Analysis of Variance (ANOVA) results in the calculation of the F Statistic and interpretation of this statistics will inform you as to...?
A. Which means significantly differ from the others.
B. How the variables are associated with each other.
C. Whether one or more of the means is significantly different from one or more of the others in the study.
D. How many means differ significantly from the "Grand mean"?
The correct answer is C. Whether one or more of the means is significantly different from one or more of the others in the study.
To understand why this is the correct interpretation of the F statistic in ANOVA, let's go over the steps involved in calculating it and interpreting the results:
1. Calculate the sum of squares (SS) for each group and the total sum of squares. The sum of squares is a measure of the variability in the data.
2. Calculate the degrees of freedom (df) for each SS. The degrees of freedom represent the number of independent observations available for calculating the SS.
3. Calculate the mean square (MS) for each group, which is obtained by dividing the SS by its corresponding degrees of freedom.
4. Calculate the F ratio by dividing the MS between groups by the MS within groups. The F ratio measures the ratio of the variability between groups to the variability within groups.
5. Determine the critical value of the F statistic based on the chosen significance level (alpha). This critical value corresponds to the cutoff point beyond which the F ratio is deemed statistically significant.
6. Compare the calculated F statistic to the critical value. If the calculated F statistic is greater than the critical value, it indicates that there is a statistically significant difference between at least one pair of group means.
7. If there is a significant difference, further post-hoc tests (e.g., Tukey's HSD or Bonferroni) can be conducted to determine which means are significantly different from each other.
Therefore, the correct interpretation of the F statistic in ANOVA is that it informs us whether one or more of the means is significantly different from one or more of the others in the study (option C). ANOVA does not directly provide information about how variables are associated with each other (option B) or the number of means that differ significantly from the "Grand mean" (option D), although post-hoc tests can be used to investigate these aspects.