What is the main purpose of delta (δ) in hypothesis testing?

The main purpose of delta (δ) in hypothesis testing is to establish a measurement difference. In the context of hypothesis testing, delta typically represents the minimum effect size or the difference in means that researchers are interested in detecting between two groups. This is particularly relevant in tests of significance where the null hypothesis posits that there is no effect or no difference. By defining delta, researchers set a benchmark for the smallest difference that would be considered practically significant, allowing them to assess whether the evidence collected from their sample is sufficient to reject the null hypothesis in favor of an alternative hypothesis that suggests the presence of a significant difference. Establishing this measurement difference is crucial for determining the power of the test, as it helps define the sensitivity of the test to detect the effect of interest.