Analyzing Enrollment Campaigns with Chi-Square: Is It the Right Approach?

[Math Is Hard]

Homework Statement

I'm trying to test a hypothesis that sending people both an email announcement and direct mail announcement produces significantly more enrollments in a free webinar than email or direct mail alone.
I'd like to do an analysis on these groups created from 400 people selected from our database and randomly assigned.


100 People who received neither email nor direct mail from us
100 People who received an email only
100 People who received a direct mail piece only
100 People who received both and email and direct email piece

Is a chi square analysis the right way to go about this? Do I need the "control group" who received no communication?

Homework Equations

Chi square analysis

The Attempt at a Solution

I think I would set up the groups like this attachment - when I get data. I've just made up some data for now.
Thanks!

 

[Redbelly98]

Hello MIH!

Yup, chi-square is the way to go on this.

While you don't need the control group for the hypothesis you stated, it may be wise to include it anyway. Somebody might ask about it after the study. And if you don't get a significant difference among the groups you are interested in, a reasonable followup hypothesis may be whether the announcements made any difference at all. You'll have the data in hand to address that.

 

[Math Is Hard]

Thanks so much, Redbelly! :-)

 

[I like Serena]

I may be a bit late to respond...

Anyway, chi-square will tell you whether it matters in general what you do.
It does not really address the hypothesis you've stated.

To test that you need a pooled two-proportion z-test. See e.g. wiki.
You would test the proportion of enrollments with both announcements against the combined proportion of enrollments with a single announcement.