# Power

Much of the emphasis in traditional statistical texts is on preventing Type I errors. Little concern seems to be given to the prevention of Type II errors. Type II errors are prevented when a statistical test has sufficient power. In hypothesis testing, power is the ability of a statistic to detect a significant relationship when one exists. That is, it is the ability of the statistic to correctly reject the null hypothesis.

Power is the ability of a test statistic to detect a significant relationship between variables when one exists in the population.

Three factors have an impact on the power of a particular statistic in a particular research situation:

1. The strength of the relationship between the variables (effect size)

2. The predetermined rejection level for the test (the alpha level)

3. The sample size

Power increases as each of these three elements increases. The strength of the relationship is important because stronger relationships are easier to detect than weaker ones. Usually this will be of a fixed magnitude and beyond the control of the researcher. The other two factors are under direct control of the researcher and can be manipulated to increase power.

When it comes to setting an alpha level, the researcher is stuck in a balancing act between committing a Type I error by setting alpha too low, and a Type II error by setting alpha too high. Many researchers have concluded that an alpha of .05 or .01 strikes such a balance. The researcher could set alpha much lower and decrease the risk of a Type I error, but much of the test’s power is sacrificed by doing so.

Selecting a sample size is a tricky matter because it is a complex undertaking. For the researcher, samples size is directly related to time and money. Selecting a sample size of 10,000 would certainly result in a powerful test, but would be cost prohibitive in most circumstances. Therefore, the researcher must strike a balance between statistical power and cost-effectiveness. Researchers are advised to conduct a power analysis to determine an adequate sample size (but those methods are beyond the scope of this text). As a consumer of research, you should ask yourself about the researcher’s sample size when the researcher reports findings that are not statistically significant.

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