# Checking normality for a t-test

I am following stats courses at the moment and I am a bit confused about performing a t-test. I know that a t-test assumes normality and enough sample size. In the course I am attending, the instructor is performing a t-test on the following samples:

a = np.array([0.28, 0.97, 1.25, 2.46, 2.51, 1.17, 1.78, 1.21, 1.63, 1.98])
b = np.array ([2.36,2.11, 0.45, 1.76, 2.09, 1.5 , 1.25, 0.72, 0.42, 1.53])

Are the samples big enough to perform a t-test? When I tried to plot histogram for both datasets it doesnt seem they are normally distributed.  Another approach I have seen when making a test for the mean is drawing bootstrap samples. In which scenarios I make bootstrap replicates and in which I can directly make the t test?

1. Are the samples big enough to perform a t-test?

T-test takes into account the number of data points you have, so yes. Nevertheless, the problem with a low amount of data is that the deviance and the mean of your data may not be the true ones (i.e. you are assuming your data is normally distributed with equal standards deviations for a t-test).

2 When I tried to plot histogram for both datasets it doesnt seem they are normally distributed

I agree, it does not seem normally distributed at all. According to this link` , you might

run the Mann-Whitney U test which is a non-parametric test that does not require the assumption of normality

3. Another approach I have seen when making a test for the mean is drawing bootstrap samples. In which scenarios I make bootstrap replicates and in which I can directly make the t test?

I reckon this is quite well answered in here.

Feel free to edit if there is something not well explained,

• @"with equal standards deviations for a t-test": although Welch's t-test doesn't make this assumption. – user244721 May 3 '19 at 10:27
• @Carles Sans Fuentes, somewhere I read the assumption is the sample mean is normally distributed – Len May 3 '19 at 11:46
• @Len the assumption is that the deviations from the means within groups have a normal distribution. – mdewey May 3 '19 at 12:17
• @ mdewey ,so it means that yes, the samples data are normally distributed right? – Len May 3 '19 at 12:27