Which measure assesses the difference between two means in terms of standard deviation?

Cohen's d is the measure that assesses the difference between two means in relation to the standard deviation. This effect size statistic provides a way to quantify the size of the difference between two groups. It is calculated by taking the difference between the two means and dividing that by the pooled standard deviation of the groups. This allows researchers to understand not just whether a statistically significant difference exists, but also the meaningfulness of that difference in practical terms.

For example, if you are comparing the effectiveness of two different therapeutic interventions, knowing that one intervention has a larger mean effect size (Cohen's d) compared to the other helps in understanding the magnitude of the difference, beyond just the statistical significance that might be indicated by a t-test.

The other options listed serve different purposes: Levene's test is used to assess the equality of variances between groups, the Kolmogorov-Smirnov test is aimed at comparing the distributions of two samples and checking for normality, and the Shapiro-Wilk test also assesses whether data is normally distributed. None of these measures directly address the difference between means in terms of standard deviation.