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Simple Tests of Relationships (Nonparametric Statistics): Laku.com belanja online grosir eceran murah dan aman
Much of the information you will need in attending to the public’s business is unique—it depends on the individual characteristics of a specific situation. You might want to know whether a proposed construction is fifty feet from the lot line, or if someone’s dog is barking outside at night, or whether your assistant is going to get that report to the committee on time for Monday’s meeting. You don’t need fancy quantitative analysis for situations like these; the facts speak for themselves. While the solution may be far from straightforward, the problem at least can be described fairly simply.

Some problems are not so simply described. It might seem that one neighborhood in the city is getting “run down.” You seem to have noticed more houses needing paint—but how many more? And is that “enough” to mean that there is a problem? Or you might wonder if the population in the region is getting older—maybe it seems that you are seeing fewer babies around lately. Both of these situations cannot be satisfactorily described by simple observation, because the really interesting information is what is going on between the observations or what is going on beyond the scope of any single observation.

Fortunately (or unfortunately, if you prefer the simple life), there are tools which can be used to summarize a large body of observations and which can be used to compare these summaries to other, similar summaries. You are probably already familiar with some of them, like “average” and “correlation” (as in, “there is a relationship between smoking and lung cancer”). Others have exotic names, like “Student’s t-Test” and “Chi-square.” All of these tools are jointly known as “statistics,” a word coined in the eighteenth century to describe information which was being collected and analyzed about affairs of state. Since then, statistics have spread to fields other than public administration, but the name remains to remind us of their importance in making sense of the public’s business. General Description

Statistical tools are grouped according to function. Some tools serve to describe a large group of information in just a few numbers. These tools are called “descriptive statistics.” Other tools tools test to see whether the information obtained is close to what should be expected. These tools are called “inductive statistics.” They have that name because they are based on inductive logic:  key terms in the formulas are derived from observation rather than deduced from a definition. In this unit, we will consider two inductive statistics (Student’s t-test and Chi-square). The next unit will be devoted to the most commonly used inductive statistics—correlation and analysis of variance. The difference between Student’s t-test and Chi-square lies in the assumptions you can make about the “true” distribution of the data. All inductive statistics work from observed data to create an estimate of the “true” or “population” distribution. Rarely will you have the luxury of actually observing the totality of the phenomenon in which you are interested; most of the time, you must settle for looking at a representative sample of the data.

Nonparametric statistics make no assumptions about the shape of the underlying distribution. Since they make fewer assumptions (they still assume the rules of probability), they can be used in more instances. There is a price to pay for the increased flexibility, however. Nonparametric statistics are also less sensitive. They are more likely than parametric statistics to overlook a small, but still significant, difference in the data. Chi-square tests whether the observed interaction between two variables could be obtained by chance from a larger population, just from knowing how many in the sample belong in the various categories of each of the variables.

Parametric statistics assume that the true distribution is “normally” distributed. The “normal” distribution is the name given to the way things distribute themselves when they are independent of each other. The sands in an hourglass come to rest in a “normal” distribution. If a test is well-constructed, scores on the test will fall into a “normal” distribution. The simplest of the parametric statistics compares an observed distribution to an ideal distribution or to another observed distribution, and tests for the fit between them. “Student’s t-Test,” a statistic you will learn in this unit, is one such tool. Since observation is based on only a sample of the entire population of events or traits, it is likely that samples drawn at different times will return slightly different observations. So it is important to know whether observed differences are small enough that they could just be due to sampling “error” (or variation), or whether the differences are large enough to justify the claim that there is a “significant” difference. In the next unit, you will learn other, even more powerful parametric statistics.

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