You are replicating a previous study in which the researchers conducted an ANOVA comparing blue-eyed, green-eyed and brown-eyed participants on a measure of anxiety, and obtained a statistically significant result. However, you are using twice as many participants. Which of the following statements is true?

Question

BlackTom AI · Accepted Answer

Question context: In an ANOVA comparing blue-eyed, green-eyed, and brown-eyed participants on anxiety, a statistically significant result was found. Now you’re using twice as many participants. We’ll evaluate each statement.

Option 1: 'The effect size would be expected to be bigger in your study.' Effect size (e.g., eta-squared or f) is a measure of the proportion of variance explained relative to total variance. Increasing sample size does not inherently increase the true effect size; it increases the precision of the estimate and the power to detect the existing effect, but the actual underlying population effect size remains the same. Therefore, this statement generally overstretches what sample size change does to effect size.

Option 2: 'The null hypothesis will be even more likely to be false in your study than in the previous study.' The null hypothesis being false in the original study was based on the observed data. Doubling the sample size increases power, which makes it more likely to reject a false null, but it does not in itself guarantee that the null is false in every replication. If the true effect in the population is the same as assumed, power increases and you are more capable of detecting it; however, you cannot claim the null is "even more likely to be false" purely from increasing N without considering the actual effect size and variability in the new sample. This statement is overstated and not guaranteed.

Option 3: 'The p-value should be approximately the same as in the previous study.' With a larger sample size, if the true effect size remains the same and variance is similar, the test statistic (F) tends to increase with N, leading to a smaller p-value, not the same one. Thus this claim is unlikely; p-values typically decrease with higher power when the effect exists, or stay small if the effect is strong, but are not expected to stay approximately the same when N doubles.

Option 4: 'The SSTOTAL would be expected to increase substantially.' In ANOVA, SSTotal (the total sum of squares) is the sum of squared deviations of all observations from the grand mean. Doubling the sample size generally increases SSTotal proportionally because you are summing more squared deviations about the same grand mean (assuming the population variability and mean do not change dramatically). Therefore, SSTotal is expected to increase with a larger N, often substantially, reflecting more data contributing to the total variability. This aligns with how SS components scale with sample size under similar conditions.

In summary, Option 1 misinterprets how sample size affects effect size, Option 2 makes an overgeneralized claim about the null being false, Option 3 mispredicts p-value behavior under increased N, and Option 4 correctly reflects the relationship between larger sample size and SSTotal in an ANOVA context. The reasoning here shows why the statement about SSTOTAL is the one that aligns with statistical properties when N is increased, while other statements misstate how effect size, p-values, and hypothesis decisions respond to a larger sample in a replication.

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