Category: Hypothesis Testing

You have compared your process data before and after an improvement. Is the difference real or just noise?  Statistical significance will help you answer that question.

You may think turnaround time has decreased from your baseline as a result of a process improvement. But has it really? The t statistic is one way to find the answer to that question.

You have retrofitted your major production machine to make it run faster. Did the retrofit really improve machine speed? A 2-Sample t-Test can be used to answer that question. 

Some say that Z is the sign of Zorro (Spanish for fox), the fictional sword wielding masked vigilante who defended and helped the poor. In statistics, it is something different. In statistics, z usually refers to the standardized score or z-score of a data point in a normal distribution. The z-score measures the number of […]

Is there a real difference between machines? Did what I changed really help? Does a relationship really exist between temperature and pressure? The answers to these questions and others can be provided by the p-value.

Hypothesis testing is a branch of statistics in which, using data from a sample, an inference is made about a population parameter or a population probability distribution.

Is there a relationship between wearing your seatbelt and whether or not you survive an auto accident? Is there a relationship between studying and whether you pass an exam? These are the types of questions a Chi-Square Test can answer.

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 […]

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. […]

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 […]

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 […]

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 […]

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, […]

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 […]

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 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 […]

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 […]

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, […]

The power of the test is the measure of how good a hypothesis test is. A “good” test should reject a null hypothesis when it is false and accept it when it is true.