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Unformatted text preview: A  1APPENDIX ABASIC STATISTICAL TECHNIQUESMuch of biology involves gathering and interpreting quantitative data. Biologicalnumbers may be interesting in themselves (house mice seldom live more than 4months), but they usually mean more in some comparative context (by contrast, littlebrown bats often live 30 years). Sometimes results are anything but clearcut. If 6out of 10 diseased mice lived after receiving a drug, but 4 out of 10 lived withoutreceiving the drug, was the drug a significant help or was the difference in survivalrate just due to chance? Statistical techniques allow biologists to describe what theyobserve in a quantitative way, and to decide whether their results really meansomething. Two general types of statistics are descriptive statisticsand teststatistics.DESCRIPTIVE STATISTICSDescriptive statisticsare numbers that describe a set of data. The most commondescriptive statistics well use for a set of data are the meanand standarddeviation.The mean, a very familiar statistic, is the average of all the data observed. If wewanted to know what a typical gorilla weighs, we can take the mean of manyobserved weights.mean weight of gorillas = (sum of all observed weights) / number of gorillasor, expressed mathematically wherex(on the left) is the mean, xirefers to each gorilla weight, nis the number ofgorillas, 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 gorillasweigh about the same, or is there a tremendous variation in weights? The standarddeviationis a statistic that expresses how "spread out" the data are. Thecalculation we use for standard deviation is:A  2standard 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 aboutthe same, close to the mean). If standard deviation is large, the data have a largespread (even though we know the mean weight of a gorilla, any particular gorillamight weigh much less or much more).Reporting the standard deviation of the data along with the mean gives a moreinformative picture than reporting the mean alone. You can calculate both statisticsby using the formulas given above, but once you understand what you are doing it willsave time to use the scientific calculator functions or spreadsheet functions for thesestatistics.TEST STATISTICSTest statisticsare numbers derived from the data that can be used to test aparticular hypothesis. In the example in the first paragraph, we might want to testthe hypothesis that the drug helped mice survive. The main kinds of questions thattest 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 preciselydefined. To understand its basis, consider an example. Let's say you think that...
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This note was uploaded on 03/10/2010 for the course MATH 202 taught by Professor Tessman during the Fall '08 term at Dickinson.
 Fall '08
 Tessman
 Logic, Statistics

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