friedman nonparametric test

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Kirthiga Sekar (08AA19)Nivetha Grace (08AA28)Rasika K.R (08AA32)Swappna Dhevi.S (08AA41)Umamaheswaran .M (08AA43)

FRIEDMAN TEST

Analysis of dataAnalysis of data

Inferential statistics Descriptive statistics

Parametric Non Parametric

Phenomena of interestDraw

inference

NON PARAMETRIC ROADMAPNON 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 Developed by US economist Milton FriedmanFriedman

►Similar to parametric repeated Similar to parametric repeated measures, ANOVAmeasures, ANOVA

►Used to detect differences in Used to detect differences in treatments across multiple test treatments across multiple test attemptsattempts

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 PERFORMWHEN TO PERFORM

►Subjects within a row must be Subjects within a row must be independentindependent

►A dependent variable that is not A dependent variable that is not interval and normally distributed (but interval and normally distributed (but at least ordinal)at least ordinal)

ASSUMPTIONASSUMPTION

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

► All observations are mutually independentAll observations are mutually independent

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

► The data can be meaningfully ranked.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.

HypothesisHypothesis

►Ho = All the related variables have the Ho = All the related variables have the same meansame mean

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

CONDITIONS FOR CONDITIONS FOR STATISTICAL PACKAGESSTATISTICAL PACKAGES

►The data need to be in a long formatThe data need to be in a long format►SPSS handles this needSPSS handles this need►Other statistical packages require the Other statistical packages require the

data to be reshaped before one can data to be reshaped before one can conduct this testconduct this test

Example - 1Example - 1

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

To conduct a Friedman testTo conduct a Friedman test

1.1. Select the Select the Analyse Analyse menumenu2.2. Click on Click on Nonparametric testsNonparametric tests and and

then on then on K Related SamplesK Related Samples to open to open the the Tests for Several Related Tests for Several Related SamplesSamples box box

3.3. Select the variables you require and Select the variables you require and then move the variables into the then move the variables into the Test Test Variable ListVariable List: box: box

4.4. Ensure the Ensure the FriedmanFriedman check box has check box has been selected.been selected.

5. Click on 5. Click on OKOK

► XX2 2 = 12.25 , p = = 12.25 , p = 0.002 0.002

► Significant Significant differences do exist differences do exist in reaction time in reaction time across drug across drug conditions.conditions.

► Drug Y appears to Drug Y appears to slow reaction slow reaction considerably.considerably.

EXAMPLE- 2EXAMPLE- 2

►To determine if there is a difference in To determine if there is a difference in the reading, writing and math scoresthe reading, writing and math scores

►Null hypothesis: The distribution of the Null hypothesis: The distribution of the ranks of each type of score (i.e., ranks of each type of score (i.e., reading, writing and math) are the reading, writing and math) are the samesame

INTERPRETATIONINTERPRETATION

►Friedman's chi-square value - 0.645 Friedman's chi-square value - 0.645 ►p-value - 0.724 p-value - 0.724 ►Not statistically significantNot statistically significant►Hence, there is no evidence that the Hence, there is no evidence that the

distributions of the three types of distributions of the three types of scores are different.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 Since this test does not make a distribution assumption, it is not as distribution assumption, it is not as powerful as the ANOVA.powerful as the ANOVA.

Try it outTry 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.