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I have a data to compare two group let say Group A and Group B. The sample size for group A is 20 and Group B is 57. The outcomes variables are normally distributed as according to Shapiro-Wilk test in SPSS. The variance between these two groups are equal (which is showed by leven's equality test). it seemed that all the assumptions of independent T-test are fulfilled.

THE t-test results showed that there is significance difference between the mean of two groups.

I am wondering whether results like this is valid? if small sample size can cause loss of power (type II ERROR high- the probablity of false negative result- probability not reject instead the hypothesis is not true), how if the sample size small and significance still presence?

Thanks.

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    $\begingroup$ "The outcomes variables are normally distributed as according to Shapiro-Wilk test in SPSS." -- no. Failure to reject the null doesn't imply the null is true. $\endgroup$ – Glen_b -Reinstate Monica Oct 11 '15 at 9:02
  • $\begingroup$ One of the main points of significance and p-values is that they have the same meaning regardless of sample size (even though, as you correctly state, small samples tend to have little power). $\endgroup$ – whuber Oct 26 '15 at 22:32
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What is the p-value you got? You must check the p-value which is the best approach to reject or accept a hypothesis in hypothesis testing. The smaller the p-value the more significant is the result.

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    $\begingroup$ -1 does not adress the concerns and presents a very naive approach to hypothesis testing. $\endgroup$ – Erik Oct 11 '15 at 13:54

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