Negligible Effect (Equivalence) Testing Based Procedures For Assessing Distributional Normality

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dc.contributor.advisorRobert A Cribbie
dc.contributor.authorLinda Sawa Dorota Farmus
dc.date.accessioned2025-07-23T15:23:22Z
dc.date.available2025-07-23T15:23:22Z
dc.date.copyright2025-05-26
dc.date.issued2025-07-23
dc.date.updated2025-07-23T15:23:22Z
dc.degree.disciplinePsychology (Functional Area: Quantitative Methods)
dc.degree.levelDoctoral
dc.degree.namePhD - Doctor of Philosophy
dc.description.abstractResearchers in psychology often assess whether a sample distribution is consistent with a normal (Gaussian) population distribution, typically to justify assumptions of statistical models. In Study 1, a novel negligible effect test (NET) for normality is proposed, which evaluates whether a sample distribution is similar enough to a normal distribution to be considered equivalent—i.e., the differences are negligible. The NET defines a negligible effect interval for shape coefficients, and any test statistic whose 100(1–2α)% confidence interval (CI) falls entirely within this interval supports the conclusion of approximate normality. Simulations compared the Type I error and power of traditional difference-based tests (Kolmogorov–Smirnov and Shapiro–Wilk) with the NET. In small samples, the NET had low power to detect normality, while traditional tests had low power to detect nonnormality. However, NET rarely falsely concludes normality in nonnormal distributions, even with small samples. In contrast, traditional methods often flag trivial deviations from normality in large samples, potentially leading to misleading conclusions. The NET avoids this issue by rarely rejecting approximate normality when deviations are minor and practically inconsequential. One limitation of the NET approach is reduced power when distributions are close to normal. Study 2 addressed this by improving CI estimation using bootstrap methods. Alternative CI approaches were tested, including stochastic bootstrap, parametric bootstrap, and Fisher’s r-to-z transformation. The stochastic bootstrap provided the best balance of Type I error and power, and is recommended for use with the NET-based test of normality.
dc.identifier.urihttps://hdl.handle.net/10315/43065
dc.languageen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subjectPsychology
dc.subjectBehavioral sciences
dc.subjectQuantitative psychology and psychometrics
dc.subject.keywordsAssumptions
dc.subject.keywordsNormality
dc.subject.keywordsDistributions
dc.subject.keywordsEquivalence testing
dc.subject.keywordsNegligible Effect Testing
dc.subject.keywordsConfidence intervals
dc.subject.keywordsBootstrapping
dc.subject.keywordsPsychology
dc.subject.keywordsSocial Science
dc.subject.keywordsAssumption violations
dc.titleNegligible Effect (Equivalence) Testing Based Procedures For Assessing Distributional Normality
dc.typeElectronic Thesis or Dissertation

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