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.
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