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The statistical procedures developed in Chapters 2 to 4 are appropriate for analyzing the results of experiments in which the variable of interest is measured on an interval scale, such as blood pressure, urine production, or length of hospital stay. Much of the information physicians, nurses, other health professionals, and medical scientists use cannot be measured on interval scales. For example, an individual may be male or female, dead or alive, or Caucasian, African American, Hispanic, or Asian. These variables are measured on nominal scales, in which there is no arithmetic relationship between the different classifications. We now develop the statistical tools necessary to describe and analyze such information.

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It is easy to describe things measured on a nominal scale: simply count the number of patients or experimental subjects with each condition and (perhaps) compute the corresponding percentages.

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For example, John Song and colleagues* wanted to study whether or not providing homeless people with personal counseling on end-of-life care and advanced directives would lead more of them to complete such directives. (This question had been studied among insured general adult populations, but not among the homeless, who have more health problems and less access to stable health care relationships.) To investigate this question, they recruited people at emergency night shelters, 24-hour shelters, a day program and treatment programs. They conducted an experiment in which volunteers were randomly assigned to either receive written material on advance directives or invited to attend a 1-hour in-person counseling session on advance directives. The outcome of the study was whether the people returned a completed advance directive within 3 months. Among the 262 people who participated in the study 37.9% of the people who received the in-person counseling returned the advanced directives within 3 months, compared with 12.8% of the people who were just given written instructions. Is this difference likely to be a real effect of the counseling or simply a reflection of random sampling variation?

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To answer this and other questions about nominal data, we must first invent a way to estimate the precision with which percentages based on limited samples approximate the true rates that would be observed if we could examine the entire population, in this case, all homeless people. We will use these estimates to construct statistical procedures to test hypotheses.

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*Song J, Ratner ER, Wall HM, Bartels DM, Ulvestad N, Petroskas D, West M, Weber-Main AM, Grengs L, Gelberg L. Effect of an end-of life planning intervention on the completion of advance directives in homeless persons. Ann Intern Med. 2010;153:76–84.

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Before we can quantify the certainty of our descriptions of a population on the basis of a limited sample, we need to know how to describe the population itself. Since we have already visited Mars and met all 200 Martians (in Chapter 2), we will continue to use them to develop ways to describe populations. In addition to measuring the ...

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