I have a dataset that includes 3 distinct knowledge questions where pre-test and post-test answers were captured. % change was calculated for the correct answer choice in the 3 questions. Is it possible or reasonable to then calculate an average % change for the 3 knowledge questions?
Example:
Knowledge question #1 Correct answer: pre (n = 837) post (n = 1164) % change = 39%
Knowledge question #2 Correct answer: pre (n = 235) post (n = 269) % change = 14%
Knowledge question #3 Correct answer: pre (54) post (261) % change = 383%
Is it reasonable to add 39% + 14% + 383% and divide by 3 to reflect a mean/average % change in knowledge for the entire assessment?
Thank you!
Whether or not this average is reasonable depends on the context and the use you have for the statistic. So your question doesn't have a mathematical answer.
Would you be OK if the average were $0$ because some things were learned and some unlearned?
If you think some of the areas are more important than others you can calculate a weighted average: $$ w_1 k_1 + w_2 k_2 + w_3 k_3 $$ where the $k$'s are the percent changes in knowledge and the $w$'s are positive weights that sum to $1$. The differing values for $n$ suggest that may be the case.
You could also add the three pre values and the three post values and calculate the percent change in the totals. That would give you an implicit weighting.
Try several strategies (easy in a spreadsheet) and settle on one that makes sense in your application.