The Influence of Individual Differences on the Role of Information Quantity in Statistical Inferences
Bibliographic record
Abstract
The Influence of Individual Differences on the Role of Information Quantity in Statistical Inferences Justin M. Gilkey (jgilkey@bgsu.edu) Department of Psychology, Bowling Green State University Bowling Green, Ohio 43402 USA Richard B. Anderson (randers@bgsu.edu) Department of Psychology, Bowling Green State University Bowling Green, Ohio 43402 USA Michael E. Doherty (mdoher2@bgsu.edu) Department of Psychology, Bowling Green State University Bowling Green, Ohio 43402 USA Keywords: Perception of Correlation; Contingency Judgment; Working Memory Capacity; Inference Results and Discussion It has been argued on statistical grounds that population correlations (ρ) are more readily detected given a small number of paired stimuli (N s ) than given a large N s (e.g., Kareev, Lieberman, & Lev, 1997). Kareev, et al. (1997, Experiment 1) tested this claim with a prediction task in which participants used a binary cue to predict a binary outcome. The researchers derived subjective correlations (ρ′) by computing the correlation between the cues and participants' predicted outcomes. Using working memory capacity (WMC) as an indirect measure of N s, ρ′ was found to be more extreme for participants with low WMC than for those with high WMC, and found to decrease with N s . Anderson, Doherty, and Gilkey (2006) manipulated N s directly. The stimuli varied on two binary dimensions, and were drawn randomly from a population in which the correlation between the two stimulus dimensions was fixed. Participants used the samples to estimate population frequencies for various combinations of the dimension levels; the researchers computed ρ′ from participants’ estimates. Contrary to Kareev et al. (1997, Experiment 1), ρ′ decreased with N s , and WMC had no effect. WMC was dichotomized via a median split. In the prediction task there was an N s × WMC interaction, F(1, 36) = 8.81, p = .005, and there was a positive effect of N s on ρ′ for participants with high WMC, F(1, 17) = 14.54, p = .01l, but not for those with low WMC. Also in the prediction task, the mean ρ′ tended to be greater for those with high WMC than for those with low WMC, but only when ρ was .4, t(36) = 2.78, p = .009. Both results are inconsistent with the theory of small sample advantages. Similarly, in the rating task, there was an N s × WMC interaction, F(1, 32) = 19.37, p < .001; the effect of N s on ρ′ was positive when WMC was high, F(1, 14) = 4.87, p = .044, and negative when WMC was low, F(1, 18) = 8.38, p = .010. The findings contrast with those of Kareev et al. (1997, Experiment 1). Overall, the study provided a direct comparison of the effects of N s in three different correlation judgment tasks, demonstrated a small sample advantage for the rating task only, and demonstrated the importance of individual differences in WMC. Acknowledgments This work was supported by a grant from the National Science Foundation. Rationale and Method Previously, the task used to assess ρ′ has tended to vary across experiments, with the potential for extraneous, between-study differences to impact the results. Therefore, the present study was designed to assess effects of task, N s , and WMC on ρ′ within a single experiment that included a prediction task, a frequency estimation task, and a rating task (see Clement, Mercier, & Pasto, 2002) in which ρ′ was assessed via a -100 to 100 scale. Participants (N = 107) saw sequences of 3, 6, 12, or 24 stimulus pairs consisting of pictures of brown or white envelopes containing a cash or credit card payment. Each stimulus sample was drawn randomly from a population in which ρ between envelope color and payment was 0, .4, or .8. Each participant’s WMC was assessed at end of the experimental session, using a digit span task. References Anderson, R. B., Doherty, M. E., & Gilkey, J. M. (2006). Effects of sampling ecology on correlational judgment. Poster presented at the Annual Meeting of the Cognitive Science Society. Clement, M., Mercier, P., & Pasto, L. (2002). Sample size, confidence, and contingency judgment. Canadian Journal of Experimental Psychology, 56, 128-137. Kareev, Y., Lieberman, I., & Lev, M. (1997). Through a narrow window: Sample size and the perception of correlation. Journal of Experimental Psychology: General 126, 278
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.049 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".