We have organized the chapter so that the basic concepts are presented ﬁrst and the more complicated concepts that require an understanding of the more basic concepts are presented afterwards. This will allow us to introduce most of the basic statistical terminology used in the rest of the book. But it will mean presenting these topics out of order compared to theorder they are done in a statistical study. These four topics relate to one another as follows: We need to measure the world to get numbers that tell us the details and then do statistical analysis to convert those details into general descriptions. In doing both measurement and analysis, we inevitably encounter error. The practice of statistics involves both the acknowledgment that error isunavoidable and the use of techniques to deal with error. Sampling is a key theoretical notion in understanding how measurements relate to the world and why error is inevitable.
What Is Statistics?
We have learned what it is that statistics does, now we need to ﬁnd out a bit about how it works. How do statistical measures describe general facts about the world? How do they helpus make inferences and decisions? There is a general logic to how statistics works and that is what we will learn about here. There will be no equations in this chapter, but we will introduce and deﬁne important technical terms.
Statistics is not a form of mathematics. The most important diﬀerence is that statistics is explicitly tied to the world. That tie is the process ofmeasurement.
WHAT IS MEASUREMENT?
The ﬁrst and most fundamental concept in statistics is the concept of measurement. Measurement is the process by which we examine the world and end up with a description (usually a number) of some aspect of the world. The results of measurement are speciﬁc descriptions of the world. They are the ﬁrst step in doing statistics, which results in general descriptions ofthe world. Measurement is a formalized version of observation, which is how we all ﬁnd out about the world every day. Measurement is diﬀerent from ordinary day-to-day observation because the procedures we use to observe and record the results are speciﬁed so that the observation can be repeated the same way over and over again. When we measure someone’s height, we take a look at a person; apply aspeciﬁc procedure involving (perhaps) a measuring tape, a pencil, and a part of the wall; and record the number that results. Let’s suppose that we measure Judy’s height and that Judy is ‘‘ﬁve foot two.’’ We record the number 62, measured in inches. That number does not tell us a lot about Judy. It just tells us about one aspect of Judy, her height. In fact, it just tells us about her height onthat one occasion. (A few years earlier, she might have been shorter.)
Use the deﬁnition sidebars and the quizzes to memorize the meaning of the technical terms in this chapter. The more familiar and comfortable you are with the terminology, the easier it will be to learn statistics.
This chapter will cover four very important topics: measurement, error, sampling, andanalysis. Sampling, measurement, and analysis are the ﬁrst three steps in doing statistics. First, we pick what we are going to measure, then we measure it, then we calculate the statistics.
PART ONE What Is Business Statistics?
Statistics uses the algebraic devices of variables and values to deal withmeasurements mathematically. In statistics, a variable matches up to some aspect of the thing being measured. In the example above, the variable is height. The value is the particular number resulting from the measurement on this occasion. In this case, the value is 62. The person who is the subject of the measurement has many attributes we could measure and many others we cannot. Statisticians...