Contents

418 PART V: Analyzing and Reporting Researchvariation alone. Results of the overall analysis, called an omnibus F-test, are reportedin an ANOVA Summary Table. A large F-ratio provides evidence thatthe independent variable had an effect. Effect size measures for a single-factorindependent groups design include Cohen’s f and eta squared ( 2 ). Comparisonsof two means may be conducted following results of an omnibus F-test in orderto more clearly specify the sources of systematic variation contributing to a significantomnibus F-test. Confidence intervals, too, may be meaningfully used tocomplement an ANOVA conducted with data from a multiple-group study andshould be reported when the results of NHST are summarized.A two-factor ANOVA is appropriate when a researcher examines simultaneouslythe effect on behavior of two or more independent variables in a complexdesign. When one independent variable represents an independent groups variable(random or natural groups) and another is a repeated measures withinsubjectsvariable, we speak of a mixed design. An omnibus F-test is carriedout to assess both main effects and the interaction effect of variables. When astatistically significant interaction effect is found, the source of the interaction effectmay be pursued by conducting simple main effects. A simple main effect isthe effect of an independent variable at only one level of a second independentvariable. Confidence intervals, too, may be used to help understand the effectof an independent variable in a complex design. A commonly used measure ofeffect size in a complex design is eta squared.KEY CONCEPTSnull hypothesis (H0) 385level of significance 385Type I error 387Type II error 387power 388t-test for independent groups 391repeated measures(within-subjects) t-test 391ANOVA 396single-factor independentgroups design 397F-test 397omnibus F-test 398eta squared ( 2 ) 402Cohen’s f 403comparison of two means 405REVIEW QUESTIONS1 What does it mean to say that the results of a statistical test are “statisticallysignificant”?2 Differentiate between Type I and Type II errors as they occur when carrying outNHST.3 What three factors determine the power of a statistical test? Which factor is the primaryone that researchers can use to control power?4 Why is a repeated measures design likely to be more sensitive than a random groupsdesign?5 Describe one advantage and one limitation of using measures of effect size.6 Why may a statistically significant result be neither scientifically nor practicallysignificant?