Statistical Thinking, 3rd Edition

CHAPTER 9Applications of Statistical Inference Tools

The great tragedy of science—the slaying of a beautiful hypothesis by an ugly fact.

—Thomas Huxley

In this chapter, we return to statistical inference tools to fill in the missing pieces in the process improvement frameworks discussed in Chapter 5, as well as in our discussion of regression analysis and designed experiments. The main learning objectives for this chapter are to develop an understanding of the concepts of statistical inference and to develop functional capability to apply some of the more commonly applied inference tools. There are many potential types of confidence/prediction intervals and hypothesis tests, and we present some of the more useful and commonly applied types in this chapter. Appendix F provides summary information for several more of these tools. Note also that the underlying theory of statistical inference, such as probability distributions, will be addressed in Chapter 10.

Statistical inference essentially means drawing conclusions about a population or process based on sample data. In other words, we are inferring about the population or process rather than doing 100% sampling. Conceptually, of course, it is impossible to do 100% sampling from a process because we cannot yet sample future output of the process. We can do 100% sampling of previous output, but if we want to draw conclusions about future output, we still have to infer. In most cases, the conclusions will be obvious from simple ...