Two-Sample T-Tests for Superiority by a Margin

Description:

Superiority-by-a-margin tests are used when you not only want to show that one group’s mean is higher (or lower) than another group’s mean, but you further want to show that the mean is higher (or lower) by at least a given amount.

Suppose that a test is to be conducted to determine if a new treatment improves bone density. The density realized by the current treatment is about 2.3 milligrams per centimeter, with a standard deviation of around 0.6. Clinicians decide that if the new treatment increases bone density by more than 10% (or 0.23 milligrams per centimeter), it generates a significant health benefit. They will assume a range of values for the standard deviation of the new treatment group.

The researchers would like to know the sample size needed to achieve 90% power, with an alpha-level of 0.025. They wish to compare sample size requirements when assuming the new treatment bone densities are between 2.7 and 3.3 milligrams per centimeter. It is expected that double the number of patients will be available for the current treatment, as compared to the new treatment.

The first part of the report shows the needed sample size for each parameter combination.

The sample size chart gives a visual comparison for the varying standard deviations and assumed mean differences. For example, there is a dramatic drop in sample size requirement if the new treatment bone density mean is assumed to be 2.8 rather than 2.7.