Factors Affecting Power

Author(s)

David M. Lane

Prerequisites

Introduction to Power, Example Calculations, Significance Testing, Type I and Type II Errors, One- and Two-Tailed Tests

Learning Objectives
  1. State five factors affecting power
  2. State what the effect of each of the factors is

Several factors affect the power of a statistical test. Some of the factors are under the control of the experimenter whereas others are not. The following example will be used to illustrate the various factors.

Sample Size

The larger the sample size, the higher the power. Since sample size is typically under an experimenter's control, increasing sample size is one way to increase power. However, it is sometimes difficult and/or expensive to use a large sample size.

Standard Deviation

Power is higher when the standard deviation is small than when it is large. Experimenters can sometimes control the standard deviation by sampling from a homogeneous population of subjects or by reducing random measurement error.

Difference between Hypothesized and True Mean

Naturally, the larger the effect size, the more likely it is that an experiment would find a significant effect.

Significance Level

There is a tradeoff between the significance level and power: the more stringent (lower) the significance level, the lower the power. Power is lower for the 0.01 level than it is for the 0.05 level. Naturally, the stronger the evidence needed to reject the null hypothesis, the lower the chance that the null hypothesis will be rejected.

One- versus Two-Tailed Tests

Power is higher with a one-tailed test than with a two-tailed test as long as the hypothesized direction is correct. Power is higher with a one-tailed test than with a two-tailed test as long as the hypothesized direction is correct. A one-tailed test at the 0.05 level has the same power as a two-tailed test at the 0.10 level. A one-tailed test, in effect, raises the significance level.

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