The bigger the difference between your experimental groups, the larger you'd expect what to be (in an ANOVA)?

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BlackTom AI · Accepted Answer

When thinking about ANOVA, the question is asking which component reflects the between-group differences, i.e., how much of the total variation is due to differences among group means.
Option 1: p-value. The p-value is a measure of statistical significance of the test statistic (often F) given the data and the chosen alpha level. While larger between-group differences can lead to a larger F and thus a smaller p-value, the p-value itself is not the quantity that directly increases with group differences. It depends on the sample size and variance as well, so this option is not the direct answer to what grows with bigger between-group differences.
Option 2: SSBETWEEN. This term stands for the sum of squares between groups, exactly capturing the variability due to differences among the group means relative to the grand mean. As between-group differences become larger, SSBETWEEN increases because the deviations of each group mean from the grand mean grow, accumulating across groups. This is the quantity the question is pointing to.
Option 3: SSWITHIN. The within-group sum of squares measures variability inside each group, not the differences between group means. If the groups diverge more from each other but within-group dispersion stays the same, SSWITHIN does not increase in direct response to between-group differences. Therefore this is not the correct quantity described by the prompt.
Option 4: The value of SSTOTAL minus SSBETWEEN. Since SSTOTAL equals SSBETWEEN plus SSWITHIN, subtracting SSBETWEEN leaves SSWITHIN. As explained above, that reflects within-group variability, not the between-group differences. Therefore this option describes the wrong component.
In summary, the key concept is that SSBETWEEN grows with larger differences among group means, while SSWITHIN and the p-value operate differently, and SSTOTAL minus SSBETWEEN yields the within-group sum of squares rather than the between-group one.

PSYC20007_2025_SM2 ANOVA, II

The bigger the difference between your experimental groups, the larger you'd expect what to be (in an ANOVA)?

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