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# One-Way Analysis of Variance

If a study is conducted in which two or more sample means are compared on one independent variable, then to test the null hypothesis the researcher would employ a procedure called one-way analysis of variance (ANOVA). ANOVA is simply an extension of the t test. Rather than using multiple t tests to compare all possible pairs of means in a study of two or more groups, ANOVA allows you to test the differences between all groups and make more accurate probability statements than when using a series of separate t tests. It is called analysis of variance because the statistical formula uses the variances of the groups and not the means to calculate a value that reflects the degree of differences in the means. Instead of a t statistic, ANOVA calculates an F statistic (or F ratio). The F is analogous to the t. It is a three- or four-digit number that is used in a distribution of F table with the degrees of freedom to find the level of significance that you use to reject or not reject the null. There are two degrees of freedom. The first is the number of groups in the study minus one, and the second is the total number of subjects minus the number of groups. These numbers follow the F in reporting the results of ANOVA. For example, in reporting F(4, 80) = 4.25, the degrees of freedom mean that five group means are being compared and 85 subjects are in the analysis.

ANOVA addresses the question: Is there a significant difference between the population means? If the F value that is calculated is large enough, then the null hypothesis (meaning there is no difference among the groups) can be rejected with confidence that the researcher is correct in concluding that at least two means are different.

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