This is not homework! I have two very different answers for a power calculation I have done on the below data -
n = 50 in total, 25 in each group hit = if the number called is then thrown on a die probability of hit = 1/6 each person has 36 dice throws control group = call random number then throw a die wish group = wish for a number, call it out and then throw die 2 groups tested by 2 sample z-test because we know distribution parameters i.e mean chance is 6 (1/6 x 36 trials), standard dev is 2.23 control group hit total is 150 wish group hit total is 180
I know the result of the 2 sample z-test (z=-1.9025). That is not the question. Q.How do I calculate the power of the study (given I am interested in the difference between the groups rather than deviation from chance)?
I think my study is under powered but have done this calculation in the pwr package of R -
h0 <-6 #control group ha <-7.2 #wish group sigma <- sqrt(36*1/6*5/6) d = (ha - h0)/sigma pwr.norm.test(d = d, n = 25, sig.level = 0.05, alternative = "greater") Mean power calculation for normal distribution with known variance d = 0.5366563 n = 25 sig.level = 0.05 power = 0.8504646 alternative = greater
I think this is wrong.