EDRM611 - Applied Statistics in Education and Psychology I

Objectives for Unit Eight
Power Analysis

1. Know the meaning of power.
Power is the probability of rejecting the null hypothesis when a difference truly exists in the population. It is 1- where is the probability of a Type II error. If a difference exists in the population you will either find it or not find it. The probability of finding it or not finding it equals 1.00. The probability of not finding it is and the probability of finding it is 1-.

2. Know the meaning of effect size and how it is reported.
As reported in research studies, effect size is the difference that is observed between the sample means (or a similar effect in other studies). When planning a study, effect size is the size of the difference between the population means that the researcher feels is important. The sample size is chosen so that if a difference between the sample means equal to the effect size is found it will be declared significant.

Effect size is commonly reported in standard deviation units. Values in common use are: small effect size = .2, medium effect size = .5 and large effect size = .8.

3. Know the factors needed to estimate power.
Power depends on four factors, the factors that influence Type II error. These are sample size (N), level of significance (), number of tails (1 or 2 tails), and effect size (d).

Power is increased using larger samples, higher levels of significance, 1-tailed tests, and looking for larger effects. The primary way researchers increase power is to increase sample size. Changing levels of significance or number of tails solely to increase power can be done but is questionable (especially with number of tails). The effect size is unknown since this is what is being investigated. In actuality the research must specify the effect size that is of interest before power can be calculated. If no intelligent estimate can be done, usually a medium effect size is specified.