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Part IV: Guesstimating and Hypothesizing with Confidence

2. Divide by the standard error of the statistic. (Different formulas for stan-
dard error exist for different problems; see Chapter 13 for detailed formulas
for standard error and Chapter 15 for formulas for various test statistics.)
Your test statistic represents the distance between your actual sample
results and the claimed population value, in terms of number of standard
errors. In the case of a single population mean or proportion, you know that
these standardized distances should at least have an approximate standard
normal distribution if your sample size is large enough (see Chapter 11). So,
to interpret your test statistic in these cases, you can see where it stands on
the standard normal distribution (Z-distribution).
Using the numbers from the varicose veins example in the previous sec-
tion, the test statistic is found by taking the proportion in the sample with
varicose veins, 0.20, subtracting the claimed proportion of all women with
varicose veins, 0.25, and then dividing the result by the standard error, 0.04.
These calculations give you a test statistic (standard score) of –0.05 ÷ 0.04 =
–1.25. This tells you that your sample results and the population claim in H
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are 1.25 standard errors apart; in particular, your sample results are 1.25
standard errors below the claim. Now is this enough evidence to reject the
claim? The next section addresses that issue.
Weighing the Evidence and
Making Decisions: p-Values
After you find your test statistic, you use it to make a decision about whether
to reject H . You make this decision by coming up with a number that mea-
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sures the strength of this evidence (your test statistic) against the claim in H .
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That is, how likely is it that your test statistic could have occurred while the
claim was still true? This number you calculate is called the p-value; it’s the
chance that someone could have gotten results as extreme as yours while H
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was still true. Similarly in a jury trial, the jury discusses how likely it is that all
the evidence came out the way it did assuming the defendant was innocent.
This section shows all the ins and outs of p-values, including how to calculate
them and use them to make decisions regarding H .
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Connecting test statistics and p-values
To test whether a claim in H should be rejected (after all, it’s all about H ) you
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look at your test statistic taken from your sample and see whether you have
enough evidence to reject the claim. If the test statistic is large (in either the
positive or negative directions), your data is far from the claim; the larger the
test statistic, the more evidence you have against the claim. You determine

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