I am calculating effect sizes (Cohen's d) for a meta-analysis to examine pre-test to post-test differences after receiving a word-learning treatment. I am using pre-test and post-test means and SDs in the following formula:
d = (mean_post - mean_pre) / Sw
Sw = ((n_pre - 1) * SD_pre + (n_post-1) * SD_post) / ((n_pre-1) + (n_post-1))
However, some studies don't report pre-test means/SDs, because they are sure that participants would achieve a score of 0 anyway (for example, when you let English-speaking people take a Chinese vocabulary test who have never studied Chinese before).
In these cases, would it be valid to calculate the pre-to-post effect size by filling in 0 for mean_pre and SD_pre?
Best Answer
That seems sensible. It is a form of imputation a bit like if you have a child recorded as missing civil status you can put "single". The only objection I can see is that if the vocabulary test was multiple choice then people with no knowledge would get a non-zero score by guessing but if you are satisfied that cannot happen in your use case then what you suggest seems OK to me.