Research That the movement pattern rather than the input pattern and the system dynamics may be more important in a later stage of learning is partly supported by 91 Fleishman and Rich's (1963) two-hand coordination tracking experiments. They administered a kinesthetic sensitivity pre-test so they could divide their subjects into a group which had high kinesthetic sensitivity and a group which had low kinesthetic sensitivity. Their experimental results showed that after 24 one-minute trials the group which had high kinesthetic sensitivity performed significantly better later in the training. Their experimental results showed the importance of kinesthetic perception at the later stage of motor learning. As shown in Figures 1 & 2 and 5 & 6, this kinesthetic perception, that is, proprioception, was mainly responsible for forming the schema of the movement pattern. It is legitimate to question, though, whether Fleishman and Rich's (1963) pre-test actually tested the kinesthetic sensitivity and not other abilities such as intelligence or attentiveness. Another phenomenon which suggests the importance of the movement pattern was the oscillatory pattern after the input or the movement changed direction (Figures 9- 13) . Especially on transfer as shown in the error trajectory (Figure 16), the pattern was very pronounced after seven seconds into a trial. It could be that even though subjects had formed the schema of the movement pattern, they could not execute it without much 92 oscillations because of physical constraints due to muscles and joints. Some episodic oscillatory patterns in the trajectory may need some models which deal with the movement characteristics of the joints and muscles (Turvey, Fitch, & Tuller, 1982). In similar research on movements, Hasan (1986) showed in his research on goal-directed movement that stiffening the joints using agonists and antagonists was needed to be optimal in effort. His results showed that with high inertia there was a small symmetrical oscillatory velocity pattern when the velocity of the movement changed direction. That pattern was similar to the oscillatory error pattern in the previous experiments (Hah, 1984; Jagacinski & Hah, 1988) even though Hasan's (198 6) pattern was more symmetrical. However, an oscillatory pattern can be induced by introducing a pure time-delay into a system (Milsum, 1966, p. 47). It may be possible to build a model which uses a time-delay as a main parameter like the Input Reconstruction Model. Such a model would not need to introduce physical constraints as parameters to describe the oscillatory error pattern. 93 The Schema of the System Dynamics The schema of the system dynamics is not a temporal schema and is a constant relationship between other schemata in the time domain. The schema of the system dynamics was defined by other variables as Kc ------for a position control system, (13) A c and 1* 'S' x - e A Kc ------for a rate control system. (14) A C Because of these characteristics, it could not be formed as an independent time-varying schema. In compensatory tracking of random inputs, the significance of the system dynamics would matter more relatively because the inputs are random and not repeated as in the current experiment. That might be the reason why McRuer and Jex's (1967) results showed the change of the system dynamics was more detrimental than the change of the 94 sine wave inputs in compensatory tracking tasks. If the same input is repeated as in the current experiment, subjects would notice the characteristics of the input or the movement patterns and pay more attention to them, which may lead to a formation of a weak schema of the system dynamics comparatively. Theoretical Implications of the Current Experimental Results Subjects might have paid attention to whatever was easy to observe and/or calculate in performing the tracking task. They might have tried to memorize the movement pattern because they could do it directly without the extensive calculation involved in forming the input schema (Figures 1, 2, 5, & 6). The input must be inferred using the error display and the proprioception of the movement. For the movement pattern he/she could form its schema directly. This implies that subjects needed less mental calculation and might have to deal with less noise in forming the schema of the movement pattern. With the rate control system they would also need to differentiate the memorized input pattern to produce the appropriate movement pattern (see Figures 3 & 4) . This 95 may be more difficult than memorizing the movement pattern directly. When the system dynamics involve a position control, the patterns of the input and the movement are same. However, with the rate control system, subjects in Condition D (I, K/s, sM) must integrate the movement pattern and subjects in Condition B (I/s, K/s, M) did not need any calculation concerning the movement pattern. This probably led to the superior performance level of Condition B (I/s, K/s, M) to that of the Condition D (I, K/s, sM) on transfer. Subjects may have concentrated on visual information early in practice because visual information processing is more dominant than any other sensory modal information processing (Jordan, 1972). As proposed in the SOP (Successive Organization of Perception) model (Krendel & McRuer, 1968) , to learn a motor task, subjects would first pay attention to displayed error which must be minimized (Error nulling mode). With more practice they would notice a consistent pattern even though only error and proprioception were available (Pursuit mode) . The consistent pattern was the input pattern since the error and the output were contaminated by subjects' control movement. However, with more prolonged practice subjects 96 would notice the relationship among the error, the movement pattern, the input pattern, and the system dynamics. They would know that the best way to minimize error would be to control the movement pattern optimally, which would be the later stage of motor skill learning (toward the Precognitive mode). Subjects would realize that after prolonged practice other information, that is, proprioception, could be utilized extensively in addition to visual information. Thus, it is quite possible that subjects might have tried to learn the input trajectory first and then the movement pattern. This argument can be tested with the current experimental design if different groups of subjects were asked to switch to the control condition after different amounts of practice to see what schemata were more dominant. It could also be true that what schemata subjects form is dependent on what schemata is more important in the task situation. For instance, in Shapiro's (1977) experiment, subjects performed complex wrist rotation tasks to move through seven target positions in 1.6 s sequentially with their right hands. On the fifth day they were asked to perform the task with their left hands. Their movement pattern in terms of proportion of time on each segment was similar. It may be in such task 97 subjects learned mostly the input pattern and the system dynamics. They might learn the movement pattern to a lesser degree. It could be a very challenging task to examine in what situation subjects would pay attention more to what schema or component than to other components. Operators would try to learn a perceptual- motor task by paying more attention to a particular schema than others. Such knowledge would be very vital in designing various man-machine interfaces. Designers of man-machine systems must improve the design so that the operator would have less difficulty to form the particular schema. Another interesting aspects of the current experimental results was that the transfer task in the current experiment was different from the previous experiments (Hah, 1984; Jagacinski and Hah, 1988). In the previous experiments, a secondary memory task was added to the tracking task. In the current experiment, subjects' task was adjusting to the new input pattern, system dynamics, and/or movement pattern. As is clearly shown in Figure 15, the oscillatory forms were quite different from the patterns of the previous experiments (Hah, 1984; Jagacinski and Hah, 1988). In the previous experiments, the regression phenomenon was like 98 regressing to Block 1 of Condition A (I, K, M) in Figure 15. However, in the present experiment, it seemed the regression occurred mostly after seven seconds into a trial and its pattern was very oscillatory. This might imply that subjects experienced qualitatively different detrimental effects due to the transfer in the current experiment. Even though there have been many views on schemata, most researchers agree that the motor control system is hierarchical. As Pew (1974) and McKay (1981) argued, the higher the hierarchical level, the more abstract the schemata. It could be assumed that the schema of the input might be at a higher level than the schemata of the system dynamics and the movement pattern. This conjecture is based on the fact that the schemata of the system dynamics and the movement pattern would be about how to manipulate arm and fingers. On the contrary the schema of the input pattern would be about an imaginary trajectory of the input pattern in space and time. As discussed above, on transfer the schema of the movement pattern was the most dominant one. However, only Condition D (I, K/s, sM) was significantly worse from the control condition in terms of the mean absolute error measure. When a change in the movement pattern was paired with a change in the input as in Condition C (si, K, sM) and Condition E (I/s, K, M/s), why was it not as detrimental as when a change in the movement was paired with a change in the system dynamics as in Condition D (I, K/s, sM) ? It may be that both the schemata of the movement pattern and the system dynamics were closer to the lower level of the schemata structure. That is, when both were in the same level, there might be more interactions and confusions if they must be changed and adjusted at the same time. It seems this argument can be tested by having subjects perform abstract tasks like memory tasks as the concurrent secondary test while performing the transfer task of the current experiment. This will give a clear idea about the high level (the input pattern schema) vs. low level (the system dynamics and the movement pattern schemata> arguments mentioned above. For instance if the experimental results with a mental task were the same as the present one, the proposal is wrong. If the experimental results showed Conditions B (I/s, K/s, M), C (si, K, sM) and E (I/s, K, M/s) were worse than Condition D (I, K/s, sM), it would mean that the input schema was at a higher level and was therefore interfered with by the 100 memory task. Similarly, it is possible to design experiments to give more lower level interference by asking subjects to perform a secondary motor task on transfer using the current experimental design. Conclusion Traditionally in manual control research the human operator has been simulated as an equation and treated as one component in a feedback control system. The present report is emphasizing that it is very important to study human perceptual-motor behavior in the total context involving the input pattern, the system dynamics, and also the movement pattern. It is important to know the relationships among the three components. This kind of research will be very important to understand human characteristics in manipulating machines and tools and also important in designing machinery and plants where people work as equipment operators. The experimental results concerning the importance of the movement pattern over the input pattern and the system dynamics are strong, even though the effects of the schemata of the input pattern and the system dynamics were not clearly identified in the current 101 experiment. We can now know that the more influential factor in transfer is the movement pattern. The results seem very important because they let us see the relationships of the inner functional dynamics of tracking behavior and motor control in general. The knowledge of the relationship can be useful in designing machinery and training a person in man-machine environments. Since the movement pattern is the prime schema, it is desirable for the machine designer to make the necessary movement pattern easy for an operator to control the machine. In training, the operator can be instructed to pay more attention to his/her movement pattern to improve the motor skill fast. For instance it has been a well-known fact that operators have difficulty in controlling higher- order control systems (Birmingham & Taylor, 1954; Kelly, 1968). Even though there would be other reasons such as the necessary calculation of the higher-order error derivatives based on the current error, one possible reason could be that operators must execute more complex movement patterns to control the higher-order control systems. It is imperative to describe mathematically the oscillatory error pattern after the movement pattern changed direction. If a dynamic model can describe the 102 experimental results of the various movement patterns in Figure 5, it will be a powerful model because many simple movements would be composed of the movement patterns shown in the figure such as a ramp-like movement (Condition E (I/s, K, M/s)), a sinewave-like movement with one directional change (Condition A (I, K, M)), and a sinewave-like movement with two directional changes (Conditions C (si, K, sM) and (I, K/s, sM)). The importance of the current experiment was to identify the movement pattern as a potential parameter in describing various perceptual-motor behavior. Hopefully, in the future the movement pattern would be used to explain various problems concerning perceptual- motor behavior in man-machine environments. APPENDIX INSTRUCTIONS TO SUBJECTS The following instructions were given to subjects on the screening day. As posted in the sign-up sheet, there will be screening trials today. If your performance level is above criteria today, you will participate in the main experiment for four consecutive days in the next week. Since you will participate in more than four-credit hour worth, you will be paid for today's participation at the end of the experiment, which will be two dollars. There will be a total of 50 subjects for this experiment. The best performer among them will be awarded with a bonus of 20 dollars. The following is a procedure for this experiment. In this experiment, your task is to maintain a moving green line over the yellow stripe at the center of the screen. The position of the moving green line can be 103 104 controlled by moving the control stick to the left and right. Before each trial begins, the green line will be placed at the left-most side of the screen for sixteen seconds. This period is a ready period and the green line will not be controllable by the control stick. During this period the control stick should be at the center position. After the ready period, the line will jump to the center and stay there for two seconds. As soon as the green line begins to move, you are supposed to center it on the screen by manipulating the control stick. The trial will last for 14 seconds. The trial is over when the green line jumps to the left-most side of the screen, and is no longer controlled by the control stick. Your average error score, namely how far you let the green line stray from the yellow stripe, will be reported to you after each trial. After each trial, please put the control stick to the center position. During the experiment, you will wear headphones through which you will hear white-noise or reports of error scores. You should try to get as small an error as possible. This can be done by keeping the green line as close to the yellow stripe as possible. The errors are calculated by averaging the distances of the green line from the center of the screen during the trial. You will have five trials today. If you find anything out 105 of the ordinary, please talk to me over the microphone. If you have any questions about your task in this experiment now, I will be glad to answer them. Thank you. The following instructions were given to subjects on the first dav of the main experiment. Today the main experiment starts. The following is the instruction. In this experiment, your task is to maintain a moving green line over the yellow stripe at the center of the screen. The position of the moving green line can be controlled by moving the control stick to the left and right. Before each trial begins, the green line will be placed at the left-most side of the screen for sixteen seconds. This period is a ready period and the green line will not be controllable by the control stick. During this period the control stick should be at the center position (or middle to the left for Condition E). After the ready period, the line will jump to the center and stay there for two seconds. As soon as the green line begins to move, you are supposed to center it on the screen by manipulating the control stick. The trial will last for 14 seconds. The trial is over when the green line jumps to the left-most side of the screen, and is no longer controlled by the control stick. Your average error score, namely how far you let the green line stray from the yellow stripe, will be reported to you after each trial. After each trial, please put the control stick to the center position (or middle to the left for Condition E). During the experiment, you will wear headphones through which you will hear white-noise or reports of error scores. You should try to get as small an error as possible. This can be done by keeping the green line as close to the yellow stripe as possible. The errors are calculated by averaging the distances of the green line from the center of the screen during the trial. You will have twelve trials per session, and four sessions per day. After each session, you will be given a two-minute break to let you take a rest. If you find anything out of ordinary, please talk to me over the microphone. If you have any questions about your task in this experiment now, I will be glad to answer them. 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