A difficult topic for those learning statistics is hypothesis testing. Solving several problems will convince new Six Sigma practitioners of the importance of this tool. And a solution template can ease the difficulties of the learning process.
New Belts may be anxious about using statistical tools, but the process doesn’t need to be daunting. By learning how to test for normality, select the right test and interpret its results, Belts can be prepared rather than scared.
When conducting the 2-sample t-test to compare the average of two groups, the data must be sampled from normally distributed populations. If that assumption does not hold, the nonparametric Mann-Whitney test is a better for drawing conclusions.
Use a two-proportions hypothesis test to determine whether a Six Sigma project actually improved the process. The test compares the percentages of two groups and only works when the raw data behind the percentages is available.
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.
Nonparametric methods are essential tools in the Black Belt's analytic toolbox. When appropriately applied, nonparametric methods are often more powerful than parametric methods if the assumptions for the parametric model cannot be met.
Most people use p 0.05 as the line where they reject the null in hypothesis testing. Yet p 0.05 means there is still a risk of making a false assertion five percent of the time. Correctly rejecting a null hypothesis is about more than just p-value.
By following a consistent reporting format, a Six Sigma team and its customers can better understand and explain hypothesis test results and conclusions.
The Mood's median test is used to test the equality of medians from two or more populations and holds no assumptions about specific distribution. Therefore, it provides a nonparametric alternative to the one-way ANOVA, which requires normality.
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.
Although the paired t-test will work for normally distributed sets of paired data, a nonparametric alternative must be used for non-normal data: the 1-sample sign test. This test makes it possible to compare observed and hypothesized medians.
Rejecting a null hypothesis when it is false is what every good hypothesis test should do. The “power of the test” is the measure of how good a test is. It is the probability that the test will reject Ho when in fact it is false.