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Statistical Power

Statistical power (SP) refers to the probability of rejecting a null hypothesis (a hypothesis of no difference) when it is actually false. When an organizational researcher retains (fails to reject) a false null hypothesis, he or she is likely to conclude, for example, that the organizational intervention did not positively affect productivity or that a selection test does not validly predict future job performance. Because an erroneous decision can have important practical implications, researchers would like to have adequate SP in order to be able to reject the null hypothesis when it is false. The amount of SP present when testing, say, the difference between two means or the relationship of two sets of values, is influenced by three factors: (a) the alpha level (α, or probability value) adopted for the statistical test, (b) the size of the sample used to obtain the means or correlation, and (3) the effect size (ES; or the magnitude of the difference or relationship). Before discussing these factors, a few words must be said about Type I and Type II errors in hypothesis testing.

Type I and Type II Errors

Figure 1 shows the interplay of accepting or rejecting a null hypothesis when it is actually true or false. A Type I error occurs when a null hypothesis (e.g., two variables that are not related or two subgroups that are not different) is rejected as being true, but it is actually true. A Type II error occurs when a null hypothesis is retained as being true, but it is actually not true. The probability of Type I error is denoted by alpha (α), and the probability of Type II error is denoted by beta (β). Statistical power—the probability of rejecting the null hypothesis when it is false—is equal to 1 minus the probability of a Type II error (1 −β).

In a statistical analysis, the likelihood that a Type I versus a Type II error will occur can be manipulated by adjusting the probability, or α level, for the statistical test. The most typical α value is .05. When α = .05, the rate of committing a Type I error is five times per 100 independent samples that might be compared. If a smaller value for α (e.g., .01) is chosen, the likelihood of committing a Type I error decreases, but the likelihood of a Type II error increases. Similarly, by increasing α (to a value greater than .05), we decrease the probability of a Type II error.

Factors Affecting Statistical Power

As noted previously, α, sample size, and ES play important roles in determining SP. According to Figure 1, SP is the converse of the probability of Type II error (SP = 1 −β). One way to decrease the likelihood of a Type II error is to increase α. Although there is nothing sacred about the commonly used α levels, one should be careful about increasing the α levels excessively. There are very few organizational interventions in which the treatment effect is truly zero; many treatments may have small effects but rarely zero effects. According to null hypothesis testing, Type I errors can only occur when the treatment effect is zero. Therefore, raising the α level without a good rationale is not recommended because the higher the α, the less rigorous the test of an effect, and the greater the chance of making a Type 1 error.

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