Non-normal Data in Repeated Measures ANOVA: Impact on Type I Error and Power
Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses, the F-statistic of repeated measures analysis of variance (RM-ANOVA) remains the most widely used procedure for analyzing differences in means. The impac...
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| Published in | Psicothema Vol. 1; no. 35; pp. 21 - 29 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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Spain
Colegio Oficial de Psicólogos (PSICODOC)
01.01.2023
Colegio Oficial de Psicólogos del Principado de Asturias |
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| Abstract | Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses, the F-statistic of repeated measures analysis of variance (RM-ANOVA) remains the most widely used procedure for analyzing differences in means. The impact of the violation of normality has been extensively studied for between-subjects ANOVA, but this is not the case for RM-ANOVA. Therefore, studies that extensively and systematically analyze the robustness of RM-ANOVA under the violation of normality are needed. This paper reports the results of two simulation studies aimed at analyzing the Type I error and power of RM-ANOVA when the normality assumption is violated but sphericity is fulfilled.
Study 1 considered 20 distributions, both known and unknown, and we manipulated the number of repeated measures (3, 4, 6, and 8) and sample size (from 10 to 300). Study 2 involved unequal distributions in each repeated measure. The distributions analyzed represent slight, moderate, and severe deviation from normality.
Overall, the results show that the Type I error and power of the F-statistic are not altered by the violation of normality.
RM-ANOVA is generally robust to non-normality when the sphericity assumption is met. |
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| AbstractList | Background:Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses, the F-statistic of repeated measures analysis of variance (RM-ANOVA) remains the most widely used procedure for analyzing differences in means. The impact of the violation of normality has been extensively studied for between-subjects ANOVA, but this is not the case for RM-ANOVA. Therefore, studies that extensively and systematically analyze the robustness of RM-ANOVA under the violation of normality are needed. This paper reports the results of two simulation studies aimed at analyzing the Type I error and power of RM-ANOVA when the normality assumption is violated but sphericity is fulfilled. Method:Study 1 considered 20 distributions, both known and unknown, and we manipulated the number of repeated measures (3, 4, 6, and 8) and sample size (from 10 to 300). Study 2 involved unequal distributions in each repeated measure. The distributions analyzed represent slight, moderate, and severe deviation from normality. Results:Overall, the results show that the Type I error and power of the F-statistic are not altered by the violation of normality. Conclusions:RM-ANOVA is generally robust to non-normality when the sphericity assumption is met. Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses, the F-statistic of repeated measures analysis of variance (RM-ANOVA) remains the most widely used procedure for analyzing differences in means. The impact of the violation of normality has been extensively studied for between-subjects ANOVA, but this is not the case for RM-ANOVA. Therefore, studies that extensively and systematically analyze the robustness of RM-ANOVA under the violation of normality are needed. This paper reports the results of two simulation studies aimed at analyzing the Type I error and power of RM-ANOVA when the normality assumption is violated but sphericity is fulfilled. Study 1 considered 20 distributions, both known and unknown, and we manipulated the number of repeated measures (3, 4, 6, and 8) and sample size (from 10 to 300). Study 2 involved unequal distributions in each repeated measure. The distributions analyzed represent slight, moderate, and severe deviation from normality. Overall, the results show that the Type I error and power of the F-statistic are not altered by the violation of normality. RM-ANOVA is generally robust to non-normality when the sphericity assumption is met. Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses, the F-statistic of repeated measures analysis of variance (RM-ANOVA) remains the most widely used procedure for analyzing differences in means. The impact of the violation of normality has been extensively studied for between-subjects ANOVA, but this is not the case for RM-ANOVA. Therefore, studies that extensively and systematically analyze the robustness of RM-ANOVA under the violation of normality are needed. This paper reports the results of two simulation studies aimed at analyzing the Type I error and power of RM-ANOVA when the normality assumption is violated but sphericity is fulfilled.BACKGROUNDRepeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses, the F-statistic of repeated measures analysis of variance (RM-ANOVA) remains the most widely used procedure for analyzing differences in means. The impact of the violation of normality has been extensively studied for between-subjects ANOVA, but this is not the case for RM-ANOVA. Therefore, studies that extensively and systematically analyze the robustness of RM-ANOVA under the violation of normality are needed. This paper reports the results of two simulation studies aimed at analyzing the Type I error and power of RM-ANOVA when the normality assumption is violated but sphericity is fulfilled.Study 1 considered 20 distributions, both known and unknown, and we manipulated the number of repeated measures (3, 4, 6, and 8) and sample size (from 10 to 300). Study 2 involved unequal distributions in each repeated measure. The distributions analyzed represent slight, moderate, and severe deviation from normality.METHODStudy 1 considered 20 distributions, both known and unknown, and we manipulated the number of repeated measures (3, 4, 6, and 8) and sample size (from 10 to 300). Study 2 involved unequal distributions in each repeated measure. The distributions analyzed represent slight, moderate, and severe deviation from normality.Overall, the results show that the Type I error and power of the F-statistic are not altered by the violation of normality.RESULTSOverall, the results show that the Type I error and power of the F-statistic are not altered by the violation of normality.RM-ANOVA is generally robust to non-normality when the sphericity assumption is met.CONCLUSIONSRM-ANOVA is generally robust to non-normality when the sphericity assumption is met. Abstract Background: Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses, theF-statistic of repeated measures analysis of variance (RM-ANOVA) remains the most widely used procedure for analyzing differences in means. The impact of the violation of normality has been extensively studied for between-subjects ANOVA, but this is not the case for RM-ANOVA. Therefore, studies that extensively and systematically analyze the robustness of RM-ANOVA under the violation of normality are needed. This paper reports the results of two simulation studies aimed at analyzing the Type I error and power of RM-ANOVA when the normality assumption is violated but sphericity is fulfilled. Method: Study 1 considered 20 distributions, both known and unknown, and we manipulated the number of repeated measures (3, 4, 6, and 8) and sample size (from 10 to 300). Study 2 involved unequal distributions in each repeated measure. The distributions analyzed represent slight, moderate, and severe deviation from normality. Results: Overall, the results show that the Type I error and power of theF-statistic are not altered by the violation of normality. Conclusions: RM-ANOVA is generally robust to non-normality when the sphericity assumption is met. |
| Author | Alarcón, Rafael Blanca, María García-Castro, F. Bono, Roser Arnau, Jaume |
| AuthorAffiliation | Universitat de Barcelona Universidad de Málaga |
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| Author_xml | – sequence: 1 givenname: María surname: Blanca fullname: Blanca, María – sequence: 2 givenname: Jaume surname: Arnau fullname: Arnau, Jaume – sequence: 3 givenname: F. surname: García-Castro fullname: García-Castro, F. – sequence: 4 givenname: Rafael surname: Alarcón fullname: Alarcón, Rafael – sequence: 5 givenname: Roser surname: Bono fullname: Bono, Roser |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/36695847$$D View this record in MEDLINE/PubMed |
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| Snippet | Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses, the... Background:Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses,... Abstract Background: Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical... |
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| SubjectTerms | Analysis of Variance Between-subjects design Computer Simulation Humans Psychology Psychology, Clinical Psychology, Developmental Psychology, Experimental Psychology, Multidisciplinary Research Design Sample Size Variance analysis Within-subjects design |
| Title | Non-normal Data in Repeated Measures ANOVA: Impact on Type I Error and Power |
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