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 |

Re: two sample t test - comparing rates

Follow this example.

Hypothesis Test: Difference in Proportions

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

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

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