# testing for significant differences among three proportions

#### bruin

##### Member
Hi,

I know that three proportions seems like a Chi-Square problem, but I'm having trouble making my problem conform to a Chi-Square.

Let's say I have three gatherings of people, and for each one I have measured the proportion of people that is over 30 years old; and I'm comfortable treating each Gathering as a random sample of a larger population.

Gathering 1 - 25% over 30
Gathering 2 - 46% over 30
Gathering 3 - 53% over 30

Chi square looks at proportions of each level of a categorical variable. You get expected proportions based on assuming all levels occur at the same frequency (.33, .33, .33 if you had a categorical variable with 3 levels).

But I certainly don't have any preconceived notion that the proportion over 30 at each gathering will be .33, .33, .33.

What I want to test is the H0 that says the sample proportions .25, .46, and .53 were all drawn from the same population.

If I were to use Chi-Square I would need to compare .25, .46, and .53 to expected proportions. So where would I get my expected proportions from?

Any help would be appreciated.

Last edited:

#### Dason

##### Ambassador to the humans
Do you have the sample sizes for each group

Yes.
n1 = 20
n2 = 24
n3 = 30

Last edited:

#### bruin

##### Member
When I said Chi-Square earlier, I was thinking of goodness of fit.

I think I actually just need a Chi-Square test of independence with:

Grouping variable: which Gathering (1, 2, or 3)

Response variable: Dichotomous Age (over 30, under 30)

Is that right?