Understanding the Basis of Statistical Power in Psychology Research Work
What is Statistical Power?
The power of a statistical test for a null hypothesis is the probability of having the basis to correctly reject a false null hypothesis (Greene, 2000). Statistical power is the probability of detecting an effect if the effect actually exists or the probability that the test will lead to a conclusion that the effect actually exists (High, 2000 & Cohen, 1988, p. 4). It is also the ability of the test to report a statistically significant effect where an actual effect of a given magnitude exists.
In simple terms, statistical power is the likelihood that a researcher will discover an effect of a certain size in a statistical test no matter how small. The analysis of the power of statistical test enables the researcher to estimate the ability of the entire research work to detect a meaningful effect. Technically, statistical power is the probability that the researcher will avoid a Type II error. Type II errors are false negatives where the test result indicates there is no effect when a real effect exists.
The analysis of statistical power is done either retrospectively, which means post hoc, or prospectively, which implies a priori. The power of a statistical test is given as 1-β, where β (beta) is the Type II error and it is the probability that the researcher fails to reject the null hypothesis when it is false. When β is less than or equals to .2, the statistical power is said to be statistically powerful because its value would be greater than .8.
According to Howell (2002), the statistical power of a test statistic like the independent t test is determined by the following three (3) parameters:
1. The size of the sample per group (N)
2. The effect size of the standardized population (d), and
3. The significance level or criterion (α)
The statistical power of a research will increase if any of these parameters is increased. For obvious...