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# Chi-Square Vs Student's T Test

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### #1 yoshi

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Posted 11 January 2015 - 05:54 AM

Hi All, my data looks like this:

Treated (4 replicates): (1) 21 positive, 178 negative (10.55% positive), (2) 25+, 166- (13.09% +), (3) 25+, 185- (11.9% +) and (4) 7+, 53- (11.67% +)

Non-Treated (3 replicates):  (1) 131 positive, 1285 negative (9.25% positive), (2) 133+, 1264- (9.25% +), (3) 139+, 1368- (9.22% +)

I want to know if there's any significant difference between treated and non-treated.

I could either do a chi-square for each replicates against one of the non-treated, so that the 2x2 table would look like this:

Treatment:          21+     178-

Non-treatment: 131+     1285-

or I could do a student's t test, in which I first calculate the mean % positive for all 4 treated samples, and compare it against the mean % positive for all 3 non-treated samples.

The problem: Results are non-significant with chi-square but they are with student's t test. I am of course very tempted to use the latter test, but I would also like to confirm with experts here that it's correct for me to do so. I know that the 2 tests are investigating slightly different questions (chi-square: association between treatment and outcome and student's t test: difference between means). But from a biologist's point of view, the distinction is not that clear. Please advise.

### #2 DRT

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Posted 11 January 2015 - 01:54 PM

If you pool the replicates you will get the same significance results for a 2x2 chi-square as for a t-test of the proportions.

A Mantel-Haenszel Test will make sure the replicates of a chi-square are not significantly different (there are other tests that do a similar thing).

### #3 yoshi

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Posted 11 January 2015 - 11:04 PM

If you pool the replicates you will get the same significance results for a 2x2 chi-square as for a t-test of the proportions.

A Mantel-Haenszel Test will make sure the replicates of a chi-square are not significantly different (there are other tests that do a similar thing).

Hi DRT, thanks. I've tried that before posting my problem here. And I just tried it again in case I have made a mistake previously. But even when I pool the samples (Treated: 78+ 482- and Non-treated: 403+ 2917-), and do a chi-square or Fisher's exact test, I got a p value of around 0.2. Have I missed something here?

### #4 DRT

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Posted 12 January 2015 - 10:59 AM

Nothing wrong with your chi-square calculations; its the number of negatives which differs between your posts.