BHS 307 Statistics for the Behavioral Sciences

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BHS 307 Statistics for the Behavioral Sciences

• Chapter 20 Tests for Ranked Data

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Nonparametric Tests

• A parameter is any descriptive measure of a
  population, such as a mean.
• Nonparametric tests make no assumptions about the
  form of the underlying distribution.
• Nonparametric tests are less sensitive and thus
  more susceptible to Type II error.

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When to Use Nonparametric Tests

• When the distribution is known to be non-normal.
• When a small sample (n lt 10) contains extreme
  values.
• When two or more small samples have unequal
  variances.
• When the original data consists of ranks instead
  of values.

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Mann-Whitney Test (U Test)

• The nonparametric equivalent of the independent
  group t-test.
• Hypotheses
• H0 Pop. Dist. 1 Pop. Dist. 2
• H1 Pop. Dist. 1 / Pop. Dist. 2
• The nature of the inequality is unspecified
  (e.g., central tendency, variability, shape).

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Calculating the U-Test

• Convert data in both samples to ranks.
• With ties, rank all values then give all equal
  values the mean rank.
• Add the ranks for the two groups.
• Substitute into the formula for U.
• U is the smaller of U1 and U2.
• Look up U in the U table.

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Interpretation of U

• U represents the number of times individual ranks
  in the lower group exceed those in the higher
  group.
• When all values in one group exceed those in the
  other, U will be 0.
• Reject the null (equal groups) when U is less
  than the critical U in the table.

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Directional U-Test

• Similar variance is required in order to do a
  direction U-test.
• The directional hypothesis states which group
  will exceed which
• H0 Pop Dist 1 gt Pop Dist 2
• H1 Pop Dist 1 lt Pop Dist 2
• In addition to calculating U, verify the the
  differences in mean ranks are in the predicted
  direction.

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Wilcoxon T Test

• Equivalent to paired-sample t-test but used with
  non-normal distributions and ranked data.
• Compute difference scores.
• Rank difference scores.
• Put plus ranks in one group, minus ranks in the
  other. Sum the ranks.
• Smallest value is T. Look up in T table. Reject
  null if lt than critical T.

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Kruskal-Wallis H Test

• Equivalent to one-way ANOVA for ranked data or
  non-normal distributions.
• Hypotheses
• H0 Pop A Pop B Pop C
• H1 H0 is false.
• Convert data to ranks and then use the H formula.
• With n gt 4, look up in c2 table.