We have a single-case experimental design and we calculated Cohen's d for effect size using the mean difference between pre and post, divided by pooled standard deviation. However, for one of the outcomes, the variance for pre test is zero and the variance for post test is zero, even though there is clearly a change in the mean scores of pre and post. What should we do in this situation? Do we need to use a different equation?
In your case --- because both samples have zero variance --- the denominator in the formula for Cohen's d will be zero. Reporting the result as "infinite" may be the only option.
As a side note, since you are looking at pre-post data, a variant of Cohen's d for paired data may be more appropriate. There appear to be some possible variants