Page 238 - Statistics for Dummies

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Part IV: Guesstimating and Hypothesizing with Confidence
Calculating a p-value
To find the p-value for your test statistic:
1. Look up your test statistic on the appropriate distribution — in this

case, on the standard normal (Z-) distribution (see the Z-table in the
appendix).
2. Find the chance that Z is beyond (more extreme than) your test statistic:

If H contains a less-than alternative, find the probability that Z is
•
a
less than your test statistic (that is, look up your test statistic on the
Z-table and find its corresponding probability). This is the p-value.
• If H contains a greater-than alternative, find the probability that
a
Z is greater than your test statistic (look up your test statistic on
the Z-table, find its corresponding probability, and subtract it from
one). The result is your p-value.
• If H contains a non-equal-to alternative, find the probability that Z
a
is beyond your test statistic and double it. There are two cases:
If your test statistic is negative, first find the probability that Z
is less than your test statistic (look up your test statistic on the
Z-table and find its corresponding probability). Then double this
probability to get the p-value.
If your test statistic is positive, first find the probability that Z is
greater than your test statistic (look up your test statistic on the
Z-table, find its corresponding probability, and subtract it from
one). Then double this result to get the p-value.
Why do you double the probabilities if your H contains a non-equal-to
a
alternative? Think of the not-equal-to alternative as the combination of the
greater-than alternative and the less-than alternative. If you’ve got a positive
test statistic, its p-value only accounts for the greater-than portion of the not-
equal-to alternative; double it to account for the less-than portion. (The dou-
bling of one p-value is possible because the Z-distribution is symmetric.)
Similarly, if you’ve got a negative test statistic, its p-value only accounts for
the less-than portion of the not-equal-to alternative; double it to also account
for the greater-than portion.
When testing H : p = 0.25 versus H : p < 0.25 in the varicose veins example
o a
from the previous section, the p-value turns out to be 0.1056. This is because
the test statistic (calculated in the previous section) was –1.25, and when you
look this number up on the Z-table (in the appendix) you find a probability
of 0.1056 of being less than this value. If you had been testing the two-sided
alternative, H : p ≠ 0.25, the p-value would be 2 ∗ 0.1056, or 0.2112.
a
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