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Chapter 3: Building Confidence and Testing Models
Determining strength of
evidence with a p-value
If you want to know whether your data has the brawn to stand up against Ho,
you want to figure out the p-value and compare it to a prespecified cutoff, α
(typically 0.05). The p-value is a measure of the strength of your evidence
against Ho. You can calculate the p-value by doing the following:
1. Calculate the test statistic. See the preceding section for more info
on this.
2. Look up the test statistic on the appropriate table (such as the t-table,
A-1 in the Appendix).
3. Find the percentage of values on the table that fall beyond your test
statistic. This percentage is the p-value.
Suppose you’re conducting a hypothesis test and have already decided you 59
will reject Ho at level α = 0.05. You collect your data and find the test statistic
(see preceding section). If your test statistic is extremely high or extremely
low compared to other values on the table (whatever that table is), then you
reject Ho.
For example, say the cutoff value for rejecting Ho at a level α = 0.05 is 1.645,
where you’re testing for the mean of one population. If you get a test statistic
of 1.7, you reject Ho. If you get a test statistic of 2.7, you really reject Ho. That
is, you have more evidence against Ho with a test statistic of 2.7 than with a
test statistic of 1.7. The two p-values of 1.7 and 2.7 are what statisticians call
marginally significant and highly significant results respectively, to use proper
terms.
Your friend, α, is the cutoff for your p-value — and the star of this chapter.
(α is typically set at 0.05 — sometimes 0.10.) If your p-value is less than your
predetermined value of α, reject Ho, because you have sufficient evidence
against it. If your p-value is greater than or equal to α, you can’t reject Ho.
For example, if your p-value is 0.002, then your test statistic is so far away
from Ho that the chance of getting this result only by chance is only 2 out
of 1,000. So, you conclude that Ho is very likely to be false. However, if your
p-value turns out to be 0.30, then this result happens 30 percent of the time
anyway, so you see no red flags there, and you can’t reject Ho. You don’t have
enough evidence against it. It doesn’t mean Ho is true, but you don’t have the
evidence to say it’s false — a subtle, but important, difference.
When I compare the p-value to the α (the cutoff value), I like to think of a foot-
ball analogy, assuming that Ho is “the opposing team can’t make a touch-
down.” The burden is on the other team to show enough evidence to reject