Since t -test is a LR test and its distribution depends only on the sample size not on the population parameters except degrees of freedom. The t-test can be applied to any size (even n>30 also). The decision depends on the t-statistic and its degrees of freedom (function of sample size). So you need not to worry about the sample size to make a decision, you can make a decision at any df. If you are rejecting the null hypothesis means, there is no sufficient evidence (data) to accept the null hypothesis. But experimentation have limitation on the sample size, which will be decided based on the reliability, cost and time constraints.

I am not sure if I get you right: are you asking about a *maximum sample size* for these tests? If yes, then the answer is that there is no maximum size. Sample size planning should depend on factors as the expected effect size and then pragmatically on participant availability. Just look in any statistics book of your choice - you will probably find a chapter about statistical power and/or sample size planning.

@Vandana: these rules of thumb (and imo they are nothing more than that), are quite often severely misleading. It is no coincidence that many research fields that apply such rules suffer from the problem of highly under-powered and thus difficult to replicate studies.

Since t -test is a LR test and its distribution depends only on the sample size not on the population parameters except degrees of freedom. The t-test can be applied to any size (even n>30 also). The decision depends on the t-statistic and its degrees of freedom (function of sample size). So you need not to worry about the sample size to make a decision, you can make a decision at any df. If you are rejecting the null hypothesis means, there is no sufficient evidence (data) to accept the null hypothesis. But experimentation have limitation on the sample size, which will be decided based on the reliability, cost and time constraints.

@vandana punia are you saying that T test should be less than 30 in case of paired and it should be more than 30 in case of independent sampling??

@Thomas Scherndl My question is that if we have already decided upon the sample size say 120 or 150 samples and we want to know that can we apply t test on it as the size is above 30 and Sir how can we decide on the expected effect size.... are there some ways/ formulas/ tests for the same?

@naveen boiroju ..by LR u mean likelihood ratio test right? and what T statistic you are referring here??

@Anu, all the t tests are Likelihood ratio tests, since it involves nuisance parameter (SD is estimated). It is well known that t-tests are used for testing of hypothesis or construction of the confidence intervals for the population means. So the determination of the sample size is independent of the t-test.

A paired t-test is only useful if you test the same subject twice. Say, you give me medication A and ask me how effective it is, then you give me medication B and ask me how effective it is.

The 2-sample t-test is valid for any sample size. You will want to look for the power of your test. If it is around 0.6-0.8, you have some good results. If the power is lower than this, your test will be more likely to be found invalid in later studies.

Are you able to collect extra data on your research subjects? in general, t-tests are really poor tests for data analysis. You can run a multiple regression analysis on your data and get much better, robust results.

@Anu: well, as mentioned before: you *can* compute a t-test with even small samples - they are probably only severely underpowered. A N of 120 is actually quite ok if you are expecting a medium effect - you will get a power of almost .80 for such a medium effect (Cohen's d of .50 - see online calculator below).

If you want to compute statistical power, you can use either a program (most are free e.g. G*Power, R with pwr package, ESCI by Geoff Cumming) or use an online calculator: http://www.danielsoper.com/statcalc3/calc.aspx?id=47

The "minimum" sample size mentioned there is relating to the statistical power. As the effect is probably a fixed value, you have only two alternatives: a) increase sample size to get higher power, or b) live with low power.

Low power is a huge problem in research. Although a power of .8 is often referred to as sufficient and desirable, this means that out of 10 tests only 8 will get you a significant (p

Actually there is no such limit. However, if you observe minutely, you would see that for sample size 30, the tabled values are almost equal to the concerned value for the case of the normal distribution.

I agree with all my peers in this forum, there is no such maximum sample size limit for applying t test.

If you are manually applying the test (you are going to compare computed t value with the tabulated t value), the standard t distribution table has degrees-of-freedom values of more than 30, in fact 120 and accommodates higher degrees of freedom.

If you use SPSS, it accepts (and does not warn you) if you have more than 30 sample size per group.

@ Andrew Ekstrom when can we use multiple regression test instead of t test ??

Thanks all for helping with your valuable inputs

I believe that the maximum size for applying t tests on samples is 30. If the sample size is more than 30, we can use other tests.

A t-test is a regression with a single binary predictor. So the coefficient for the predictor is the difference between the means. And the t-value you see in your multiple regression is the t-value of the t-test.

The advantage of using multiple regression is that it allows you to conduct a t-test while controlling for confounding variables.

The other advantage of regression is the modern software implements Huber-White robust variance estimation which corrects the standard errors for clustering in the data, a problem that is more or less ubiquitous in real-life data. 

Hello

I have a question about sample size for doing independent-t and paired t-test:

When the sample size be more than 30, so could we use t-test without assessing assumptions of the tests (e.g., independent and equally variance). In other words, if sample size > 30, we use the tests always or the other assumptions should be accepted?

your attention is highly appreciated.

Thank you