Consider the following information computed for differences between 25 pairs of scores: M = 5, s = 12. Based on this information, what is Cohen's d for the corresponding paired-samples t test, when rounded to two decimal places? When answering this question, please use a typical null hypothesis indicating no differences between the populations.

Question

Consider the following information computed for differences between 25 pairs of scores: M = 5, s = 12.  Based on this information, what is Cohen's d for the corresponding paired-samples t test, when rounded to two decimal places?  When answering this question, please use a typical null hypothesis indicating no differences between the populations.

BlackTom AI · Accepted Answer

We start by identifying the formula for Cohen's d in a paired-samples design. In this case, d = mean difference / standard deviation of differences.

Option A: d = 1.44
This would require a ratio around 1.44, which would imply a much larger mean difference relative to the standard deviation of differences than what we have. Given M = 5 and s = 12, the calculation 5/12 yields a much smaller value, so 1.44 is not consistent with the data.

Option B: d = 0.50
This value is plausible as an approximate effect size, but it does not match the exact calculation from the provided numbers. The precise ratio 5/12 equals 0.4167, which rounds differently than 0.50 when rounded to two decimals.

Option C: d = 0.42
This option aligns with the computed ratio. Computing directly: d = M / s = 5 / 12 = 0.416666..., which rounds to 0.42 when rounded to two decimal places. This is the value derived from the given information.

Option D: d = 0.86
This would require a substantially larger mean difference relative to the standard deviation, or a much smaller s, than what is provided. With M = 5 and s = 12, the resulting ratio is far from 0.86, making this option inconsistent with the data.

In summary, the only option that matches the direct computation from the given M and s is the one that equals approximately 0.4167, i.e., 0.42 when rounded to two decimals, while the others do not correspond to 5/12 and are thus incorrect.

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