I am planning a study for comparing tear levels (which I will measure with the Schirmer test) between two groups. Group 1: persons with normal blood vitamin D levels and Group 2: persons with low blood vitamin D levels. When I try to calculate required sample size using "power and sample program" (in independent t test) with α = 0.05, Power = 0.80, difference in population means = 15 and ratio of Group 1 size to Group 2 size = 1 ,the result comes out "3". Is it really true? Where am I going wrong?
You have left out an essential part of the equation: variability within groups. Remember that a t-test assesses the mean difference between groups in light of the typical differences that occur within groups. If the mean difference is 15 while the standard deviation (s) within each group is much smaller, i.e., 3, then yes, the required sample size per group (N) would be only 3 (assuming your test is 2-tailed as is most common). On the other hand, if s were 150, the required N would be over 1,500.