Statistical Power (Overview)

This week we'll be covering statistical power (also known as power analysis). Power is not a statistical technique like correlation, t-test, and chi-square. Rather, power involves designing your study (particularly getting a large enough sample size) so that you can use correlations, t-tests, etc., more effectively. The core concept of power, like so much else, goes back to the distinction between the population and a sample. When there truly is a basis in the population for rejecting the null hypothesis (e.g., a non-zero correlation, a non-zero difference between means), we want to increase the likelihood that we reject the null from the analysis of our sample. In other words, we want to be able to pronounce a result significant, when warranted. Here are links to my previous entries on statistical power.

Introductory lecture

Why a powerful design is needed: The population may truly have a non-zero correlation, for example, but due to random sampling error, your sample may not; plus, some songs on statistical power!

Remember that there's also the opposite kind of error: The population truly has absolutely no correlation, but again due to random sampling error, you draw a sample that gives the impression of a non-zero correlation.

How to plan a study using power considerations

Chi-Square

My introductory stat notes for methods class have some introductory information on chi-square.

Here are direct links to some old chi-square blog postings. This one discusses the reversibility error and how properly to read an SPSS printout of a chi-square analysis. The other one illustrates the null hypothesis for chi-square analyses in terms of equal pie-charts.

The following photo of the board, containing chi-square tips, was added on November 15, 2011 (thanks to Selen).

Plus a song (added November 1, 2011):

One Degree is Free

Lyrics by Alan Reifman

(May be sung to the tune of “Rock and Roll is Free,” Ben Harper)

Look at your, chi-square table,

If it is, 2-by-2,

One cell can be filled freely,

While the others take their cue,

The formula that you can use,

Come on, from the columns, lose one,

And one, as well, from the rows,

Multiply the two, isn’t this fun?

One degree is free, in your table,

With con-tin-gen-cy, in your table,

One degree is free, in your table,

…free in your table,

…free in your table,

Say, your table is larger,

Maybe it’s 2-by-4,

Multiply one by three,

3 df are in store,

The df’s are essential,

To check significance,

Go to your chi-square table,

And find the right instance,

Three degrees are free, in your table,

With con-tin-gen-cy, in your table,

Three degrees are free, in your table,

…free in your table,

…free in your table,

(Guitar Solo)