Page 235 - Statistics for Dummies

Chapter 14: Claims, Tests, and Conclusions
Suppose the claim is that the percentage of all women with varicose veins
is 25%, and your sample of 100 women had 20% with varicose veins. The
standard error for your sample percentage is 4% (according to formulas in
Chapter 11), which means that your results are expected to vary by about
twice that, or about 8%, according to the Empirical Rule (see Chapter 12). So
a difference of 5%, for example, between the claim and your sample result
(25% – 20% = 5%) isn’t that much, in these terms, because it represents a
distance of less than 2 standard errors away from the claim.
However, suppose your sample percentage was based on a sample of 1,000
women, not 100. This decreases the amount by which you expect your
results to vary, because you have more information. Again using formulas
from Chapter 11, I calculate the standard error to be 0.013 or 1.3%. The
margin of error (MOE) is about twice that, or 2.6% on either side. Now a dif-
ference of 5% between your sample result (20%) and the claim in H (25%) is
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a more meaningful difference; it’s way more than 2 standard errors.
Exactly how meaningful are your results? In the next section, you get more 219
specific about measuring exactly how far apart your sample results are from
the claim in terms of the number of standard errors. This leads you to a spe-
cific conclusion as to how much evidence you have against the claim in H .
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Understanding standard scores
The number of standard errors that a statistic lies above or below the mean
is called a standard score (for example, a z-value is a type of standard score;
see Chapter 9). In order to interpret your statistic, you need to convert it from
original units to a standard score. When finding a standard score, you take
your statistic, subtract the mean, and divide the result by the standard error.
In the case of hypothesis tests, you use the value in H as the mean. (That’s
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what you go with unless/until you have enough evidence against it.) The
standardized version of your statistic is called a test statistic, and it’s the main
component of a hypothesis test. (Chapter 15 contains the formulas for the
most common hypothesis tests.)
Calculating and interpreting
the test statistic
The general procedure for converting a statistic to a test statistic (standard
score) is as follows:
1. Take your statistic minus the claimed value (the number stated in H ).
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