What minimum sample size do you need to conduct parametric tests (student t test)?

Question

In hypothesis testing (in both paired and unpaired situation), when you deal with small samples you cannot use the student t test. Instead, you have to rely on nonparametric tests. They are called nonparametric because unlike the t test, they do not rely on the assumption that the underlying distribution is normal (with a relevant mean and standard deviation).

The question is how small is small? Different sources mention different minimum sample size so you can use the t test. Otherwise, you can't.

So, in your expert opinion what size sample do you need? Make sure to explain why and mention your background and reference. Explanation, credentials, reference will be heavily weighted in my rating the answer.

Some of the early answers interpreted the question as what size sample do you need to obtain significant results.
That's not the issue. The question refers to the sample size cut-off. Above that minimum size you can use the student t test. But, below that minimum size you have to use a nonparametric test. What is this minimum size? That size is not dependent on the size of the population. It is not even dependent on the distribution of the population.

Answer 1

In my opinion, it doesn't take that large of a sample in order for the CLT to take effect. Although in many classes, it is said that a sample larger than or equal to 25 is needed, that's not always necessary.

It does really depend on the shape of the population, though. If the population is roughly symmetric, then a sample of 10 or possibly less might be sufficient. If not, if the population is skewed and/or has outliers, then a larger sample would be necessary.

An elemetary stats book by Weiss has some good guidelines. I don't really remember what exactly they are, but, basically, you should look at the histogram and the normal qq plot of the of the data. Look at the histogram is roughly symmetric, and the normal qq plot is roughly linear.

One of my instructors once usually looked at the estimates for the skewness and the kurtosis to make the determination. I think that if the skewness is less than 2 in absolute value and kurtosis is less than 2.5, then the t test would be OK.

edit: (This is the email I sent you earlier)
I said the skewness and the kurtosis is less than those numbers, not greater than.

You can use Jarque-Bera as well as looking at the skewness and kurtosis.

Also, when I say kurtosis, I mean that it is the regular kurtosis minus 3, since 3 is the kurtosis of the normal.

In terms of what is considered minimum, well, the absolute minimum number of values you need is 2 of course. But again, that's only if the population is considered normal.

The CLT converges much faster in some populations versus others. So sometimes 10 is enough, sometimes not. That's why I didn't set a particular number.

edit: Yes, nonparametric tests can be used for pretty much any sample size. But again, the sample size in which you transfer from parametric to nonparametric should depnd on the shape of the population.

Also, alyxsylvr, you would know that standard errors typically do not depend on the sample size as compared to the population size; it depends on the absolute size of the sample.

Answer 2

Your minimum sample size is relative to the total population size you are concerned about.
These sizes have best been determined in the science of polling eg. political results.
There we find that they can get accurate results with very insignificant percentages however their results are only accurate to so many points 19 times out of twenty for example.
So you have to determine how accurate you wish you result to be. And how much you wish to depend on them. And possibly the cost of collecting them.
If the population is small say a university body then 2 or 3 classrooms of students when tested may give a suitable answer assuming that one picks the classes well eg. not all male or special needs students.

College Instructor

Answer 3

if they failed the test, keep teaching until they pass. If there has been problems in the students' lives, i would see what can be done to fix it. Any act of violence between peers will result in juvenile detention and probation. course if the whole students failed, it is the teacher's fault, but you must be able to fix that problem rationally and in common sense.

Answer 4

Looking for an answer on this too

Answer 5

Thanks everyone for the answers!