Good Morning! Today we are going to learn about

the Friedman Test

Justin and friends

The Friedman Test

Prepared by:Irene Victoria Gabiana

But first, let us review what we’ve learned previously.

Background on Similar Tests

Things to remember:

1 dependent variable (ordinal, interval, or ratio)

1 independent variable with one group OR two “matched-pairs” groups

2 sets of scores from different occasions or conditions Ex. Condition 1: Pre-test

Condition 2: Post-test

Wilcoxon 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 two

occasions, Friedman allows for the analysis or assessment of two OR MORE occasions/conditions.

© Wilcoxon’s parametric alternative is the dependent t-test (paired samples t-test), Friedman’s alternative is the one-way repeated-measures ANOVA.

Do 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?

The Research Question

Let’s look at the SPSS Procedure of the Friedman Test

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 Dance

We need to use the Bonferroni adjustment to avoid a Type 1 error. It is very easy to calculate.

The Bonferroni Adjustment

Steps: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.

Frequency Distributions Demonstrating the Mean, Median, Mode

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

Parametric Test Goal for Parametric Test

Non-Parametric Test

Goal for Non-Parametric Test

Two Sample T-Test To see if two samples have identical population means

Wilcoxon Rank-Sum Test To see if two samples have identical population medians

One Sample T-Test To test a hypothesis about the mean of the population a sample was taken from

Wilcoxon Signed Ranks Test

To test a hypothesis about the median of the population a sample was taken from

Chi-Squared Test for Goodness of Fit

To see if a sample fits a theoretical distribution, such as the normal curve

Kolmogorov-Smirnov Test

To see if a sample could have come from a certain distribution

ANOVA To see if two or more sample means are significantly different

Kruskal-Wallis Test To test if two or more sample medians are significantly different

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.

Kendall’s W

Kendall's W (also known as Kendall's coefficient of concordance) is a non-parametric statistic. It is a normalization of the statistic of the Friedman test, and can be used for assessing agreement among raters. Kendall's W ranges from 0 (no agreement) to 1 (complete agreement).

Suppose, for instance, that a number of people have been asked to rank a list of political concerns, from most important to least important. Kendall's W can be calculated from these data.

If the test statistic W is 1, then all the survey respondents have been unanimous, and each respondent has assigned the same order to the list of concerns. If W is 0, then there is no overall trend of agreement among the respondents, and their responses may be regarded as essentially random. Intermediate values of W indicate a greater or lesser degree of unanimity among the various responses.

While tests using the standard Pearson correlation coefficient assume normally distributed values and compare two sequences of outcomes at a time, Kendall's W makes no assumptions regarding the nature of the probability distribution and can handle any number of distinct outcomes.

THE END

PSYCH 224 QUIZ  1. 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?

HoursRat = 1 to 8; Food consumption (g) per hour = data in

bold

1 2 3 4 5 6 7 8

02472

3.5 3.7 1.6 2.5 2.8 2.0 5.9 2.5 5.9 8.1 8.1 8.6 8.1 5.9 9.5 7.9 13.9 12.6 8.1 6.8 14.3 4.2 14.5 7.9

2. Which test should you use and why? 3. How strong is the relationship between the three experimental conditions?