I have been asked to evaluate the below results from a fundraising campaign, and conclude whether there are any differences between the TEST and CONTROL groups. Specifically, i need to decide whether the response rate and income per £ invested are significantly higher in the TEST group.
I would be grateful for any help with this, i think i may have the answer for the response rate test. I believe this would involve a two sample t test using Mailing volume as the 'n1' and 'n2', and estimating the sample standard deviation as SQRT(p*(1-p)) where p is the observed response rate in both samples, given that these are bernoulli trials. I would be grateful if anyone could confirm this approach, and how i could carry out a similar analysis for income per £ invested (which doesnt constitute a bernoulli trial).
CONTROL VS TEST Mailing Volume Responses Income Cost response rate income per £ invested TEST 2140 211 £8,845 £1,070 0.099 8.27 CONTROL 576 32 £1,489 £288 0.056 5.17