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.