Purpose
The test sensitivity is how much observable difference needs to be detected in a hypothesis test of the mean in order for an effect to be practically significant when the amount of risk for both alpha and beta has been fixed. This difference is referred to as “delta sigma”.
Anatomy
Reference: The Vision of Six Sigma
Terminology
A. (delta) - The difference in means that we want to be able to detect with the test.
B. Control Distribution - Distribution associated with the null (H0) hypothesis.
C. Confidence level: confidence that an observed outcome in the sample is “real”.
D. Contrast Distribution - Distribution associated with the alternate (Ha) hypothesis.
E. Power of the test: chance of detecting a specified change in the population with the sample if the difference is actually there to detect.
F. The difference in means that we want to be able to detect with the test expressed in standard deviation units. It is a direct measure of test sensitivity; i.e., the difference between two means expressed in standard deviation units.
By fixing this value in advance of a test, we are able to align practical significance with statistical significance. We are able to dial in the degree of change we need the hypothesis test to detect in order to proclaim that a particular effect is significant in the real world.
Should an effect not reach the prescribed value, then we would say that the effect is not influential enough to be of practical concern. Note that we would be able to make this statement with (1-beta)100 percent confidence.
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