In calculating an effect size (ES) as defined here, which formula is used?

In calculating an effect size (ES) as defined here, which formula is used?

• A. mean of change scores/standard deviation of change scores
• B. mean of change scores/standard deviation of initial scores
• C. standard deviation of change scores
• D. mean of initial scores/standard deviation of follow-up scores

Answer: (B)

When expressing how big a change is in a standardized way, anchor the change to a stable reference point. Here, the average change score (post minus pre) represents how much participants improved on average. To put that improvement on a common scale, divide by the variability that existed before any intervention—the standard deviation of the initial (baseline) scores. This yields an effect size in units of baseline standard deviations, making the magnitude of change comparable across studies that started with different baselines or used different measures. Using the baseline standard deviation as the denominator has a key advantage: it reflects how much people differed at the start, before any treatment effect could influence outcomes. It avoids letting the amount of change be distorted by how dispersed the post-treatment scores ended up or by the amount of change across individuals (which can depend on the correlation between pre and post). In contrast, standardizing by the standard deviation of change scores would tie the effect size to how much individuals varied in their change itself—a quantity that can be unstable and heavily influenced by pre-post correlation—making cross-study comparisons less straightforward. Dividing by follow-up SD or other alternatives would distort the interpretation by focusing on post-treatment dispersion rather than the size of the observed change relative to where participants began.

When expressing how big a change is in a standardized way, anchor the change to a stable reference point. Here, the average change score (post minus pre) represents how much participants improved on average. To put that improvement on a common scale, divide by the variability that existed before any intervention—the standard deviation of the initial (baseline) scores. This yields an effect size in units of baseline standard deviations, making the magnitude of change comparable across studies that started with different baselines or used different measures.

Using the baseline standard deviation as the denominator has a key advantage: it reflects how much people differed at the start, before any treatment effect could influence outcomes. It avoids letting the amount of change be distorted by how dispersed the post-treatment scores ended up or by the amount of change across individuals (which can depend on the correlation between pre and post).

In contrast, standardizing by the standard deviation of change scores would tie the effect size to how much individuals varied in their change itself—a quantity that can be unstable and heavily influenced by pre-post correlation—making cross-study comparisons less straightforward. Dividing by follow-up SD or other alternatives would distort the interpretation by focusing on post-treatment dispersion rather than the size of the observed change relative to where participants began.