Page 77 - Statistics for Dummies

Chapter 4: Tools of the Trade
A variety of hypothesis tests are done in scientific research, including t-tests
(comparing two population means), paired t-tests (looking at before/after
data), and tests of claims made about proportions or means for one or more
populations. For specifics on these hypothesis tests, see Chapter 15.
p-values
Hypothesis tests are used to test the validity of a claim that is made about a
population. This claim that’s on trial, in essence, is called the null hypothesis.
The alternative hypothesis is the one you would believe if the null hypothesis
is concluded to be untrue. The evidence in the trial is your data and the sta-
tistics that go along with it. All hypothesis tests ultimately use a p-value to
weigh the strength of the evidence (what the data are telling you about the
population). The p-value is a number between 0 and 1 and interpreted in the
following way:
✓ A small p-value (typically ≤ 0.05) indicates strong evidence against the 61
null hypothesis, so you reject it.
✓ A large p-value (> 0.05) indicates weak evidence against the null hypoth-
esis, so you fail to reject it.
✓ p-values very close to the cutoff (0.05) are considered to be marginal
(could go either way). Always report the p-value so your readers can
draw their own conclusions.
For example, suppose a pizza place claims their delivery times are 30 minutes
or less on average but you think it’s more than that. You conduct a hypothesis
test because you believe the null hypothesis, H , that the mean delivery time
o
is 30 minutes max, is incorrect. Your alternative hypothesis (H ) is that the
a
mean time is greater than 30 minutes. You randomly sample some delivery
times and run the data through the hypothesis test, and your p-value turns out
to be 0.001, which is much less than 0.05. You conclude that the pizza place
is wrong; their delivery times are in fact more than 30 minutes on average,
and you want to know what they’re gonna do about it! (Of course you could
be wrong by having sampled an unusually high number of late pizzas just by
chance; but whose side am I on?) For more on p-values, head to Chapter 14.
Statistical significance
Whenever data are collected to perform a hypothesis test, the researcher is
typically looking for something out of the ordinary. (Unfortunately, research
that simply confirms something that was already well known doesn’t make

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