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A - 1 APPENDIX A BASIC STATISTICAL TECHNIQUES Much of biology involves gathering and interpreting quantitative data. Biological numbers may be interesting in themselves (house mice seldom live more than 4 months), but they usually mean more in some comparative context (by contrast, little brown bats often live 30 years). Sometimes results are anything but clear-cut. If 6 out of 10 diseased mice lived after receiving a drug, but 4 out of 10 lived without receiving the drug, was the drug a significant help or was the difference in survival rate just due to chance? Statistical techniques allow biologists to describe what they observe in a quantitative way, and to decide whether their results really mean something. Two general types of statistics are descriptive statistics and test statistics . DESCRIPTIVE STATISTICS Descriptive statistics are numbers that describe a set of data. The most common descriptive statistics we’ll use for a set of data are the mean and standard deviation . The mean , a very familiar statistic, is the average of all the data observed. If we wanted to know what a typical gorilla weighs, we can take the mean of many observed weights. mean weight of gorillas = (sum of all observed weights) / number of gorillas or, expressed mathematically where x (on the left) is the mean, x i refers to each gorilla weight, n is the number of gorillas, and is a summation sign meaning to add up all the weights. The mean conveys only a limited picture of gorilla weights, however. Do all gorillas weigh about the same, or is there a tremendous variation in weights? The standard deviation is a statistic that expresses how "spread out" the data are. The calculation we use for standard deviation is:
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A - 2 standard deviation (S.D.) = where the symbols are the same as for the mean, and x is the mean of all x values. If the standard deviation is small, the data are very clumped (all gorillas weigh about the same, close to the mean). If standard deviation is large, the data have a large spread (even though we know the mean weight of a gorilla, any particular gorilla might weigh much less or much more). Reporting the standard deviation of the data along with the mean gives a more informative picture than reporting the mean alone. You can calculate both statistics by using the formulas given above, but once you understand what you are doing it will save time to use the scientific calculator functions or spreadsheet functions for these statistics. TEST STATISTICS Test statistics are numbers derived from the data that can be used to test a particular hypothesis. In the example in the first paragraph, we might want to test the hypothesis that the drug helped mice survive. The main kinds of questions that test statistics help to answer are "Are the two groups significantly different?" and "Are the results significantly different from what I predicted?" In a statistical context, the term " significant " has a special meaning that is precisely defined. To understand its basis, consider an example. Let's say you think that about 20 percent of people are left-handed.
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