non parametric tests: mann-whitney and wilcoxon

• in order to interpret the Mann-whitney test

  1. calculated value U (given to you)
  2. hypothesis (one or two tailed)
  3. experimental design
  4. critical values (given to you)
  5. level of significance (stated on stem, if not assume it's 5%)
  6. no. of participants (found on stem)
• calculated value U must be equal to or less than the critical value for the data to be significant

  therefore we can accept the alternative hypothesis and reject the null hypothesis
• calculated value U= 22 N1 = 10 N2 = 10 one tailed test 5%

  22 (calculated) < 27 (critical)

  results are significant as the calculated value of U (22) is lower than the critical value of U (27). therefore the null hypothesis can be rejected
• calculated value U = 18 N1 = 8 N2 = 8 two tailed test 5%

  18 (calculated) > 13 (critical)

  results are not significant as the calculated value of U = 18 is higher than the critical value of U (13). therefore the null hypothesis can be accepted
• calculated value U = 37 N1 = 12 N2 = 13 two tailed test 5%

  37 (calculated) < 41 (critical)

  results are significant as the calculated value of U (37) is lower than the critical value of U (41). therefore the null hypothesis can be rejected
• to interpret wilcoxon test

  • calculated value (given to you)
  • hypothesis, one or two tailed
  • experimental design
  • critical values table (given to you)
  • level of significance (if not given, assume its 5%)
  • no. of participants (found on stem)
• explain whether or not the result is significant (wilcoxon)

  since the calculated value 22 is less than the critical value 25, the result is significant at the 0.05 level

  this indicates that the anger management program had a statistically significant effect on reducing anger scores for the offenders at this level of significance
• explain why the psychologists decided to use a wilcoxon signed ranks test to analyse the data

  the anger scores from the questionaire are ordinal, meaning they represent rankings rather than equal intervals

  test is suited for repeated measures as it is a related design, where each offender's anger score before and after the program is compared
• name an appropriate statistical test that could be used to analyse the number of verbal errors in the table. explain why the test you have chosen would be a suitable test in this case

  Mann-whitney would be the most appropriate test because the data should be treated as ordinal.

  Verbal errors cannot be assumed to be of equal size, meaning one verbal error is not equivalent to another. the experimental design involves independent groups (unrelated) and the psychologist is looking for a difference between the two conditions