Cognitive Aging and Adaptive Strategy Selection - Supplemental Information 1

Supplemental Information for “The Aging Decision Maker: Cognitive Aging and the Adaptive Selection of Decision Strategies”

Rui Mata, Lael Schooler, & Jörg Rieskamp

1. Using Elementary Information Processes (EIPs) to Quantify the Cognitive Demand of

the TTB, Take Two, and WADD Strategies

We computed the number of elementary information processes (EIPs; Payne, Bettman

& Johnson, 1993) each decision rule involves to quantify the cognitive effort associated with the use of the different decision strategies considered in the study. The elementary information processes considered were READ, COMPARE, ADD, MULTIPLY, GUESS, and

DECIDE. For example, per cue looked up, TTB required reading into a memory store two cue values associated with each of the two options (READ), comparing these two (COMPARE), and provided that this cue discriminated, making a decision (DECIDE). If the cue did not discriminate, another two cue values were read and compared, and so on until a decision was made or no more cues were available, leading the algorithm to choose randomly between the two options (GUESS). WADD required reading each of the cue values on the two alternatives

(READ), multiplying each cue value with the cue’s predictive value (MULTIPLY), adding this weighted cue value to the alternative’s tally (ADD), comparing the tallies of the two alternatives (COMPARE), and making a decision (DECIDE) or guessing if the tallies did not discriminate between alternatives (GUESS). The final EIP counts for the three different strategies considered in our study are presented in Table S.1. The results reflect the different cognitive demands implied in the use of TTB, Take Two, and WADD. An inspection of this table shows a clear difference between strategies, with TTB and Take Two being the least effortful due to their stopping information search when finding, respectively, one or two pieces of discriminating evidence favoring an alternative. In comparison, WADD is the most effortful strategy, always looking up all available information. Cognitive Aging and Adaptive Strategy Selection - Supplemental Information 2

2. Cognitive Measures

The battery of 11 psychometric tests was administered to all participants. The tests assessed various intellectual abilities including verbal knowledge (spot-a-word, vocabulary;

Lindenberger et al., 1993), processing speed (boxes, digit symbol substitution, identical pictures; Lindenberger et al., 1993), reasoning (figural analogies, letter series, practical problems; Lindenberger et al., 1993), and memory (operation span, Hamm, 2002; Brown-

Peterson task, Kane & Engle, 2000; forward digit span, Wechsler, 1981). A detailed description of the psychometric properties of the tests can be found in the respective references provided. In what follows we present a description of the tasks used to assess each ability.

Verbal knowledge

Spot-a-word. Twenty items containing one word and four pronounceable nonwords were presented successively on the screen. The task of the participants was to touch the word on the screen. Three practice items were provided. The total number of words correctly identified was the dependent measure (Lindenberger et al., 1993).

Vocabulary. Sixteen words were presented one-by-one on the screen and participants had to explain their meaning. Participants’ answers were coded, each word receiving a score of 0 (wrong), 1 (partially correct), or 2 (correct) (Lindenberger et al., 1993).

Processing speed

Boxes. Participants tapped for a limited time period (90 s) on boxes appearing at different positions on a computer screen. Median time between taps was used as the dependent measure.

Digit symbol substitution. Participants had to follow a scheme relating a set of symbols to digits by writing below rows of digits as many symbols as possible within 90 s. A paper- and-pencil format was used (Wechsler, 1981).

Reasoning Cognitive Aging and Adaptive Strategy Selection - Supplemental Information 3

Identical pictures. In this task 32 items were presented. For each item, a target figure was presented in the upper part of the screen and five possible responses were shown in the lower part. As quickly as possible, participants had to touch the lower figure that matched the target figure. Testing ended after 80 s. The dependent variable was the total number of correct answers (Lindenberger et al., 1993).

Figural analogies. Items in this test followed the format “A is to B as C is to ?”.

Problems were presented in the upper part of the screen while possible answers were presented in the lower part. Participants gave their answers by touching the screen

(Lindenberger et al., 1993).

Letter series. Sixteen items containing five letters followed by a question mark (e.g.,

“c e g i k ?”) were displayed in the upper half of the screen while five candidates to replace the question mark were presented in the lower half (e.g., “p m l o n”). Items followed simple rules, such as +1, -1, or +2. Participants gave their answers by touching the screen. The score was based on the total number of correct answers (Lindenberger et al., 1993).

Practical problems. Twelve items depicting everyday problems such as interpreting a bus schedule were used. For each item a problem was presented in the upper part of the screen while five response alternatives were shown in the lower part. Participants gave their answers by touching the screen. The test phase was terminated if participants made three consecutive false responses, if they reached the time limit of 10 min, or when they answered the last item.

The total number of problems correctly solved was the dependent measure (Lindenberger et al., 1993).

Memory

Operation span. The stimuli of Hamm (2002) were used for this task. Participants saw individual operation–word strings (e.g., IS (8/4)-1=1? bear). They had to solve the math problems, each of which was followed by a lowercase word, which was to be read aloud. On hearing each word, the experimenter would press a key that would cause the presentation of Cognitive Aging and Adaptive Strategy Selection - Supplemental Information 4 the next string. After a set of these operation–word strings, participants recalled the words.

The dependent measure was the cumulative number of words recalled from perfectly recalled trials.

Brown–Peterson task. Participants viewed three lists of items from the category

“professions” followed by one list of the category “animals.” Between lists participants had to recall the items. Additionally, before the recall they had to perform a distracting task consisting of counting aloud from, for instance, D-32 (e.g., D-32, E-33, F-34) for 16 seconds.

The dependent variable was the difference between the numbers of correct items recalled in the first and second list (see Kane & Engle, 2000). Higher values on this measure indicate less resistance to proactive interference.

Forward digit span. This task corresponds to the Wechsler Adult Intelligence Scale-

Revised digit span subscale (Wechsler, 1981). Sequences of digits with an increasing number of elements (3–9 digits) were presented. The participants were instructed to recall the digits in the correct sequence at the end of the presentation. After a correct response the number of digits presented was increased by one. When the participants made a mistake, an alternative sequence of the same length was shown. If the participant failed again, the test was finished.

The maximum number of correctly recalled digits was used as the dependent variable.

3. Strategy Classification

Our simulation results support the use of an outcome-and-search classification method and we therefore relied on this classification procedure. The strategy that predicted the most inferences correctly for a participant was assigned to the participant. Recall that TTB’s stopping rule consists of stopping search after seeing the first discriminating cue. Take Two involves stopping search after seeing two discriminating cues favoring the same alternative.

Finally, for WADD we assumed that all cue values had to be searched on both objects.

Participants for whom the fit of two or more strategies coincided were left unclassified.

To further examine the validity of our classification we determined to what extent the Cognitive Aging and Adaptive Strategy Selection - Supplemental Information 5 different strategies could predict the final choices, search behavior, or both of participants classified as TTB, Take Two, and WADD according to the outcome-and-search method (see

Table S.2). The strategy fit based on outcome only is similar to that reported by others (e.g.,

Bröder, 2000, with best fits falling in the [.63, .98] interval). The strategies’ fit in predicting the search behavior was substantially lower compared to the fit in predicting the choices. One plausible explanation is that search behavior is more loosely connected with the applied strategy, for example, people may search for additional information to consolidate a preliminary decision (see also Rieskamp & Otto, 2006). Supporting our classification method, the strategy assigned to a group of participants was by and large better than the competing strategies in predicting the decision, search, or both aspects of those participants’ behavior.

For example, for participants classified as TTB users, TTB could predict the decisions and search for on average 40% of their trials compared with a fit of 4% and 1% for Take Two and

WADD, respectively. Consequently, the low fit values for the outcome-and-search method are due only to the strictness of the method, which considers that both outcome and search need to match to classify a trial as evidence for the use of a particular strategy. Cognitive Aging and Adaptive Strategy Selection - Supplemental Information 6

Table S.1

Means and Standard Deviations of Elementary Information Processes (EIPs) as a Function of Decision Strategy in our Experiment

Decision strategy EIP TTB Take Two WADD M SD M SD M SD Read 143 6 349 11 800 0 Compare 72 3 174 6 50 0 Add ― ― 123 2 400 0 Multiply ― ― ― ― 400 0 Decide 50 0 50 0 50 0 Guess ― ― ― ― 2 2 Total 265 8 696 18 1702 2 Cognitive Aging and Adaptive Strategy Selection - Supplemental Information 7

Table S.2

Mean Fit of Strategies to Choices (Outcome only), Information Search (Search only), or Both

(Outcome and search) of Participants Classified as TTB, Take Two, or WADD According to the Outcome and Search Method

Strategy users TTB Take Two WADD Outcome only a TTB users .81 .65 .60 b Take Two users .76 .76 .70 c WADD users .68 .74 .79 Search only a TTB users .43 .06 .02 b Take Two users .06 .22 .05 c WADD users .01 .02 .51 Outcome and search a TTB users .40 .04 .01 b Take Two users .05 .19 .03 c WADD users .01 .02 .38

Note. an = 19; bn = 38; cn = 103. Each row of the table represents the fit of the strategy TTB, Take Two, or

WADD for one group of participants (TTB, Take Two, or WADD users as classified by the outcome and search method).