Parameter fundamentals of Power Analysis (Effect Sizes, Power, Correlation)

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:

  1. 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 Introduction to power in significance tests (video) | Khan Academy, and also which is more preferable? having a less, balanced (near 0.5) or higher power for experiment, and why?
  2. 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?
  3. 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

This topic was automatically closed 60 days after the last reply. New replies are no longer allowed.

If you have a query related to it or one of the replies, start a new topic and refer back with a link.