Discovering statistics using IBM SPSS statistics by Andy Field, fifth edition – Summary chapter 7

Non-parametric tests can be used when the assumptions of the regular statistical tests have been violated. Non-parametric tests use fewer assumptions and are robust. A non-parametric test has less power than parametric tests if the sampling distribution is normally distributed.

Ranking the data refers to giving the lowest score the rank of 1, the next highest score a rank of 2 and so on. This eliminates the effect of outliers. It does neglect the difference in magnitude between the scores. If there are two scores that are the same, there are tied ranks. These scores are ranked by the value of the average potential rank for those scores (e.g. rank 3 and 4 will become rank 3.5).

There are several alternatives to the four most used non-parametric tests:

  1. Kolmogorov-Smirnov Z
    It tests whether two groups have been drawn from the same population. It has more power than the Mann-Whitney test when the sample sizes are less than 25 per group.
  2. Moses Extreme Reaction
    It tests the variability of scores across the two groups and is a non-parametric form of the Levene’s test.
  3. Wald-Wolfowitz runs
    It looks at clusters of scores in order to determine whether the groups differ. If there is no difference, the ranks should be randomly interspersed.
  4. Sign test
    It does the same as the Wilcoxon-signed rank test but it is only based on the direction of the difference. The magnitude of change is neglected. It lacks power unless the sample size is really small.
  5. McNemar’s test
    It uses nominal, rather than ordinal data. It is useful when looking for changes in people’s scores. It compares the number of people who changed their response in one direction to those who changed in the opposite direction.
  6. Marginal homogeneity
    It is an extension of McNemar’s test and is similar to the Wilcoxon test.
  7. Friedman’s 2-way ANOVA by ranks (k samples)
    It is a non-parametric ANOVA to compare two groups but has low power compared to the Wilcoxon signed-rank test.
  8. Median test
    It assesses whether samples are drawn from a population with the same median.
  9. Jonckheere-Terpstra
    It tests for trends in the data. It tests for an ordered pattern of the medains of the group. It does the same as the Kruskal-Wallis test but incorporates the order of the groups. This test should be used when a meaningful order of medians is expected.
  10. Kendall’s W
    It tests the agreement between raters and ranges between 0 and 1.
  11. Cochran’s Q
    It is a Friedman test on dichotomous data.

The effect size for both the Wilcoxon rank-sum test and the Mann-Whitney test can be calculated using the following formula:

 denotes the total sample size.

WILCOXON RANK-SUM TEST
This test can be used to compare the distributions in two conditions containing scores from different entities. It uses the difference in sum rank between two conditions. The test statistic is the lower sum of rank or if the sample sizes are unequal, the sum of the group with the smallest sample size.

The mean and the standard error can be calculated in the following way:

The z-score can be calculated using the standard z-score formula.

MANN-WHITNEY TEST
This test can be used to compare the distributions in two conditions containing scores from different entities. It uses the difference in sum rank between two conditions. The test statistic can be calculated in the following way:

 denotes the sum of ranks for group 1.

WILCOXON SIGNED-RANK TEST
This test is used when two sets of scores that are related are compared (e.g. within-subject design). It ranks the differences between scores in the two conditions. A sign (plus or minus sign) is added to the difference. Scores that have a difference of zero are excluded from the ranking. A sum of negative ranks and a sum of positive ranks is calculated. The sum of positive ranks is the test statistic.

The mean and the standard deviation can be calculated in the following way:

The z-score can be calculated using the standard formula for the z-score. The effect size uses the same formula as the effect size for the Mann-Whitney test.

KRUSKAL-WALLIS TEST
This test compares more than two independent conditions. It assesses the hypothesis that multiple independent groups come from different populations. This test ranks data. The test statistic can be calculated in the following way:

It uses a chi-square distribution. The degrees of freedom is k-1.

The conclusion of this test is whether the groups differ or not but it does not show which groups differ. This can be checked using pairwise comparisons, compare all pairs of groups. This can be done by using a stepped procedure. This compares two groups until one differs. Then the groups that are equivalent to each other form a sub-group and the non-equivalent group is used in further comparisons. This creates homogeneous groups.

An effect size for the Kruskal-Wallis test is not useful. However, the effect size for the pairwise tests is useful and uses the same formula as the effect size of the Mann-Whitney test.

FRIEDMAN’S ANOVA
This tests the difference between three or more conditions when the scores across conditions are related. The ranks are per person instead of per group, therefore, every person has k ranks.

The test statistic uses the following formula:

 denotes the sum of ranks for each group.

Image

Access: 
Public

Image

Join WorldSupporter!
This content is used in:

Scientific & Statistical Reasoning – Summary interim exam 4 (UNIVERSITY OF AMSTERDAM)

Summary of Discovering statistics using IBM SPSS statistics by Andy Field - 5th edition

Search a summary

Image

 

 

Contributions: posts

Help other WorldSupporters with additions, improvements and tips

Add new contribution

CAPTCHA
This question is for testing whether or not you are a human visitor and to prevent automated spam submissions.
Image CAPTCHA
Enter the characters shown in the image.

Image

Spotlight: topics

Check the related and most recent topics and summaries:
Institutions, jobs and organizations:
Activities abroad, study fields and working areas:
This content is also used in .....

Image

Check how to use summaries on WorldSupporter.org

Online access to all summaries, study notes en practice exams

How and why use WorldSupporter.org for your summaries and study assistance?

  • For free use of many of the summaries and study aids provided or collected by your fellow students.
  • For free use of many of the lecture and study group notes, exam questions and practice questions.
  • For use of all exclusive summaries and study assistance for those who are member with JoHo WorldSupporter with online access
  • For compiling your own materials and contributions with relevant study help
  • For sharing and finding relevant and interesting summaries, documents, notes, blogs, tips, videos, discussions, activities, recipes, side jobs and more.

Using and finding summaries, notes and practice exams on JoHo WorldSupporter

There are several ways to navigate the large amount of summaries, study notes en practice exams on JoHo WorldSupporter.

  1. Use the summaries home pages for your study or field of study
  2. Use the check and search pages for summaries and study aids by field of study, subject or faculty
  3. Use and follow your (study) organization
    • by using your own student organization as a starting point, and continuing to follow it, easily discover which study materials are relevant to you
    • this option is only available through partner organizations
  4. Check or follow authors or other WorldSupporters
  5. Use the menu above each page to go to the main theme pages for summaries
    • Theme pages can be found for international studies as well as Dutch studies

Do you want to share your summaries with JoHo WorldSupporter and its visitors?

Quicklinks to fields of study for summaries and study assistance

Main summaries home pages:

Main study fields:

Main study fields NL:

Follow the author: JesperN
Work for WorldSupporter

Image

JoHo can really use your help!  Check out the various student jobs here that match your studies, improve your competencies, strengthen your CV and contribute to a more tolerant world

Working for JoHo as a student in Leyden

Parttime werken voor JoHo

Statistics
2423