Informal versus formal judgment of statistical models: The case of normality assumptions
| Autor: | Christian Conley, Jiexiang Li, Anthony J. Bishara |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Anderson–Darling test
media_common.quotation_subject Population Normal Distribution Experimental and Cognitive Psychology 050105 experimental psychology 03 medical and health sciences Normality test Judgment 0302 clinical medicine Arts and Humanities (miscellaneous) Developmental and Educational Psychology Statistical inference Econometrics Humans 0501 psychology and cognitive sciences education Normality Statistical hypothesis testing media_common education.field_of_study Models Statistical 05 social sciences Statistical model Sample size determination Sample Size Psychology 030217 neurology & neurosurgery |
| Zdroj: | Psychonomic bulletinreview(For textbooks, † indicates Amazon Best Sellers list, and ‡ indicates top library holdings via WorldCat.). 28(4) |
| ISSN: | 1531-5320 |
| Popis: | Researchers sometimes use informal judgment for statistical model diagnostics and assumption checking. Informal judgment might seem more desirable than formal judgment because of a paradox: Formal hypothesis tests of assumptions appear to become less useful as sample size increases. We suggest that this paradox can be resolved by evaluating both formal and informal statistical judgment via a simplified signal detection framework. In 4 studies, we used this approach to compare informal judgments of normality diagnostic graphs (histograms, Q-Q plots, and P-P plots) to the performance of several formal tests (Shapiro-Wilk test, Kolmogorov-Smirnov test, etc.). Participants judged whether or not graphs of sample data came from a normal population (Experiments 1-2) or whether or not from a population close enough to normal for a parametric test to be more powerful than a nonparametric one (Experiments 3-4). Across all experiments, participants' informal judgments showed lower discriminability than did formal hypothesis tests. This pattern occurred even after participants were given 400 training trials with feedback, a financial incentive, and ecologically valid distribution shapes. The discriminability advantage of formal normality tests led to slightly more powerful follow-up tests (parametric vs. nonparametric). Overall, the framework used here suggests that formal model diagnostics may be more desirable than informal ones. |
| Databáze: | OpenAIRE |
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