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Application of Design and Analysis of 23 Factorial Experiment in Determining Some Factors Influencing Recall Ability in Short Term Memory

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Application of Design and Analysis of 23 Factorial Experiment in Determining Some Factors Influencing Recall Ability in Short Term Memory 371 GLOBAL JOURNAL OF PURE AND APPLIED SCIENCES VOL. 14, NO. 3, 2008: 371 - 374 COPYRIGHT (C) BACHUDO SCIENCES CO. LTD. PRINTED IN NIGERIA. 1SSN 1118 - 0579 APPLICATION OF DESIGN AND ANALYSIS OF 23 FACTORIAL EXPERIMENT IN DETERMINING SOME FACTORS INFLUENCING RECALL ABILITY IN SHORT TERM MEMORY E. J. EKPENYONG, C. O. OMEKARA AND A. E. USORO (Received 20 October 2007; Revision Accepted 21 February 2008) ABSTRACT In this paper, we consider a 23 factorial experiment of factors influencing recall ability in short – term memory. The factors of interest are word length, word list and study time; and these factors tested on a group of students. The data obtained from the experiment are analyzed using the analysis of variance (ANOVA) of 23 factorial experiment (Yates Algorithm). The results show that recall ability in short term memory depends on word list, word length, study time and the interaction effect of list length and word length. KEYWORDS: 23 factorial experiment, word length, design of experiment, Yate’s Algorithm, Analysis of Variance. INTRODUCTION average. Henderson (1972) cited various studies on the recall of spatical locations or of items in those locations, conducted Before now, complicated experiments, which involve by Scarborough (1971) and Posner (1969), to make the point many levels of factors were analyzed and concluded using that there is a “new magic number 4 ±1.” Broadbent (1975) certain descriptive statistics that could not give accurate and proposed a similar limit of 3 items on the basis of more varied comprehensive interperations. Lawrence, A. J., (1996) sources of information including, for example, studies showing designed a factorial experiment with students in order to that people form clusters of not more than three of four items investigate characteristics of short-term memory. He finally in recall. A similar limit in capacity was discussed, with various used binomial regression analysis to analyse the data theoretical interpretations, by others such as Halford. collected from the experiment. Mayberry, and Bain (1988), Halford, Wilson, Philips (1998), This work therefore seeks to design specifically a 23 Luck and Vogel (1997), and Schneider and Detweiler (1987). factorial experiment and to employ the analysis of variance According to some current theories, there is no limit in method (Yates Algorithm) other than any other method to storage capacity per se, but a limit in the duration for which an analyse the result of the experiment. Montgomery (1976) item can remain active in short-term memory without rehearsal defined factorial experiments as experiments in which each (Baddeley, 1986). This has led to debate about whether the complete trial or replication of the experiment, involves limitation is a “magic number or magic spell” (Schweickert and investigation of all possible combinations of the levels of the Boruff, 1986) or whether rehearsal really plays a role (Brown factors. In other words, it is an experiment where the design and Huline, 1995). consists of two or more factors, each with discrete possible One possible resolution is that the focus of attention values or ‘levels’ and where the experimental units take on all is capacity –limited whereas various supplementary storage possible combinations of these levels across all such factors. mechanisms, which can persist temporarily without attention, Thus experiments involving the influences of certain are time-limited rather than capacity – limited (Cowan, 1988). factors on recall ability in short – term memory are factorial. Mclean and Gregg (1967) stated that if someone is O’Brien (1994) defined a short-term memory as the ability to given new material for immediate recall and can look at the remember or recall over short periods of up to about one material long enough before responding, new associations minute or thereabout. He also stated that short-term memory between the original items can be formed, resulting in larger lasts for about 20 to 30 seconds without rehearsal of the Chunks, or at least, conglomerates with non-zero associations information. More so, short-term memory is measured by recall between items. Miller (1956) also said that the half life of short- from list of words under controlled condition. Unless passed terms memory is approximately fifteen seconds and its from short-term memory (STM) to long term memory (LTM), capacity is approximately seven items (chunks) of information. items are forgotten by delay over time and replacement of Many studies in short –term memory reveals that short-term interference from more recent items. Earlier experiments on memory is limited by the amount of time that has elapsed short – term memory by Miller (1956) mainly concentrated on rather than by the number of items that can be held the memory span or storage capacity. He showed that average simultaneously (Baddley, 1986). Service (1998) stated that the human memory span can be expressed as 7±2, which is effect of word length on recall depends on phonological regarded as the “magical number seven” in short-term complexity, not on articulatory duration. Possible factors memory. This means that people can remember about seven influencing recall ability include the study time of the wordlist, chunks (items), but normally remember between five and nine delay time between viewing and recalling of words, length of chunks in short-term memory. These Chunks or items could be words used or number of syllables in words, number of words numbers, letter, nonsense syllable or words. Although Miller’s presented in the list and simultaneous or sequential ambivalence was, at the time a sophisticated and cautious presentation (Lawrence A. J. 1996). response to available evidence, a wealth of subsequent The statistical focus revolves around seeing the information suggests that there is a relatively constant limit in, sense of varying several factors simultaneously in a small the number of items that can be recalled in a wide variety of factorial design and then identifying the effects of the factors tasks; but that limit is only three to five items as the population individually and looking for any combination (interaction) E. J. Ekpenyong, Department of statistics, Akwa Ibom State Polytechnic, Ikot Osurua, Nigeria. C. O. Omekara, Department of Maths/ Statistics/ Computer Science, Micheal Okpara University of Agriculture, Umudike, Nigeria A. E. Usoro, Department of statistics, Akwa Ibom State Polytechnic, Ikot Osurua, Nigeria. 372 E. J. EKPENYONG, C. O. OMEKARA and A. E. USORO effects. Factorial designs have several advantages: They are The method of analysis used in analyzing this 23 more efficient than one-factor –at-a-time experiments. factorial experiment is Yates Algorithm in Analysis of Variance Furthermore, a factorial design is necessary when interaction (ANOVA) method, which tries to partition the total variation into may be present to avoid misleading conclusions. It also allows individual variation of the factors and interactions involved. effects of a factor to be estimated at several levels of the other Yates Algorithm eases the use of complete formulae. The factors yielding conclusions that are valid over a range of treatment combinations are always written down in standard experimental condition (Box, G. E. et al 2005). order, and the column labeled “response” contains the The Design of 23 factorial experiments involves corresponding observation (or total of all observations) at that determination of what factors to use and at what factors to use treatment combination. The first half of column (1) is obtained and at what levels. by adding the responses in adjacent pairs. The second half of column (1) is obtained by changing the sign of the first entry in MATERIAL AND METHODS each of the pairs in the response column and adding the adjacent pairs. In this work, study time, list length and word length After obtaining the sum of square for the effects on are the factors under study. To design this experiment, the contrasts, the total sum of squares SST is obtained using subjects are shown a list of unconnected words that is then the usual formula: withdrawn. Sets of students that are randomly selected without Y 2 ... replacements are asked to recall the words with primary result 2 SST = ∑∑∑ Y ijk − k where Yijk = each number being number correctly recalled. The factors to be studied are kji n2 made to be at two levels and these two levels are sufficiently of words recalled in the experiment and Y … = grand total of different as to have an effect to avoid the experiment being a the number of words recalled in the experiment. flop. The guiding requirement is that the subjects should have The sum of squares of the effects (SS ) is given by played no part in constructing the list on which he or she is eff 2 tested. With the use of three factors-study times, list length of (Contrasts) words and word length of two levels each; eight different types SSeff = k Where k is the number of factors and of test will be produced. This suggests a 23 factorial n2 experiment. That is study time – two levels of 15 and 30 n is the number of replication. Also the sum of squares of error seconds respectively; list length of words-two levels of 12 and (SSe) is obtained by subtracting all the sums of squares of 6 words and words length- 3 syllables and 1 syllable as levels. effects from the total sum of squares. This makes a total of eight treatment combinations. Six It should be noted that the assumptions are that the students using 48 from a group of 50 carry out each type of factors are fixed, the design is completely randomized and the test. Fifty students were randomly selected without normality conditions are satisfied. replacement from one hundred students of the same class. Thereafter six student were sub-sampled using the same DATA ANALYSIS method to carry out each type of test.
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