BHS 307 Statistics for the Behavioral Sciences

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BHS 307 Statistics for the Behavioral Sciences

• Chapter 11 More About Hypothesis Testing

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Why Hypothesis Tests?

• The first step in any study is to test against
  chance.
• We cannot draw any conclusions about our results
  without making sure our results are not
  accidental.
• We never know for sure what the true situation
  is, but we try to minimize possibility of error.

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Hypothesis Test Outcomes

• A hypothesis test has four possible outcomes
• H0 is true and H0 is retained a correct
  decision.
• H0 is true but H0 is rejected a Type I error
  (false alarm).
• H1 is true and H0 is rejected (H1 is retained)
  a correct decision.
• H1 is true but H1 is rejected and H0 is retained
  a Type II error (miss).

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Strong and Weak Decisions

• Retaining the null hypothesis (H0) is a weak
  decision because it is ambiguous and
  uninformative.
• H0 could be true but is not probably true.
• Rejecting the null hypothesis is a strong
  decision because it implies that H0 is probably
  false.

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Decisions are Usually Correct

• We never actually know what is true, H0 or H1.
• Our test procedure produces a result that is
  usually correct when H0 is either true or
  seriously false.
• Type I error rejecting a true null hypothesis.
• Type II error retaining a false null hypothesis.

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Probabilities of Error

• Probability of a Type I error is a.
• Most of the time a .05
• A correct decision exists .95 of the time (1- .05
  .95).
• Probability of a Type II error is b.
• When there is a large effect, b is very small.
• When there is a small effect, b can be large,
  making a Type II error likely.

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Influence of Sample Size

• Increasing the sample size decreases the standard
  error of the mean sx.
• A smaller standard error results in less overlap
  between true and hypothesized distributions.
• Both distributions shrink toward their true
  means.
• To reduce the possibility of Type II error,
  increase the sample size.

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Sample Sizes

• Too large may produce an extra sensitive test
  that detects very small, unimportant effects.
• Too small produces an insensitive test that
  will miss even a very large, important effect.
• Sizes in the 100s are too large, less 5 is too
  small.

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Power Curves

• Power equals the probability of detecting an
  effect.
• Power 1 - b
• Power curves show how power varies with sample
  size.
• They do not predict the true effect size but
  specify what sample size will show an effect if
  it is present.
• A way around arbitrary sample sizes.

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One-Tailed Two-Tailed Tests

• Two-tailed tests (nondirectional) divide the
  probability of error (a) between the two tails.
• Expressed using equality signs.
• One-tailed tests (directional) place all of the
  probability of error in a single tail in the
  direction of interest.
• Expressed using inequality signs (lt, gt)

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Deciding Which to Use

• When identifying the type of test in an exam
  question or report
• If the null hypothesis is expressed using
  inequalities, it is directional.
• When choosing a test-type during research
• Use a non-directional (two-tailed) test unless
  you have a strong reason to do otherwise.