Manuals/calci/FRIEDMANTEST

FRIEDMAN(Array,SignificanceLevel,logicalValue)

• $Array$ is the array of values to find the test statistic.
• $SignificanceLevel$ is the value between 0 and 1.
• $Logicalvalue$ is either TRUE or FALSE.

Description

• This function gives the Test statistic summary of FriedMan Test.
• Friedman's test is a nonparametric test that compares three or more paired groups.
• It is the alternative to 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.
• This test is simelar to the Kruskal Wallis test.
• The data of the Fried Man test having the following assumptions:
• 1. One group that is measured on three or more different occasions.
• 2.Group is a random sample from the population.
• 3.The dependent variable should be measured at the ordinal or continuous level.
• 4.Samples do not need to be normally distributed.
• Steps for Fried man Test:
• 1.Define Null and Alternative Hypotheses:Null Hypotheses:There is no difference between the conditions.Alternative Hypotheses:There is a difference between the conditions.
• 2.State Alpha:Alpha=0.05.
• 3.Calculate degrees of freedom:df = k – 1, where k = number of groups.
• 4.State Decision Rule:From the Chi squared table calculate the critical value.
• Suppose the chisquared(symbol)is greater than the critical value then reject the null hypothesis
• 5.Calculate the Test Statistic:$M={\frac {12}{nk(k+1)}}\sum _{j=1}^{k}{R_{j}}^{2}-3n(k+1)$
• k = number of columns (often called “treatments”)
• n = number of rows (often called “blocks”)
• Rj = sum of the ranks in column j.
• If there is no significant difference between the sum of the ranks of each of the columns, then M will be small, but if at least one column shows significant difference then M will be larger.
• 6.State Results:In this step we have to take a decision of null hypothesis either accept or reject depending on the critical value table.
• 7.State Conclusion:To be significant, our obtained U has to be equal to or LESS than this

critical value.

Example

White	Red	Rose
10	7	8
8	5	5
7	8	6
9	6	4
7	5	7
4	7	5
5	9	3
6	6	7
5	4	6
10	6	4
4	7	4
7	3	3

1. =FRIEDMANTEST(A1:C13,0.05,TRUE)

TEST-STATISTICS RANKS

White	Red	Rose
3	1	2
3	1.5	1.5
2	3	1
3	2	1
2.5	1	2.5
1	3	2
2	3	1
1.5	1.5	3
2	1	3
3	2	1
1.5	3	1.5
3	1.5	1.5

ANALYSIS
	White	Red	Rose
Sum Of Ranks	27.5	23.5	21
SS	756.25	552.25	441
Qr	1.7916666666666572
df	2
AsymSig	0.4082672341468858

See Also

• LEVENESTEST
• MOODSMEDIANTEST
• RIEMANNZETA

References

• Friedman test documentation on Wikipedia
• Friedman test on Excel