# T-test on percentage values (among experimental replicate values)

My experiment involves looking at the precentage of cells in a slide that have a particular property under condition A and condition B. I have one slide for each condition. I have done this experiment 3 times and lets assume the data looks like this:

        Cond.A  Cond.B
Exp. 1   32%     40%
Exp. 2   31%     41%
Exp. 3   35%     44%


Can I now do a T-test between conditions A and B? Or should I just pool all the fractions per condition and do categorical data statistics?

I assumed I can do a t-test because at least within the realm of this data, it seems continuous and uncensored. Or am I wrong?

• It might be worth reading: stats.stackexchange.com/questions/11296/… Commented Feb 4, 2015 at 18:02
• You state no hypotheses. What are you trying to find out? If you think you can do a test, what are you going to use for the denominator of the statistic (i.e. how are you going to estimate standard deviation?) Commented Jun 20, 2015 at 9:42

Yes the t-test is powered to detect differences in mean proportion between these samples. It is likely not an exact test (where data are normally distributed), so may not be of the correct size (usually such issues lead to conservative tests, which are okay). However, the t-test is asymptotically consistent, and robust to departures from normality in even modest sample sizes.

t-test assumes that your data is normally distributed, what is simply not true about proportions - you should rather assume distributions such as Binomial. There are statistical tests that are especially designed for proportions data like Proportions test (prop.test in R) or Binomial test (binom.test in R) (see here, here, or here). In medical research odds ratios and logistic regression are commonly used for proportions. So there are multiple tools to choose from.

Take also look at this thread.

• Thank you for your input.. I did consider doing statistics applied to proportions (mainly Logistic regression) but then the main point here is that I'm only comparing Conditions A and B, and I have three numbers for each of these conditions from Experiments 1, 2 and 3. My data is well contained within a range far from 0 and 100% values. So given that it looks reasonably continuous and is not censored (32, 31 and 35 vs 40, 41 and 44) , I could do statistics applied to such distributions. Is that not correct? Commented Feb 4, 2015 at 19:22
• There is multinomial logistic regression: ats.ucla.edu/stat/r/dae/mlogit.htm
– Tim
Commented Feb 4, 2015 at 19:40
• Tim; in large samples the proportions may be close to normally distributed, but even then they won't have constant variance. Commented Jun 20, 2015 at 9:44
• @Tim the actual percentage is the point that was measured. And the asymptotic t-test does not assume data are normally distributed. Simulation studies show that the small sample properties of the asymptotic t-test are quite favorable in samples as small as 20. For that reason, the notion that a t-test "requires normally distributed data" should be rejected outright. Commented Jul 28, 2015 at 22:55
• super late, but I think logistic or multinomial logistic cannot be done here, let assume he has a sample from Exp. 1 to Exp. 1000 so that we can see clearer the outcome is A and B not the proportion. Commented Mar 19, 2018 at 15:16