From the course: Six Sigma: Green Belt

Tests for means

From the course: Six Sigma: Green Belt

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Tests for means

- In your Six Sigma projects, you may need to test for differences in means. For example, you want to test the theory that the mean delivery time from one pizza restaurant is more than 20 minutes. And, you are interested in testing the theory that mean delivery times are different across restaurants in your pizza chain. Let's take a look at the tests needed to compare means. To start, let's compare the mean of one group to a target. Which is also known as the One Sample T-test. For example, we want to determine if, in the long run, the mean processing time of group A is more than the target mean of 20 minutes. Here's a dotplot of the sample data. If the data is normal, use the One Sample T-Test. A normality tests, such as the Anderson-Darling test can be run to determine normality. The One Sample T-Test requires normal data. Here are the generic, null and alternate hypothesis when comparing the population mean of one group to the target. If the practical theory is that the mean delivery time is not equal to 20 minutes, then the null hypothesis is, population mean is equal to 20, and alternate hypothesis is not equal to 20. If the practical theory is that the population mean is less than 20, then the alternate hypothesis uses the less than sign. Similarly, to prove that the mean is more than 20, then the alternate hypothesis uses the greater than sign. Basically, what you want to prove is stated as the alternate hypothesis. The null hypothesis is a statement of no difference or null difference, hence the term null hypothesis. Running a One Sample T-Test with the help of software returns a P value of 0.0001. Assuming our value was set at 0.05, this p value is less than alpha. So the conclusion is reject the null hypothesis. Translating that particle conclusion, the mean delivery time is significantly different from 20 minutes. What if you want to compare the means of two groups? If the data is normally distributed, use a Two Sample T-Test. Here are the generic hypothesis for our Two Sample T-Test. The difference value can be zero, or some other number. For example, if the theory is that the difference in mean delivery times between two restaurants is 10 minutes, then 10 is the difference value. Say you want to compare the mean processing times of two groups, A and B. Here are the dotplots of sample data of their delivery times. To test the theory that the population means of these two groups are different, the hypothesis are shown here. Using alpha equals 0.05, a Two Sample T-Test using software such as Minitab returns a P value of 0.0088. Since it is less than the alpha value of 0.05, reject the null hypothesis. When you translate this into a practical conclusion, the population mean delivery times of A and B are different. Now let's compare the means of more than two groups. Here are the dotplots and boxplots of delivery times samples from four restaurants. The particle theory is, are population mean delivery times difference across these pizza restaurants? In general, the hypotheses for comparing the means of more than two groups are written as shown here. Translated into statistical terms, the null hypothesis is that there is no difference in the population means. And the alternate hypothesis is, at least one is different. Assuming the data follows a normal distribution, and the variances are equal, the appropriate test is ANOVA. In Six Sigma projects, software such as Minitab is used to run all these analysis. After running the test, the output is the ANOVA table. It returns a P value of 0.0047. Since it is less than alpha, assuming alpha 0.05, the conclusion is, reject the null hypothesis. Remember, when the P value is low, the null must go. So the practical conclusion is, the mean delivery times are different across those four restaurants. The next time you want to test the theory that the mean delivery times among your pizza restaurants are different, you can use ANOVA. If comparing one restaurant to a target, use the One Sample T-Test. And for comparing two restaurants, use the Two Sample T-Test. For more details on running the analysis shown in this video check out my course, Introduction to Minitab.

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