Space is too short for a full discussion on the importance of statistical power. Some suggested reading can be found at:
Power (in brief)
In statistical testing data sets are usually tested to see if they are significantly different (e.g. Student t-Test etc.) from each other, that is, for example, did the drug cause an effect when compared to a control (no drug). If there is no difference (so called null hypothesis) then the null hypothesis is accepted, if there is a difference then the null hypothesis is rejected.
Two types of error can result from this sort of analysis. Type I errors occur when the null hypothesis is rejected when the null hypothesis is in fact true (i.e. a false positive). Type II errors occur when the null hypothesis is retained when in fact it should be rejected (i.e. a false negative). In other words, a type II error means that an important effect may be missed. To guard against type II errors power analysis can be carried out to obtain a sample size that decreases the chance of a type II error occurring. This analysis can be carried out prior to the main (large) experiment being performed (a priori testing) using data from pilot or previous studies, or it can be carried out after the main experiment (post hoc testing) to assess the power of the statistical tests performed.
The power of a statistical test is the probability, assuming that the null hypothesis is false (i.e. an effect is significant) of obtaining a result that will allow the rejection of the null hypothesis.
There are four components that influence the power of a test:
Usually, experimenters can only change the sample size (population) of the study and/or the alpha value.
At present Power on X will perform power calculations based on one and two-tailed t-Tests of means or correlations. Calculations can be a priori (performed on data derived from a pilot or previous studies) or post hoc where the data has already been derived.