A power primer.
Cohen (1992)
Psychological Bulletin
The tables of this article are missing
Effect-size indexes and conventional values for these are given for operationally defined small, medium, and large effects.
Statistical power analysis exploits the relationships among the four variables involved in statistical inference.
- Sample size (N)
- Significance certerion (α)
- Population effect size (ES)
- Statistical power
Each is a function of the other three. It is most useful to determine the N necessary to have a specified power for given α and ES.
The significance criterion α
α represents the maximum risk of mistakenly rejecting the null hypothesis (committing a Type I error). This is usually .05. α risk may be defined as one or two sided.
Power
The statistical power of a significance test is the long-term probability, given the population ES, α, and N of rejection the H0. When the ES is nit equal to zero, H0 is false, so failure to reject it also incurs an error (Type II error). For any given ES, α, and N, its probability of occurring is β. Power is 1 – β, the probability of rejecting a false H0.
Taken the conventional α = .05, power of .80, there is a α:β ratio of 4:1 of the two kinds of risks.
Sample size
In research planning, the investigator needs to know the N necessary to attain the desired power for the specified α and hypothesized ES. N increases with an increase in the power desired, a decrease in the ES and in α.
For statistical tests involving two or more groups, N is the necessary size for each group.
Effect size
The effect size (ES) is the degree to which the H0 is believed to be false.
In the Neyman-Pearson method of statistical inference, an alternative hypothesis H1 is counterpoised against H0. The degree to which H0 is false is indexed by the discrepancy between H0 and H1 and is called the ES. Each statistical test has its own ES index. All the indexes are scale free and continuous, ranging upward from zero. For all, the H0 is that ES = 0.
To convey the meaning of any given ES index, it is necessary to have some idea of its scale.
The ES index for the t test of the difference between independent means is d, the difference expressed in units of the within-population standard deviation.
The most common test in psychological research
- The t-test for the difference
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