I am Beginner, and I am exploring Power Analysis using R pwr packages, with the help of this reference: Quick-R: Power Analysis in several attempts of understanding, all I know that with these examples:
library(pwr)
pwr.t.test(d=0.2,n=60,sig.level=0.10,type="one.sample",alternative="two.sided")
pwr.t2n.test(d=0.6,n1=90,n2=60,alternative="greater")
pwr.r.test(r=0.1,power=0.80,sig.level=0.05,alternative="two.sided")
pwr.chisq.test(w=0.1,df=(5-1)*(6-1),power=0.80,sig.level=0.05)
pwr.p.test(h=0.2,power=0.95,sig.level=0.05,alternative="two.sided")
pwr.f2.test(u=5,v=89,f2=0.1/(1-0.1),sig.level=0.05)
pwr.anova.test(f=0.28,k=4,power=0.80,sig.level=0.05)
#Effect Sizes notes:
#Cohen suggests that f values of 0.1, 0.25, and 0.4 represent small, medium, and large effect sizes respectively.
#Cohen suggests that f2 values of 0.02, 0.15, and 0.35 represent small, medium, and large effect sizes
#Cohen suggests that r values of 0.1, 0.3, and 0.5 represent small, medium, and large effect sizes respectively.
#Cohen suggests that d values of 0.2, 0.5, and 0.8 represent small, medium, and large effect sizes respectively.
#Cohen suggests that h values of 0.2, 0.5, and 0.8 represent small, medium, and large effect sizes respectively.
This can be use to calculate types of Statistical Power, which are available for t-test, chi square-test, proportion test, and also general Linear Model testing.. and most important parameters, which is power, effect sizes (which varies for kinds of statistic test d/r/h), n (observation numbers) are computable one after another, Here is my couple of question:
- If I have Power calculated from t.test 0.7 (example:
pwr.t.test(d=0.2,n=170,sig.level=0.05,type="one.sample",alternative="two.sided")), does that mean the test said that, given the 170 observation number and 0.2 effect sizes, I will have a data more likely a false positive rate than false negative rate? since power is a probability of making a Type I Error by this introduction https://www.khanacademy.org/math/ap-statistics/tests-significance-ap/error-probabilities-power/v/introduction-to-power-in-significance-tests, and also which is more preferable? having a less, balanced (near 0.5) or higher power for experiment, and why? - I mostly read that Effect Sizes are about an interpretation of strong relationship of 1 to another variables, almost similiar but not same to the correlation, so can I assume that Effect Sizes and Correlation value will not differ so much? or are there a lot of cases that Effect Sizes differ so much with Correlation in interpretation?
- Effect Sizes computation for each statistical tests seems different, is there any reference of how to compute each effect sizes that applies in above implementation?
Thank You in Advances, I hope that this question is still make sense to answer