In a study, subjects are randomly assigned to one of three groups: control, experimental A or experimental B. After treatment, the mean scores for the three groups are compared. The appropriate statistical test for comparing these means is:
Question
In a study, subjects are randomly assigned to one of three groups: control, experimental A or experimental B. After treatment, the mean scores for the three groups are compared. The appropriate statistical test for comparing these means is:
Solution
The appropriate statistical test for comparing the means of three groups is the Analysis of Variance (ANOVA). This test is used when you want to compare the means of more than two groups to see if they are significantly different from each other. The steps for this analysis would be:
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Calculate the overall mean (grand mean) of all groups combined.
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Calculate the sum of squares between (SSB), which measures the variance between the groups, and the sum of squares within (SSW), which measures the variance within each group.
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Calculate the mean square between (MSB) and the mean square within (MSW) by dividing the sum of squares by the respective degrees of freedom.
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Calculate the F statistic, which is the ratio of MSB to MSW.
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Determine the degrees of freedom for the numerator (k-1, where k is the number of groups) and the denominator (N-k, where N is the total number of observations).
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Use the F distribution with the appropriate degrees of freedom to find the p-value associated with the calculated F statistic.
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If the p-value is less than the chosen significance level (often 0.05), reject the null hypothesis that the group means are equal. This would mean that there is a significant difference in the means of at least two of the groups.
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