# Power Curve of a Mean Test

Power Curve of a Mean Test

The power of a hypothesis test is the probability of correctly rejecting the null hypothesis. Power is shown as the shaded area in the plot on the left and as a function of the noncentrality parameter, , in the plot on the right. Power depends on the effect size, , as well as the sample size, , and the significance level, .

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The blue curve in the plot on the left is the student distribution and the red curve is the noncentral distribution. The blue vertical line is the critical value of for rejecting the null hypothesis. The noncentrality parameter, , equals . As the mean, , approaches , approaches 0 and the power of the test decreases. For a typical experimental design, is chosen in advance (normally 0.05), and the standard deviation, , cannot be controlled by the experimenter. Thus the sample size is chosen to achieve the desired power.

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