# Math Help - two sample t test - comparing rates

1. ## two sample t test - comparing rates

Hi

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).

Many thanks
Colin

 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

2. ## Re: two sample t test - comparing rates

Hypothesis Test: Difference in Proportions

Make $p_1$ the response rate for the test group and $p_2$ the response rate for the control group

Use the case where $H_0: p_1 - p_2 \geq 0$

3. ## Re: two sample t test - comparing rates

Thanks for this very quick response. But if i need to estimate the standard deviation would it not be a t-test (as opposed to analysis using the Normal Distribution)? Im fine with the logic other than that.

Also, can you advise how i might compare 'income per £ invested' in the same way?

I really appreciate the help here

Bests,
Colin