### Overview

Statistical power is the probability of correctly rejecting the null hypothesis when it is false in a given sample. For further discussion of Power Analysis, see Jacob Cohen's classic 1992*Psychological Bulletin*Power Primer or Statsoft, or Faul, Erdfelder, Lang, and Buchner, 2007.

Power analysis is particularly useful when planning a study. There are many trade-offs when designing a study. Awareness of the trade-offs and how they relate to statistical power is particularly important. For example, you might be confronted with the decision of whether to use a subtle experimental manipulation (small effect size) that is of greater applied relevance or a stronger experimental manipulation (large effect size) which is less realistic. Being aware of the relative power of the two options helps to highlight whether the less realistic, but more statistically powerful, option is the better choice.

The website for G-Power 3 contains help material for many common scenarios. G*Power 3 makes it easy to get precise values of your statistical power for your given scenario. If G*Power 3 is insufficient for your needs, you may want to consider writing a simulation in a language such as R (see William Revelle's comments)

The following four plots show examples of the great plots that G*Power 3 can generate. I've also selected these four plots because I think that researchers in psychology should have an intuition about the statistical power of what may be the most common statistical tests: (a) the t-test of differences between independent groups, and (b) the correlation coefficient. Most studies in psychology have many variables and many hypotheses. However, many, but not all, of these hypotheses can be reduced to correlations between two numeric variables (e.g., IQ and job performance) or differences in a numeric variable between two groups (happiness levels between those receiving counselling and those not receiving counselling). Thus, internalising the approximate values of these four plots should help you when you design studies and when you read and evaluate the research literature.

#### What statistical power do I have given my sample size and assumed population correlation?

The rough rules of thumb can help: r = .1 is small; r = .3 is medium; r = .5 is large.#### What statistical power do I have given my sample size and assumed population difference between group means?

Rough rules of thumb: d = .2 is small; r = .5 is medium; r = .8 is large.#### What sample size do I need given a desired power an assumed population correlation?

The following two plots are useful when deciding what sample you need.#### What sample size do I need given a desired power an assumed population difference between group means?

### Related Resources

- Quick-R on Power Analysis in R
- Notes and audio from a talk I gave on Power Analysis, Null Hypothesis Significance Testing, and effect size
- Slides with notes form a talk I gave on descriptive statistics. The latter part of the talk is on power analysis.

This is actually a really great and helpful program. Some of the professors who created it taught me and therefore we have been using it a lot at our Uni back home(Germany).

ReplyDeleteThe third edition runs a lot nicer than the older ones as well ;)

... the name in the link is slightly misspelled by the way, it's supposed to be Erdfelder ;)

ReplyDeleteHI Johanna,

ReplyDeleteThanks for your comment and my thanks to your professors.

updated the name spelling. Cheers

ReplyDeleteI'll let them know ;) It's great that this useful piece of programming has made it's way over to Oz!

ReplyDeleteI don't know if anyone here is doing research that requires multinomial tree models, but if so, you might wanna check this one out, which I've been using back home:

ReplyDeletehttp://psycho3.uni-mannheim.de/index.php?n=Main.MultiTree

thought I'd share it, just in case it comes in handy for someone ;)

cheers

Thanks Johanna. MultiTree looks interesting

ReplyDeleteI can't get G*Power to fit on the screen of my MacBook, even at the highest resolution. Anybody have any suggestions?

ReplyDeleteExternal monitor might be an option

DeleteHi,

ReplyDeleteI would be grateful if you could send me some references to understand what you say when you are talking about "Popular Correlation".

When I try to do an "a priori" Power Analysis of F-test with reapeated measures, G*Power 3 requests me the data "Corr among rep measures" but I can't understand what it is.

Thanks!