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Hebb effect and error learning
ONLINE SUPPLEMENTARY MATERIAL
Response-learning analysis
The measure of response learning requires calculating the probability of producing a given response as a function of the specific number of times that response has been previously recalled. Probabilities were calculated for the seven correct responses (one for each serial position) and for twelve transposition errors involving the most common errors in immediate serial recall, that is, transpositions between temporally adjacent items. Two types of transpositions were possible for individual items: an item initially presented in position p could be transposed to position p – 1 or p+1 (such transpositions alone explain around 50% of errors in the recall of sequences of bursts of white noise, see Parmentier & Jones, 2000). Each of the seven serial positions was associated with two types of transpositions, position p – 1 or p + 1, except for the first and the final serial positions for which only one transposition can occur, p + 1 for the first serial position or p – 1 for the final one. The transpositions considered in the current analysis were: T1 + 1, T2 – 1, T2 + 1, T3 – 1, T3 + 1, T4 – 1, T4 + 1, T5 – 1, T5 + 1, T6 – 1, T6 + 1, T7 – 1. This notation is centered on the position of the error and the + 1 or – 1 indicates where the response should have been given. For instance, a T2 + 1 transposition involves an incorrect item recalled on serial position 2 which should have been recalled on serial position 3.
Probabilities of producing a given response were computed separately. The analysis involved sorting responses according to the number of occurrences of that response in the preceding repeated trials. We calculated the observed probability of repeating a response given the number of past occurrences of that response. The repetition index, i.e., “Repetition x”, was used as short for “x number of past occurrences of that response”. Each response recalled by a participant counted as an occurrence of that response within the context of that participant’s history. The responses considered in the present analysishad one of nineteen possible identities (one of seven correct responses or twelve +1/-1 transposition errors) andcounted as an occurrence of that response for Repetition x (x depending on the number of past identical responses observed in the previous repeated sequences). The objective of the analysis was to calculate the probability of observing a given response as a function of the repetition index of that response. Response learning was operationalized as an increase in the observed probability of a response across successive repetitions of that response. Response probabilities (at a given repetition index) were derived by dividing the number of occurrences of a response by the number of opportunities for producing that response (i.e., the total number of responses at that serial position for a specific repetition index).
Example 1. Suppose that a participant responded to all eight presentations of the repeated sequence and that for position 3, the responses correspond to: P3, T3+1, T3+2, P3, T3-1, P3, P3, T3+1. Table S1 shows the number of occurrences and opportunities for the three response types most relevant to our analysis, namely the correct response (P3) and the two nearest transpositions (T3-1 and T3+1). To calculate the number of opportunities for repeating P3 for the first time (Repetition 1), one must count the number of responses at that serial position in subsequent presentations of the repeated sequence until the response is repeated (or arriving at the last repeated sequence). The repeated response also counts as an opportunity for that repetition gradient. Subsequent responses count as opportunities for the next value of the repetition index, until it is repeated once more, and so on. Hence, there were three opportunities to repeat P3 after the first time that it had been recalled, and one occurrence (note that for individuals, occurrences always have a value of one if the response is repeated, or zero if not). Table S2 identifies the occurrences and opportunities found in this example for the correct answer (P3) as a function of the repetition index. Note that occurrences and opportunities for a same response type must later be pooled across participants to calculate response probabilities (see example 2 below).
Table S1
Number of occurrences and opportunities of a response as a function of past recalls for three response types in Example 1.
Table S2
Specific occurrences and opportunities for the correct response in Example 1.
For each repetition (Repetition 1, Repetition 2, etc.), probabilities are calculated by counting the number of occurrences of a response and dividing it by the number of opportunities. Response opportunities correspond to the number of presentations of the repeated sequence (those associated with a same number of past occurrences) in which the response was produced or could have been produced. Since the analysis is generic and focuses on response types rather than actual outputs, we pooled the number of occurrences and opportunities of a given response for all participants and computed the overall probability of repeating that response as a function of past recalls. Finally, we estimated the overall learning trend by calculating the slope of change in the probability of occurrence of each response across repetitions and then calculating the average learning slope for the twelve transpositions and the seven correct responses.
Example 2. Let us calculate the probability of producing the (generic) transposition error “T1+1” (i.e., recalling in serial position 1 the item originally presented in Position 2) as a function of the number of previous occurrences of that response. Each time a participant produced this response (i.e., each occurrence), we computed the number of times that this response was provided by that participant in the previous presentations of the repeated sequence. Each time a participant provided a response for Serial Position 1, it counted as an opportunity of producing error T1+1—at the relevant repetition index. To estimate response probabilities for each repetition, we divided the total number of occurrences by the total number of opportunities for all the participants. For example, if transposition T1+1 was produced 12 times out of 80 opportunities for Repetition 1, then its estimated probability of being recalled was 0.15. At Repetition 2, if it was produced 18 times out of 60 opportunities, then its estimated probability of occurrence was 0.3. Couture et al. (2008) provided two additional examples on how to compute response probabilities for correct responses and errors.
Analysis of the repeated sequence. For the present analysis, response probabilities were calculated only for repetitions with at least 10 opportunities (across all 20 participants) in order to ensure that the computed probabilities were sufficiently reliable. Indeed, especially for errors (which are less frequent than correct responses), there were many cases in which the low number of observations produced noisy or extreme results (e.g., probabilities of 1). The analysis focused on Repetitions 1, 2 and 3 rather than 1 to 4 as in Couture et al. (2008) because too few errors were repeated four times, probably due to the fact that there were only eight (rather than twelve) presentations of the repeated sequence.
The probabilities for each correct response and transposition, as a function of the number of past occurrences, are listed in Table S3 and Table S4. For each response, we calculated the slope of the estimated probabilities for Repetition 1 to 3. A positive slope suggests that learning occurred. For completeness, Table S5 and Table S6 list the number of opportunities and occurrences on which these calculations were based.
Table S3
Observed response probabilities and slopes for correct responses on the repeated sequence as a function of prior occurrences of that response (Repetition 1-3).
Table S4
Observed response probabilities and slopes for position p - 1 or p + 1 transposition errors on the repeated sequence as a function of prior occurrences of that response (Repetition 1-3).
Table S5
Observed occurrences and opportunities for correct responses on the repeated sequence as a function of prior occurrences of that response (Repetition 1-3).
Table S6
Observed occurrences and opportunities for position p - 1 or p + 1 transposition errors on the repeated sequence as a function of prior occurrences of that response (Repetition 1-3).
Analysis of filler lists. For the response learning analysis, the filler lists can be viewed as a control condition that precludes the possibility of response learning. Responses given on the filler lists (the first filler in each epoch) are analyzed in exactly the same way as those for the repeated sequence. If the learning measure is sound, then response probabilities for the filler lists should not increase as a function of the number of prior occurrences of that response (the generic response regardless of label, since the filler lists are not the same). Table S7 and Table S8 list the probabilities for each correct response and transposition, as a function of the number of past occurrences, for the filler lists. Table S9 and Table S10 list the number of opportunities and occurrences on which these calculations were based.
Table S7
Observed response probabilities and slopes for correct responses on the filler lists as a function of prior occurrences of that response (Repetition 1-3).
Table S8
Observed response probabilities and slopes for position p - 1 or p + 1 transposition errors on the filler lists as a function of prior occurrences of that response (Repetition 1-3).
Table S9
Observed occurrences and opportunities for correct responses on the filler lists as a function of prior occurrences of that response (Repetition 1-3).
Table S10
Observed occurrences and opportunities for position p - 1 or p + 1 transposition errors on the filler lists as a function of prior occurrences of that response (Repetition 1-3).
Table S11 shows the unconditional response probabilities observed in the experimental data. These probabilities were used to generate one-thousand simulations designed to estimate the risk of obtaining slopes of the magnitude observed for correct responses and errors in the repeated series, in the absence of response learning.
Table S11
Unconditional response probabilities in Experiment 1 from Parmentier et al. (2008).
Finally, Table S12 and S13 present the results of two related analyses designed to examine the plausibility of an alternate explanation for the apparent error learning observed for the Hebb sequences. Table S12 reports the average distance between the position of a recalled item and its correct position for each of the seven items and for each repetition of the Hebb sequence. Table S13 reports the proportion of responses that were recalled at least two positions away from their correct position for each of the seven items and for each repetition of the Hebb sequence.
Table S12
Average distance between the position of a recalled item and its correct position for each position and each repetition of the Hebb sequence.
Table S13
Proportion of responses that were recalled at least two positions away from their correct position for each positions and each repetition of the Hebb sequence.