Type IV Errors and Analysis of Simple Effects

Betz, M. Austin; Gabriel, K. Ruben

doi:10.2307/1164881

Cited by 12 publications

(28 citation statements)

References 7 publications

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“…More important, SPSS MANOVA cannot construct simultaneous confidence intervals on simple effect contrasts in a coherent analysis using the methods outlined by Betz and Gabriel (1978) and Betz and Levin (1982). A simple effect contrast (such as B 1 |a 2 ) is not a member of any of the families of contrasts defined by the two-factor ANOVA model, even though certain differences between simple effect contrasts (such as B 1 |a 2 -B 1 |a 3 ) are members of the interaction family.…”

Section: Two-factor Between-subjects Designsmentioning

confidence: 99%

Confidence Intervals for Effect Sizes in Analysis of Variance

Bird

2002

Educational and Psychological Measurement

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Although confidence interval procedures for analysis of variance (ANOVA) have been available for some time, they are not well known and are often difficult to implement with statistical packages. This article discusses procedures for constructing individual and simultaneous confidence intervals on contrasts on parameters of a number of fixedeffects ANOVA models, including multivariate analysis of variance (MANOVA) models for the analysis of repeated measures data. Examples show how these procedures can be implemented with accessible software. Confidence interval inference on parameters of random-effects models is also discussed.Analysis of variance (ANOVA) is the standard method used to generate confident statistical inferences about systematic differences between the means of normally distributed outcome measures in randomized experiments. The traditional approach to inference in ANOVA relies so heavily on null hypothesis significance testing that many experimenters appear to believe that "running an ANOVA" necessarily involves statistical significance testing. If this were true, then it would be difficult or impossible to reform the practice of ANOVA along the lines suggested by the American Psychological In its 1999 report, the APA Task Force strongly emphasized that effect sizes should always be reported and that effect size reporting is essential to good research

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Section: Two-factor Between-subjects Designsmentioning

confidence: 99%

Confidence Intervals for Effect Sizes in Analysis of Variance

Bird

2002

Educational and Psychological Measurement

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“…Although researchers frequently compute simple effect tests following a significant interaction, such tests do not probe the interaction hypothesis. 3 Cogent discussions of this point have been presented in the literature~e.g., see Betz & Gabriel, 1978;Boik, 1993;Lix & Keselman, 1996!. The presentation of simple effect tests, therefore, is intended for those researchers who compute these tests not as a means of probing interactions but as means for examining differences between treatments at a fixed level of one variable, when such comparisons have interpretive meaning within a particular research context~e.g., see Toothaker, 1991, pp.…”

Section: Assessing the Interaction Effectmentioning

confidence: 99%

Testing treatment effects in repeated measures designs: An update for psychophysiological researchers

KESELMAN¹

1998

Psychophysiol.

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In 1987, Jennings enumerated data analysis procedures that authors must follow for analyzing effects in repeated measures designs when submitting papers to Psychophysiology. These prescriptions were intended to counteract the effects of nonspherical data, a condition know to produce biased tests of significance. Since this editorial policy was established, additional refinements to the analysis of these designs have appeared in print in a number of sources that are not likely to be routinely read by psychophysiological researchers. Accordingly, this paper includes additional procedures not previously enumerated in the editorial policy that can be used to analyze repeated measurements. Furthermore, I indicate how numerical solutions can easily be obtained.

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“…Hence, the hypotheses to be tested could be (1) H E and HA, or (2) H,, H A B , ElEIA,, and HE,,,;, where H E I A s are the simple B effects at each level of A . The hypotheses enumerated in the above two caes are sub-hypotheses of the overall hypothesis that the B simple effects at all levels of A are null (see Betz & Gabriel, 1978). Consequently, i t would be wasteful, powerwise, to use the STP critical value specified in Section 2.2 of this paper as it is larger than i t need be for the sub-hypotheses given above which imply a less restrictive composite hypothesis.…”

Section: Discussionmentioning

confidence: 98%

“…Similarly, if the overall hypothesis is non-significant, none of its sub-hypotheses can be significant. Betz & Gabriel (1978) demonstrated how the STP eliminates the concern for Type IV error when examining interaction and simple effect tests (see Levin & Marascuilo, 1972;Games, 1973) if the appropriate composite hypothesis and its critical value are used to test for these effects.…”

Section: =Omentioning

confidence: 99%

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Type I error control and the power to detect factorial effects

Keselman

1987

Brit J Math & Statis

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The probability of detecting factorial effects (main, interaction, simple) with experimentwise and per hypothesis Type I error protection are compared. The effects of level of significance, sample size and size of the true factorial effect are discussed. For researchers working in the personality, social or clinical area, where effects are presumed to be small, the power to detect treatment effects is very low. On the other hand, investigations of large factorial effects in such areas as experimental and physiological psychology are likely to have reasonable power even if a 0.01 per hypothesis criterion of significance is adopted.

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Type IV Errors and Analysis of Simple Effects

Cited by 12 publications

References 7 publications

Confidence Intervals for Effect Sizes in Analysis of Variance

Confidence Intervals for Effect Sizes in Analysis of Variance

Testing treatment effects in repeated measures designs: An update for psychophysiological researchers

Type I error control and the power to detect factorial effects

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