How to Test Hypotheses
This lesson describes a general procedure that can be used to test
statistical hypotheses.
How to Conduct Hypothesis Tests
All hypothesis tests are conducted the same way. The
researcher states a hypothesis to be tested, formulates an
analysis plan, analyzes sample data according to the plan,
and accepts or rejects the null hypothesis, based on results
of the analysis.
- State the hypotheses. Every hypothesis test requires the analyst
to state a
null hypothesis
and an
alternative hypothesis. The hypotheses are stated in such
a way that they are mutually exclusive. That is, if one is
true, the other must be false; and vice versa.
- Formulate an analysis plan. The analysis plan describes
how to use sample data to accept or reject the null
hypothesis. It should specify the following elements.
- Significance level. Often, researchers choose
significance levels
equal to
0.01, 0.05, or 0.10; but any value between 0 and
1 can be used.
- Test method. Typically, the test method involves a
test statistic and a
sampling distribution.
Computed from sample data, the test
statistic might be a mean score, proportion,
difference between means, difference between proportions,
z-score, t statistic, chi-square, etc. Given a test statistic
and its sampling distribution, a researcher can
assess probabilities associated with the test
statistic. If the test statistic probability is less
than the significance level, the null hypothesis is
rejected.
- Analyze sample data. Using sample data, perform computations
called for in the analysis plan.
- Interpret the results. If the sample findings are unlikely, given
the null hypothesis, the researcher rejects the null hypothesis.
Typically, this involves comparing the P-value to the
significance level,
and rejecting the null hypothesis when the P-value is less than
the significance level.
Applications of the General Hypothesis Testing Procedure
The next few lessons show how to apply the general hypothesis testing
procedure to different kinds of statistical problems.
At this point, don't worry if the general procedure for testing hypotheses seems
a little bit unclear. The procedure will be clearer after you read through a
few of the examples presented in subsequent lessons.
Test Your Understanding
Problem 1
In hypothesis testing, which of the following statements is
always true?
I. The P-value is greater than the significance level.
II. The P-value is computed from the significance level.
III. The P-value is the parameter in the null hypothesis.
IV. The P-value is a test statistic.
V. The P-value is a probability.
(A) I only
(B) II only
(C) III only
(D) IV only
(E) V only
Solution
The correct answer is (E). The P-value is the probability of
observing a sample statistic as extreme as the test statistic.
It can be greater than the significance level, but it can also be
smaller than the significance level. It is not computed from
the significance level, it is not the parameter in the null hypothesis,
and it is not a test statistic.