Explain when ANOVA is used and how it works.
Analysis of variance (ANOVA) is a family of tests for comparing the means of three or more groups. Between-subjects, one-way ANOVA is used to compare the means of two or more independent samples when there is just one explanatory variable.
Between-subjects, one-way ANOVA separates variability in scores into that due to the different ways the groups are treated and that due to variability between cases. If there is more variability between groups due to treatment than within groups due to individual differences, then there is a statistically significant difference among the groups.
Complete a between-subjects, one-way ANOVA.
To complete an ANOVA, the assumptions must be met and the hypotheses set. The null hypothesis says that all population means are the same and the alternative that at least one population mean differs from the others. The decision rule compares the observed F ratio (variability due to treatment divided by variability due to individual differences) to the critical value of F . Calculating an F ratio involves finding sums of squares and degrees of freedom for three sources of variability (between group, within group, and total) and organizing that information in an ANOVA summary table.
Interpret the results of a between-subjects, one-way ANOVA.
If the results are statistically significant, at least one population mean differs from at least one other. Then calculate the size of the effect using r2 and use post-hoc testing with the Tukey HSD to which pair(s) of means differ.
If results are not statistically significant, then there is not enough evidence to conclude any population means are different. Nonetheless, calculate r2 in order to consider the possibility of Type II error.
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ANOVA is an extension of the t test, so let’s extend the DIY from the independent-samples t test to the between-subjects, one-way ANOVA. In that DIY, you were asked to compare two groups of states, say, northern states vs. southern states, on some outcome variable, say, murder rate. Now, divide states into three groups, say, northern, middle, and southern states, and compare them on your outcome variable.