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?