Wilcoxon TestThings to remember:1 dependent variable (ordinal, interval, or ratio)1 independent variable with one group OR two “matched-pairs” groups2 sets of scores from different occasions or conditions Ex. Condition 1: Pre-test Condition 2: Post-test
In SPSS:Click Analyze Nonparametric Tests 2- Related Samples...Similarities of Wilcoxon and Friedman Tests Both are non-parametric Both test the median between groups Both used in skewed distributions Both try to determine if subjects changed significantly across occasions/conditions.
Friedman Test• Overview• The Friedman Test is the non-parametric alternative to the one-way ANOVA with repeated measures. It is used to test for differences between groups when the dependent variable being measured is ordinal. It can also be used for continuous data that has violated the assumptions necessary to run the one-way ANOVA with repeated measures; for example, marked deviations from normality.
Assumptions• One group that is measured on three or more different occasions.• Group is a random sample from the population.• One dependent variable that is either ordinal, interval or ratio• Samples do NOT need to be normally distributed.
Differences of Wilcoxon and Friedman Wilcoxon assess participants on twooccasions, Friedman allows for theanalysis or assessment of two OR MOREoccasions/conditions. Wilcoxon’s parametric alternative is thedependent t-test (paired samples t-test), Friedman’s alternative is the one-way repeated-measures ANOVA.
The Research QuestionDo the employees’ medians on concern for job pay, job climate, and job security ratings differ in the population? What is the independent variable? What is the dependent variable? Are the participants measured repeatedly?
Post-hoc Analysis• If the result of the Friedman Test is significant (there is a significant difference between the occasions/conditions where the group was tested), you need to run post-hoc analysis which determines where the specific differences lie.• This will be accomplished by using the Wilcoxon Signed- Rank Test (because it compares differences between two groups of the same subjects). Since we want to conduct multiple comparisons: 1. None to Classical 2. None to Dance 3. Classical to DanceWe need to use the Bonferroni adjustment to avoid a Type 1 error. It is very easy to calculate.
The Bonferroni AdjustmentSteps: 1. Take the significance level that you were using (ex. Alpha level .05) and divide it by the number of tests you are running, in our case, there are 3. 0.05/3 = 0.017 Then, if the P value is larger than 0.017, then it is not significant, therefore, there is no significant difference between the three comparisons.
How would you describe a parametric test?• It compares means,• It makes use of real values,• It has a large number of observations – thirty or more observations. (observations are the values in the rows of your SPSS in “Data view”),• Its samples are normally distributed. A normal distribution has the highest frequency at the middle of the curve in a graph.
What are non parametric tests?• Non parametric tests are a comparison of medians.• PLEASE OBSERVE THE NEXT SLIDE FOR AN ILLUSTRATION
Tests for non-parametric statistics are similar to the tests covered in AP stats, but each is slightly different. There are non-parametric tests which are similar to the parametric tests. The following table shows how some of the tests match up.Parametric Test Goal for Non-Parametric Goal for Non- Parametric Test Test Parametric TestTwo Sample T-Test To see if two samples Wilcoxon Rank-Sum Test To see if two samples have identical population have identical means population mediansOne Sample T-Test To test a hypothesis about Wilcoxon Signed Ranks To test a hypothesis the mean of the Test about the median of the population a sample was population a sample was taken from taken fromChi-Squared Test for To see if a sample fits a Kolmogorov-Smirnov To see if a sample couldGoodness of Fit theoretical distribution, Test have come from a such as the normal curve certain distributionANOVA To see if two or more Kruskal-Wallis Test To test if two or more sample means are sample medians are significantly different significantly different
Kendalls W (also known as Kendallscoefficient of concordance) is a non-parametric statistic. It is a normalizationof the statistic of the Friedman test, andcan be used for assessing agreementamong raters. Kendalls W ranges from 0(no agreement) to 1 (completeagreement).
Suppose, for instance, that a number of peoplehave been asked to rank a list of politicalconcerns, from most important to least important.Kendalls W can be calculated from these data. If the test statistic W is 1, then all the surveyrespondents have been unanimous, and eachrespondent has assigned the same order to the list ofconcerns. If W is 0, then there is no overall trend ofagreement among the respondents, and theirresponses may be regarded as essentially random.Intermediate values of W indicate a greater or lesserdegree of unanimity among the various responses.
While tests using the standardPearson correlation coefficientassume normally distributed valuesand compare two sequences ofoutcomes at a time, Kendalls Wmakes no assumptions regarding thenature of the probability distributionand can handle any number of distinctoutcomes.
PSYCH 224 QUIZ1. The following data on amount of food consumed (g) by eight rats after 0, 24, and 72 hours of food deprivation appeared in the paper “The Relation Between Differences in Level of Food Deprivation and Dominance in Food Getting in the Rat”. Does the data indicate a difference in the true mean rank of food consumption for the three experimental conditions? Rat = 1 to 8; Food consumption (g) per hour = data in bold Hours 1 2 3 4 5 6 7 8 0 3.5 3.7 1.6 2.5 2.8 2.0 5.9 2.5 24 5.9 8.1 8.1 8.6 8.1 5.9 9.5 7.9 72 13.9 12.6 8.1 6.8 14.3 4.2 14.5 7.92. Which test should you use and why?3. How strong is the relationship between the three experimentalconditions?