TESTS OF SIGNIFICANCE – MOTIVATING EXAMPLE
The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures
students’ study habits and attitude toward school. Scores range from 0 to 200. The mean
score for U.S. college students is about 115. A teacher suspects that older students have
better attitudes toward school. She gives the SSHA to an SRS of 35 students who are at
least 30 years old. The sample results are = 125.7 and
s
= 30.1. Is this good evidence
that older students, on average, have better study habits and attitudes toward school than
the typical college student?
THE MAIN CONCEPTS OF HYPOTHESIS TESTING
A statistical test begins by supposing for the sake of argument that the effect we seek is
not present. We then look for evidence against this supposition and in favor of the effect
we hope to find.
• For the null hypothesis, Ho, state a claim that we will try to find evidence against.
The null hypothesis is often a statement of "no effect" or "no difference". Nothing
special has occurred, no change has taken place -- the "status quo" hypothesis.
• The statement we hope or suspect is true instead of Ho is the alternative
hypothesis, Ha.
A significance test looks for evidence against the null hypothesis and in favor of the
alternative hypothesis. The evidence is strong if the outcome we observe would rarely
come up when the null hypothesis is true.
That is, if the sample results can easily occur when Ho is true, we attribute the relatively
small discrepancy between the null hypothesis and the sample results to chance.
If the sample results cannot easily occur when Ho is true, we explain the relatively large
discrepancy between the null hypothesis and the sample results by concluding that Ho is
not true (and so we conclude that Ha is true).
Hints: (1) The null hypothesis will always contain equality.
(2) It's often easier to write down the alternative hypothesis first.
(3) P-value helps us assess the amount of evidence the sample provides against
Ho and in favor of Ha. P-value tells us how unlikely the sample results are
when Ho is true. Very small p-values mean the sample results are very
unlikely to occur when Ho is true and therefore the evidence against Ho is
strong.
(4) Language: Based on the p-value, we either "reject Ho in favor of H1" or we
"fail to reject Ho." (Sometimes I say “retain Ho” instead of “fail to reject Ho.)
