**11 ONE-WAY ANALYSIS OF VARIANCE (ANOVA)
**The 11th Minitab tutorial is about the ball bearings used by Smartboard Company for skateboard wheels. An important criterion for the fit is the outer diameter of the ball bearings. Smartboard Company compares three new ball bearing suppliers for this purpose. This training session focuses on the question of, whether the outer diameters of the ball bearings from the three suppliers differ significantly from one another. We will see that the special feature of this task is, that we are now dealing with more than two processes, or more than two sample averages, and therefore the hypothesis tests we have learned so far will not help. Before we start with the actual analysis of variance – often abbreviated to the acronym ANOVA, we will first use descriptive statistics in this Minitab tutorial to get an overview of the location and dispersion parameters of our three supplier data sets. Before starting the actual analysis of variance, a discriminatory power analysis must be carried out to determine the appropriate sample size. In order to understand the principle of variance analysis. For didactic reasons we will first get to know the relatively complex variance analysis step by step on a generally small data set and then use this preliminary work and information to enter into the so-called one-way analysis of variance, which is often referred to as one-way ANOVA, in day-to-day business. So that we can use this analysis approach to determine the corresponding scatter proportions that make up the respective total scatter. We will take a closer look at the ratio of these scatter proportions by using the so-called F-distribution, in reference to its developer, Sir Ronald Fisher. We will learn how to use the F-distribution to determine the probability of a scattering ratio occurring, simply called the F-value. For a better understanding, we will also use the graphical method to derive the p-value for the respective F-value. In the final step, the associated hypothesis tests are used to properly determine whether there are significant differences between the ball bearing suppliers. Interesting and very useful in the context of this one-way analysis of variance, are the so-called grouping letters, generated with the help of the Fisher pairwise comparison test, which will always help us very quickly in our day-to-day business to recognize which ball bearing manufacturers differ significantly from each other.

MAIN TOPICS MINITAB TUTORIAL 11

- Setting up the hypothesis tests as part of the one-way ANOVA
- Adj SS and Adj MS values within the framework of the one-factorial ANOVA
- Derivation of the F-value within the framework of the one-factorial ANOVA
- Derivation of the F-distribution within the framework of the one-factorial ANOVA
- Error bar chart as part of the one-way ANOVA
- Pair difference test according to Fisher
- Interpretation of the grouping letters based on the Fisher LSD method
- Interpretation of the Fisher individual test for differences of mean