Types of Hypothesis Test

Hypothesis testing is not a one-size-fits-all activity. Different types of data, distributions, and questions require different statistical tests. Selecting the right test is essential for drawing valid conclusions in the Analyze phase. The wrong test can lead to incorrect decisions, wasted effort, and misguided improvement strategies. 

Broadly, hypothesis tests fall into several categories based on the type of data and the question being asked. The first distinction is between parametric and non-parametric tests. Parametric tests assume that the data follows a specific distribution—usually normal. Non-parametric tests make fewer assumptions and are used when data is skewed, ordinal, or otherwise non-normal. 

Another key distinction is between tests of means, tests of medians, tests of proportions, and tests of variance. Each addresses a different aspect of process behavior. 

Tests of means, such as t-tests and ANOVA, evaluate whether average performance differs across groups. These are commonly used when comparing cycle times, processing durations, or measurement values. Tests of medians, such as Mann-Whitney or Mood’s Median, are used when data is non-normal or ordinal. Tests of proportions evaluate differences in defect rates or pass/fail outcomes. Tests of variance assess whether variability differs across groups, which can be critical in processes where consistency is as important as central tendency. 

Hypothesis tests also differ based on the number of samples and whether the samples are independent or paired. One-sample tests compare a sample to a known standard. Two-sample tests compare two independent groups. Paired tests compare measurements taken from the same units before and after a change. Multi-sample tests, such as ANOVA, compare three or more groups simultaneously. 

Directionality is another consideration. Two-tailed tests evaluate whether groups differ in either direction. One-tailed tests evaluate whether one group is specifically greater or less than another. While one-tailed tests can increase power, they must be justified by the practical question being asked. 

Choosing the right test requires understanding the data type, distribution, sample structure, and the practical question at hand. When you select the appropriate test, your conclusions are more reliable, your decisions are more defensible, and your improvement efforts are more focused.