Hypothesis Testing

Reporting Format for Hypothesis Testing

Hypothesis testing is a powerful way to analyze data. But to make the most progress, a Six Sigma team must not only be able to perform a hypothesis test, it must also be aware of the test’s limits of practical significance. Two groups of stakeholders are involved with the results of statistical analysis. The team’s need…


Hypothesis Testing: Fear No More

When analyzing data as part of a Lean Six Sigma project, some Belts can become confused to the point of fear when their coach tells them they need to perform a hypothesis test. This fear often comes from two sources: 1) the selection of the appropriate hypothesis test and 2) the interpretation of the results….


Making Sense of the Two-Proportions Test

Consider a production process that produced 10,000 widgets in January and experienced a total of 100 rejected widgets after a quality control inspection (i.e., failure rate = 0.01, success rate = 0.99). A Six Sigma project was deployed to fix this problem and by March the improvement plan was in place. In April, the process…

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Making Sense of the Two-Sample T-Test

The two-sample t-test is one of the most commonly used hypothesis tests in Six Sigma work. It is applied to compare whether the average difference between two groups is really significant or if it is due instead to random chance. It helps to answer questions like whether the average success rate is higher after implementing…


Understanding the Uses for Mood’s Median Test

When comparing the average of two or more groups with the help of hypothesis tests, the assumption is that the data is a sample from a normally distributed population. That is why hypothesis tests such as the t-test, paired t-test and analysis of variance (ANOVA) are also called parametric tests. Nonparametric tests do not make…


Rejected! The Ugly Truth About Hypothesis Testing

You’ve got data. You’ve got a hypothesis. You’ve got Minitab… but you don’t have statistical significance at a p-value equal to or less than 0.05. You must have missed the critical Xs in the Define phase, right? It’s time to go figure out what variables you missed and collect more expensive, time-consuming and team-irritating data,…

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Using the 1-Sample Sign Test for Paired Data

The paired t-test is used to check whether the average differences between two samples are significant or due only to random chance. In contrast with the “normal” t-test, the samples from the two groups are paired, which means that there is a dependency between them. The following example illustrates the difference between the regular t-test…

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Making Sense of Mann-Whitney Test for Median Comparison

When conducting the 2-sample t-test to compare the average of two groups, the data in both groups must be sampled from a normally distributed population. If that assumption does not hold, the nonparametric Mann-Whitney test is a better safeguard against drawing wrong conclusions. The Mann-Whitney test compares the medians from two populations and works when…


Nonparametric: Distribution-Free, Not Assumption-Free

Nonparametric or distribution-free methods have several advantages or benefits. They may be used on all types of data including nominal, ordinal, interval and ratio scaled. They make fewer and less stringent assumptions than their parametric counterparts. Depending on the particular procedure, nonparametric methods may be almost as powerful as the corresponding parametric procedure when the…


A Solution Template to Help in Hypothesis Testing

One of the most difficult topics for those learning how to use statistics is hypothesis testing. Solving a number of examples will help convince potential and new Six Sigma practitioners of the importance of the concepts behind this tool. However, the necessary steps and their formulation take some additional effort. An appropriately designed solution template…


Using Efficient Process Tolerance and Mean Shift Tests

The sequential probability ratio test, or SPRT, can be used as an efficient tool for process tolerance and mean shift determinations. It also provides for simplifying insights into the nature of random mean shifts when process tolerances and Type I/II errors are selected. The cumulative sum design of the test naturally compensates for random errors,…