# Control Charts. An Introduction to Statistical Quality by Edward S. Smith

By Edward S. Smith

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Statistics helps in thinking about alternative methods of measuring a quantity. When introducing a new apparatus or new technique to measure a quantity of interest, validation against the old method is useful. In considering subjective ratings by different people (even when the subjective rating is given as a numerical scale), it often turns out that a quantity is not measured in the same fashion if the measurement method is changed. A new laboratory apparatus may measure consistently higher than an old one.

There would then be an investigation in the human population to see whether the assumption is valid. The results of an observational study carried out in one country may be extended to other countries. This is not always appropriate. Much of the “bread and butter” of epidemiology consists of noting that the same risk factor seems to produce different results in different populations, or in noting that the particular endpoint of a disease occurs with differing rates in different countries. There has been considerable advance in medical science by noting different responses among different populations.

2 Graphs Graphical displays frequently provide very effective descriptions of samples. In this section we discuss some very common ways of doing this and close with some examples that are innovative. Graphs can also be used to enhance certain features of data as well as to distort them. A good discussion can be found in Huff [1993]. One of the most common ways of describing a sample pictorially is to plot on one axis values of the variable and on another axis the frequency of occurrence of a value or a measure related to it.