Industrial Statistics with Minitab

Part Two

HYPOTHESIS TESTING. COMPARISON OF TREATMENTS

Part 2 begins with two short chapters which are somewhat unique because they are not directly devoted to data analysis. Chapter 7 is about generating random numbers, which allows the resolution of problems by simulation (in that chapter we offer a simple example), and testing what would happen if data had some regularity as indicated by a specific distribution. The chapter also explains how to enter data in a patterned way, something useful when we want to identify the origin of each observation. Chapter 6 is about computing probabilities with Minitab. It finishes with an application: calculating the sigmas of a process (the famous 3.4 ppm of a Six Sigma process appears here).

The core of Part 2 is dedicated to hypothesis testing, the name given to the reasoning procedure that we follow when performing a statistical test. The skeleton of this frequently-used reasoning procedure is the following:

1. State the null hypothesis and the alternative hypothesis. The null hypothesis is considered to be true unless the data (an objective representation of reality) are in contradiction with it. We do not prove that the null hypothesis is true; the test is designed to see if we have enough evidence to reject the null hypothesis, thus assuming then the certainty of the alternative hypothesis. Imagine we have data that we think comes from a Normal distribution, but we want to be sure that these data are not in contradiction with our hypothesis ...