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Part IV: Guesstimating and Hypothesizing with Confidence
accurate. To avoid bias when selecting a sample, make it a random sample
(one that’s got the same chance of being selected as every other possible
sample of the same size) and choose a large enough sample size so that the
results will be accurate. (See Chapter 11 for more information on accuracy.)
Data is collected in many different ways, but the methods used basically boil
down to two: surveys (observational studies) and experiments (controlled
studies). Chapter 16 gives all the information you need to design and critique
surveys, as well as information on selecting samples properly. In Chapter 17,
you examine experiments: what they can do beyond an observational study, the
criteria for a good experiment, and when you can conclude cause and effect.
Compiling the Evidence: The Test Statistic
After you select your sample, the appropriate number-crunching takes
place. Your null hypothesis (H ) makes a statement about the population
o
parameter — for example, “The proportion of all women who have varicose
veins is 0.25” (in other words, H : p = 0.25); or the average miles per gallon of
o
a U.S.-built light truck is 27 (H : μ = 27). The data you collect from the sample
o
measures the variable of interest, and the statistics that you calculate will
help you test the claim about the population parameter.
Gathering sample statistics
Say you’re testing a claim about the proportion of women with varicose veins.
You need to calculate the proportion of women in your sample who have
varicose veins, and that number will be your sample statistic. If you’re testing
a claim about the average miles per gallon of a U.S.-built light truck, your
statistic will be the average miles per gallon of the light trucks in your sample.
And knowing you want to measure the variability in average miles per gallon
for various trucks, you’ll want to calculate the sample standard deviation. (See
Chapter 5 for all the information you need on calculating sample statistics.)
Measuring variability using standard errors
After you’ve calculated all the necessary sample statistics, you may think you’re
done with the analysis part and ready to make your conclusions — but you’re
not. The problem is you have no way to put your results into any kind of
perspective just by looking at them in their regular units. That’s because you
know that your results are based only on a sample and that sample results are
going to vary. That variation needs to be taken into account, or your conclusions
could be completely wrong. (How much do sample results vary? Sample
variation is measured by the standard error; see Chapter 11 for more on this.)

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