If the difference between two group means is 50 units and the within-group standard deviation is 60 units, which best characterizes the situation?

• A. The effect is large and statistically significant.
• B. There is large variability and substantial overlap relative to the effect size.
• C. The sample size must be very large.
• D. The p-value will be exactly 0.05.

Answer: (B)

When comparing two group means, you want to know how large the difference is relative to the typical spread within each group. Here the difference is 50 units while the within-group standard deviation is 60 units. The ratio 50/60 is about 0.83, which means the effect size is noticeable but the variability within each group is still large. Because the spread is large, the two distributions overlap substantially, so you don’t get clean separation between groups even though the difference isn’t negligible. This combination—meaningful difference but substantial overlap due to high variability—fits best with the idea of large variability and substantial overlap relative to the effect size. The other ideas depend on factors not determined by these numbers alone, such as exact sample size or p-value calculations.