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396 PART V: Analyzing and Reporting Researchwould need to decide if practical or theoretical decisions should be made on thebasis of this result or if “more research is needed.” Should you pursue advancedstudy in psychology, you will want to explore more about power analysis.DATA ANALYSIS INVOLVING MORE THAN TWO CONDITIONSThus far we have discussed the stages of data analysis in the context of an experimentwith two conditions, that is, two levels of one independent variable.What happens when we have more than two levels (conditions) or, as is oftenthe case in psychology, more than two independent variables? The most frequentlyused statistical procedure for analyzing results of psychology experimentsin these situations is the analysis of variance (ANOVA).We illustrate how ANOVA is used to test null hypotheses in four specificresearch situations: single-factor analysis of independent groups designs;single-factor analysis for repeated measures designs; two-factor analysis forindependent groups designs; and two-factor analysis for mixed designs. Werecommend that, before proceeding, you review the information presented inChapters 6, 7, and 8 that describes these research designs.ANOVA FOR SINGLE-FACTOR INDEPENDENT GROUPS DESIGN• Analysis of variance (ANOVA) is an inferential statistics test used todetermine whether an independent variable has had a statisticallysignificant effect on a dependent variable.• The logic of analysis of variance is based on identifying sources of errorvariation and systematic variation in the data.• The F-test is a statistic that represents the ratio of between-group variationto within-group variation in the data.• The results of the initial overall analysis of an omnibus F-test are presented inan analysis of variance summary table; comparisons of two means can then beused to identify specific sources of systematic variation in an experiment.• Although analysis of variance can be used to decide whether anindependent variable has had a statistically significant effect, researchersexamine the descriptive statistics to interpret the meaning of theexperiment’s outcome.• Effect size measures for independent groups designs include eta squared( 2 ) and Cohen’s f.• A power analysis for independent groups designs should be conductedprior to implementing the study in order to determine the probabilityof finding a statistically significant effect, and power should be reportedwhenever non significant results based on NHST are found.• Comparisons of two means may be carried out to identify specific sources ofsys tematic variation contributing to a statistically significant omnibus F-test.Key ConceptOverview Statistical inference requires a test to determine whether or not theoutcome of an experiment was statistically significant. The most commonlyused inferential statistics test in the analysis of psychology experiments is theANOVA. As its name implies, the analysis of variance is based on analyzing