Neath, I., & Brown, G. D. A. (2005). Scale Invariance and Primacy and Recency Effects in an Absolute Identification Task. Memory Lab Technical Report 2005-01, Purdue University. Scale Invariance and Primacy and Recency Effects in an Absolute Identification Task IAN NEATH Purdue University, West Lafayette, Indiana and GORDON D. A. BROWN University of Warwick, Coventry, UK Two experiments investigate absolute identification of tones that vary only in frequency. Experiment 1 used a narrow, a medium, and a wide range of tones and found performance identical in the three conditions, supporting the idea of scale invariance. Experiment 2 tested two different sets of tones designed to rule out ordinal explanations and to illustrate primacy and recency effects. In typical absolute identification experiments, subjects see a set of stimuli that vary along only one dimension (e.g., frequency, length). Subjects are shown one stimulus and are asked to identify it (i.e., indicate whether it is Stimulus 1, Stimulus 2, etc), and then receive feedback about the correct response.1 Brown, Neath, and Chater (2002) describe a model of scale invariant memory and perceptual learning called SIMPLE. The two experiments reported here are designed to provide data to answer the following two questions: (1) Is there evidence of scale invariance in absolute identification experiments? (2) Is there evidence of similarities between the serial position effects observed in absolute identification and those observed in more traditional serial learning paradigms? This paper provides the detailed presentation of the experiments, the statistical analysis of the data, and addresses various issues about how best to score the data. The modeling is reported as part of Neath and Brown (2006). Correspondence may be addressed to Ian Neath at ineath@mun.ca; or to G. D. A. Brown at G.D.A.Brown@warwick.ac.uk. Last updated: July 1 2006. http://memory.psych.mun.ca/pubs/reports.shtml 1 EXPERIMENT 1 Performance in absolute identification experiments is largely unaffected by the spacing of items along the perceptual scale; that is, increasing the spacing by a constant factor typically has almost no effect, provided the items are not sufficiently similar to be confused when presented pairwise. Experiment 1 was designed to replicate this scale invariance in absolute identification and to provide data for modeling. The experiment, therefore, examined subjects ability to identify individual tones from sets of nine tones varying in frequency. Three sets of nine tones were used; the difference between them was the spacing between them - the spanned range varied from 140 Hz (narrowly-spaced set of nine tones) to 191 Hz (medium spacing) to 290 Hz (wide spacing). Method Subjects. Sixty Purdue University undergraduates volunteered to participate in exchange for credit in introductory psychology courses and were assigned to one of three groups. No subject reported any history of
2 NEATH & BROWN hearing problems. Materials and Design. Three sets of nine sine-wave tones were generated and stored digitally at a sampling rate of 22.5 khz on an Apple Macintosh LC computer. In the narrow group, each tone was approximately 3.73% higher in frequency than the previous tone; in the medium group, each tone was 5% higher than the previous; and in the wide group, each tone was 7.59% higher then the previous. Table 1 in the appendix lists the exact frequencies used. These frequencies were chosen such that all three sets would have three frequencies in common (420.00, 486.20, and 562.84 Hz). The tones were presented over Sony MDR V5 headphones, and subjects were allowed to adjust the stimuli to a comfortable level of loudness. Each tone lasted 500 ms, with the first and last 50 ms ramped in amplitude. Procedure. First, each subject heard all nine tones twice times, once in increasing and once in decreasing order. The tone with the lowest frequency was labeled 1 and the tone with the highest frequency was labeled 9. As each tone was played, its number was shown on the screen. Following this, each subject received 135 identification trials, 15 trials on each of the nine stimuli; the order of these trials was randomized for each subject. An identification trial consisted of the presentation of a single tone. Immediately after, the computer presented nine different buttons on the screen, each labeled with a digit 1 through 9. The subject was asked to use a mouse to click on the appropriate button that identified the tone that had just been played. Immediate feedback was then given to the subject, informing them that they had made the correct response, or informing them what the correct response should have been. Subjects were given a short break half-way through. Results The data were scored in two ways for analysis. First, "raw" proportion correct is the number of times a subject correctly identified a stimulus divided by the number of times the stimulus was presented. Second, adjusted proportion correct is the number of times a subject correctly identified a stimulus divided by the total number of times the subject used that particular response. Figure 1 shows the results (as well as a third way of representing the data that is used solely for model fitting; see below). Three aspects of the data are noteworthy: (1) Performance is roughly comparable in all three conditions, indicative of scale invariance; (2) Performance is largely symmetrical in all three conditions, suggesting that the stimuli were indeed equally spaced perceptually; and (3) there is no major difference between the three ways of representing the data. Consistent with scale invariance, overall accuracy did not vary across the groups regardless of whether the analysis was performed on the raw data, 0.441 vs 0.432 vs 0.473, (F(2,57) = 0.927, MSE = 0.091, p > 0.40) or the adjusted data, 0.459 vs 0.452 vs 0.489, (F(2,57) = 0.723, MSE = 0.096, p > 0.40). (The appendix lists all of the means.) Performance on the first tones (420.00, 400.00, and 362.80 Hz) was equivalent: 0.653, 0.647, and 0.660 with raw scoring and 0.659, 0.656, and 0.673 with adjusted scoring in the narrow, medium, and wide groups respectively. Similarly, performance on the last tones (562.80, 591.00, and 651.60 Hz) was equivalent: 0.647, 0.623, and 0.670 with raw scoring and 0.696, 0.709, and 0.731 with adjusted scoring in the narrow, medium, and wide groups respectively. Planned contrasts showed no difference (F(1,57) < 1 for all comparisons). For the purposes of model fitting, the group data were scored in a third way: The response matrix was iteratively normalized (see Neath et al., in 2006). Each response probability is divided by the summed response probability with the result that all response probabilities sum to 1.0. The response
ABSOLUTE IDENTIFICATION 3 Figure 1. Performance in the narrow, medium, and wide conditions in Experiment 1 as a function of 3 different scoring methods. probability matrix is then renormalized so that the stimulus presentation probabilities return to unity, and the process is repeated iteratively until both stimulus probabilities and response probabilities are 1.0. This is done to allow direct comparisons between the data and the model without taking a strong stance on the best way to handle response bias. As Figure 1 shows, this iterative procedure did not substantively change the pattern of the data, thus allowing it to be used for model fitting (see Neath & Brown, 2006). EXPERIMENT 2 One claim of SIMPLE is that in both memory retrieval and absolute identification, serial position effects arise due to differential discriminability of items along a particular dimension (cf. Murdock, 1960), and Experiment 2 was designed to illustrate this idea within the context of an absolute identification paradigm. Two sets of tones were created such that, according to the SIMPLE model
4 NEATH & BROWN but not an ordinal-code model, one set should lead to more accurate identification of the lowest numbered items (the primacy condition) whereas the second should lead to more accurate identification of the highest numbered items (the recency condition). This was done by separating ordinal position and frequency differences. This experimental manipulation can be achieved by increasing the separation on the frequency scale of tones at one or other end of the series. Serial position effects as well as scale invariance can be partially predicted by a simple account that we will call the ordinal guessing model. Assume that subjects are able to judge only whether a given tone is higher than or lower than the tone presented on the preceding trial, and that participants then guess randomly between available responses. For example, participants hear tone 6 on trial n-1, and receive feedback ( that was tone 6 ). Participants then hear tone 8 on trial n, and correctly judge this to be higher in frequency than the previous tone. The tone must therefore be tone 7, 8, or 9, and participants choose randomly from these responses, resulting in 33% correct responses. This process of accurate ordinal judgment followed by guessing will lead to serial position curves with advantages for the end-series items, because when end-series items are presented there will be fewer guessable responses and so the correct response will be picked more often by chance alone. 1 To the extent that participants can make only ordinal judgments, then performance should be the same in the primacy and recency conditions. Method Subjects. Forty Purdue University undergraduates volunteered to participate in exchange for credit in introductory psychology courses and were assigned to one of two groups. No subject reported any history of hearing problems and no subject had participated in Experiment 1. Materials and Design. Two new sets of nine sine-wave tones were generated and stored digitally at a sampling rate of 22.5 khz on an Apple Macintosh LC computer. In the primacy condition, the tones increased in frequency by decreasing ratios. For example, tone 2 was 10% higher than tone 1, tone 3 was 9% higher than tone 2, and so on. In the recency group, the tones increased in frequency by increasing ratios. For example, tone 2 was 3% higher than tone 1, tone 3 was 4% higher than tone 2, and so on. The exact frequencies used are listed in Table 2; note that the first and last tones were identical in the two groups. The tones were presented over Sony MDR V5 headphones, and subjects were allowed to adjust the stimuli to a comfortable level of loudness. Each tone lasted 500 ms, with the first 50 ms and last 50 ms ramped. Procedure. The procedure was identical to that of Experiment 1. Results The results from the primacy condition are the mirror image of the results from the recency condition, as Figure 2 shows. Overall accuracy did not vary between the groups regardless of whether the analysis was performed on the raw data, 0.437 vs 0.431 (F(1,38) = 0.029, MSE = 0.096, p > 0.85) or the adjusted data, 0.454 vs 0.465 (F(1,38) = 0.123, MSE = 0.088, p > 0.70). (The appendix lists all of the means.) Performance on the first tone in the primacy group was the same as performance on the last tone in the recency group: 0.723 and 0.717 with raw scoring and 0.690 and 0.784 with adjusted scoring. Similarly, performance on the last tone in the primacy group was the 1 An implementation of the guessing model is available at http://memory.psych.mun.ca/models/
ABSOLUTE IDENTIFICATION 5 Figure 2. Performance in the primacy and recency conditions in Experiment 2 as a function of 3 different scoring methods. same as performance on the first tone in the recency group: 0.503, and 0.555 with raw scoring and 0.553 and 0.555 with adjusted scoring. Planned contrasts showed no difference (F(1,38) < 1) for all comparisons except adjusted scoring for the first item in the primacy group compared to adjusted scoring for the last item in the recency group (F(1,38) = 4.179, MSE = 0.021, p <.05). GENERAL DISCUSSION Experiment 1 found evidence for scale invariance in absolute identification and Experiment 2 found evidence against simple guessing and other ordinal models. In addition, Experiment 2 also provides evidence to strengthen the claim the serial position effects in both absolute identification and serial learning are similar. REFERENCES BROWN, G. D. A., NEATH, I, & CHATER, N. (2002). SIMPLE: A ratio model of memory. Unpublished manuscript. MURDOCK, B. B. (1960). The distinctiveness of stimuli. Psychological Review, 67, 16-31. NEATH, I., BROWN, G. D. A., MCCORMACK, T., CHATER, N., & FREEMAN, R. (2006). Distinctiveness models of memory and absolute identification: Evidence for local, not global, effects. Quarterly Journal of Experimental Psychology, 59, 121-135.. NEATH, I., & BROWN, G. D. A. (2006). SIMPLE: Further applications of a local distinctiveness model of memory. In B. H. Ross (Ed.), The psychology of learning and motivation (pp. 201-243). San Diego, CA: Academic Press. (Appendix follows)
6 NEATH & BROWN Table A1. The frequency (Hz) of each of the nine tones in each of the three groups, and performance according to three ways of scoring in Experiment 1. Narrow Medium Wide Freq. Raw Adj. Iterate Freq. Raw Adj. Iterate Freq. Raw Adj. Iterate 362.8 0.660 0.673 0.673 390.4 0.450 0.441 0.430 400.0 0.647 0.656 0.650 420.0 0.653 0.659 0.662 420.0 0.453 0.458 0.433 420.0 0.397 0.426 0.411 435.7 0.473 0.449 0.447 441.0 0.367 0.361 0.360 451.9 0.353 0.398 0.386 451.9 0.383 0.441 0.423 463.1 0.313 0.416 0.379 468.7 0.327 0.383 0.360 486.2 0.327 0.400 0.361 486.2 0.300 0.333 0.321 486.2 0.367 0.411 0.397 504.3 0.340 0.323 0.339 510.5 0.383 0.364 0.358 523.1 0.400 0.381 0.384 523.1 0.413 0.386 0.392 536.0 0.380 0.345 0.352 542.6 0.447 0.444 0.435 562.8 0.647 0.696 0.612 562.8 0.420 0.427 0.412 562.8 0.437 0.412 0.401 591.0 0.623 0.709 0.643 605.6 0.480 0.481 0.494 651.6 0.670 0.731 0.667
ABSOLUTE IDENTIFICATION 7 Table A2. The frequency (Hz) of each of the nine tones in both groups, and performance according to three ways of scoring in Experiment 2. Primacy Recency Freq. Raw Adj. Iterate Freq. Raw Adj Iterate 360.0 0.723 0.690 0.708 360.0 0.483 0.555 0.547 396.0 0.453 0.464 0.453 370.8 0.403 0.341 0.351 431.6 0.377 0.418 0.398 385.6 0.327 0.286 0.300 466.2 0.357 0.452 0.416 404.9 0.297 0.329 0.326 498.8 0.323 0.423 0.390 429.2 0.340 0.420 0.412 528.7 0.383 0.338 0.351 459.3 0.400 0.419 0.395 555.2 0.413 0.358 0.383 496.0 0.437 0.465 0.453 577.4 0.400 0.387 0.389 540.6 0.480 0.584 0.539 594.7 0.503 0.553 0.493 594.7 0.717 0.784 0.637