Friedman Nonparametric Test

FRIEDMAN TEST

Kirthiga Sekar Nivetha Grace Rasika K.R Swappna Dhevi.S Umamaheswaran .M

(08AA19) (08AA28) (08AA32) (08AA41) (08AA43)

Analysis of data Draw inference

Inferential statistics

Parametric

Non Parametric

Phenomena of interest

Descriptive statistics

NON PARAMETRIC ROADMAP

Definition ► It

is a non-parametric test (distribution-free) used to compare observations repeated on the same subjects. ► This is also called a non-parametric randomized block analysis of variance.

Friedman's Test ► Developed

by US economist Milton

Friedman ► Similar to parametric repeated measures, ANOVA ► Used to detect differences in treatments across multiple test attempts

Friedman's Test ► Popular

K-related sample test ► Similar to the Wilcoxon test, except that you can use it with three or more conditions. ► Each subject does all of the experimental conditions ► With more than two related samples on ordinal data

WHEN TO PERFORM ► Subjects

within a row must be independent ► A dependent variable that is not interval and normally distributed (but at least ordinal)

ASSUMPTION ►

Unlike the parametric repeated measures ANOVA or paired t-test, this non-parametric makes no assumptions about the distribution of the data (e.g., normality).

►

All observations are mutually independent

►

The rows are mutually independent. That is, the results in one block (row) do not affect the results within other blocks.

►

The data can be meaningfully ranked.

How the Friedman test works ► The

test compares three or more paired groups. ► The test first ranks the values in each matched set (each row) from low to high. ► Each row is ranked separately. ► It then sums the ranks in each group (column).  If the sums are very different, the P value will be small.

Hypothesis ► Ho

= All the related variables have the same mean ► HA = All the related variable do not have the same mean

CONDITIONS FOR STATISTICAL PACKAGES ► The

data need to be in a long format ► SPSS handles this need ► Other statistical packages require the data to be reshaped before one can conduct this test

Example - 1 ► Reaction

times for eight subjects were measured under placebo condition, a drug X and a drug Y condition. It was hypothesized that reaction times would differ significantly across drug conditions.

To conduct a Friedman test Select the Analyse menu ► Click on Nonparametric tests and then on K Related Samples to open the Tests for Several Related Samples box ► Select the variables you require and then move the variables into the Test Variable List: box ► Ensure the Friedman check box has been selected. ►

5. Click on OK

► X2 =

12.25 , p = 0.002 ► Significant differences do exist in reaction time across drug conditions. ► Drug Y appears to slow reaction considerably.

EXAMPLE- 2 ► To

determine if there is a difference in the reading, writing and math scores ► Null hypothesis: The distribution of the ranks of each type of score (i.e., reading, writing and math) are the same

INTERPRETATION ► Friedman's

chi-square value - 0.645 ► p-value - 0.724 ► Not statistically significant ► Hence, there is no evidence that the distributions of the three types of scores are different.

APPLICATIONS ► Rank

data separately for each block (matching level) ► Find sum of ranks for each of the comparison groups ► Use statistic – to know order of importance

ADVANTAGES ► Since

the Friedman test ranks the values in each row, it is not affected by sources of variability that equally affect all values in a row (since that factor won't change the ranks within the row). ► The test controls experimental variability between subjects, thus increasing the power of the test.

DISADVANTAGES ► Since

this test does not make a distribution assumption, it is not as powerful as the ANOVA.

Try it out Effects on worker mood of different types of music: ► Five workers. Each is tested three times, once under each of the following conditions:  condition 1: silence.  condition 2: "easy-listening” music.  condition 3: marching-band music. ► DV: mood rating ("0" = unhappy, "100" = euphoric). ► Ratings - so use a nonparametric test.