Final answer:
To test for differences between means in ANOVA, both the between-group and within-group variances are used to compute the F statistic, which determines if differences are statistically significant. option d is the correct answer.
Step-by-step explanation:
When conducting an analysis of variances, specifically a one-way ANOVA test, to test for differences between means, the variances used are both the between-group variance and the within-group variance. The between-group variance (MSbetween) reflects the variation due to differences between the means of the various groups. In contrast, the within-group variance (MSwithin) measures the variation within each group. By comparing these two variances through the F statistic, we can determine if the differences in group means are statistically significant beyond what could be expected due to random chance alone. Thus, the correct answer would be (d) Both a and b.
The variances used to test for differences between means in an analysis of variances (ANOVA) are both the between-group variance and the within-group variance. In ANOVA, the between-group variance measures the differences between the means of different groups, while the within-group variance measures the differences within each group. By comparing these variances, ANOVA determines if there is a significant difference between the means of the groups being compared.