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Power and sample size

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QXL Stat Tools Tab > Hypothesis tests > Power and Sample Size

Power and sample size analysis

Power and Sample Size analysis is useful when planning for an experiment. You can compute the statistical power of the test for a given sample size or calculate the required sample size. Power is helpful when planning to prevent selecting sample sizes which are too small or too large. If you select too small a sample size, then the hypothesis test may fail to find a difference even though one exists. With too many samples, resources are wasted.

Power

Two types of errors can be made when running a hypothesis test --Type I and Type II error.

The Statistical Power of hypothesis tests is (1-β) where β is the probability committing Type II error (Type II error is failing to reject a null hypothesis when it is actually false).

Typically, when performing a hypothesis test, we are looking for evidence to reject the null hypothesis. Power represents our ability to find that evidence.

Power of the test depends on the following factors:

  • Sample size. A larger sample size results in more statistical Power.

  • Effect size. This is the difference between the true value and hypothesized value. The bigger the effect size, the easier it will be to detect it. Therefore, the power of the test increases as the effect size increases.

  • Alpha level. This is the probability of committing a Type I error (probability of rejecting the null hypothesis when it is true). If the alpha level (decision criteria) is increased, it will be more likely to reject the null hypothesis. Therefore we have less chance of committing Type II error, and by the definition, the power of the test is greater.

Supported tests

Power and sample size analysis are calculated differently for different hypothesis tests. Quantum XL supports the following tests: