BHS 307 Statistics for the Behavioral Sciences

1
BHS 307 Statistics for the Behavioral Sciences

• Chapter 16 One and Two-Tailed Tests

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Why Do a Hypothesis Test?

• Before we can conclude anything about our study,
  we must measure the effect of chance.
• The hypothesis test rules out chance as a
  potential explanation for our results.
• It is not certain but is better than not doing a
  test at all.

3
Strong vs Weak Decisions

• H0 is retained when the observed z is a common
  event.
• Failure to reject H0 is a weak decision because
  it does not mean there is no difference.
• H0 is rejected when the observed z is a rare
  event.
• Rejection of H0 means H0 is probably false a
  strong decision.

4
Why We Test H0 not H1

• The research hypothesis (H1) lacks precision to
  be tested directly.
• The null hypothesis (H0) is a single number but
  H1 is not.
• Acceptance of H1 is supported by a strong
  decision (rejection of H0).
• A research hypothesis could still be true even if
  H0 is retained (not rejected).

5
Directional Hypotheses

• Sometimes the alternative hypothesis specifies
  the expected result.
• The population mean verbal score will be less
  than the sample mean.
• Our group will score higher than the national
  average on a spelling test.
• People in Seattle earn a higher average wage than
  people in the nation as a whole.

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One-Tailed vs Two-Tailed Tests

• In a two-tailed test, the hypotheses are
• H0 m equals 500
• H1 m does not equal 500
• In a one-tailed test, directionality is
  specified, so hypotheses are
• H0 m gt 500 m lt 500
• H1 m lt or 500 m gt or 500
• All possibilities must be covered.

7
Significance Level

• With a directional test, all of the probability
  is in one tail, not split between two.
• This makes the test more sensitive -- able to
  identify smaller differences as significant.
• Unless there is a reason not to, use a
  significance level of .05.