Statistics Guide - APPENDIX A BASIC STATISTICAL TECHNIQUES...

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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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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.