Non-Parametric Test

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Wilcoxon T statistic is the smaller of the sum of positive ranks, W+ and the sum of negative ranks, W-. Page 8. Wilcoxon Signed Rank Test. For larger samples, a ...
Non-Parametric Test

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BASTALINGUM Vianee JAGOO Girish MARDIAPOULLÉ Yeldy.E NITHOO Lovena PAREANEN Krisen

What is a Non-Parametric Test? Data not normally distributed

Data used is of ordinal or nominal data type

The tests involve the ranking of data

The usual central measure is the median

Classification of Non-Parametric Test Non Parametric Tests

Wilcoxon Signed Rank Test

Sign Test

Two Dependent Samples

Mann Whitney U-Test

Two Independent Samples

Kruskal Wallis H-Test

Three or more Dependent Samples

Friedman Test

Three or more Independent Samples

Normality Test : Shapiro-Wilk Test •

Used to determine whether samples of data chosen are normally distributed or not .



The test should be rejected to perform a Non-Parametric test.

Non Parametric Tests

Wilcoxon Signed Rank Test ASSUMPTIONS: Paired data coming from same sample Data used is of interval measurement scale Each pair is independent

FORMULAE USED: The null and alternate hypotheses:  

Wilcoxon Signed Rank Test The paired difference, d is calculated and then ranked   where: x , y : pairs of observations

Wilcoxon T statistic is the smaller of the sum of positive ranks, W+ and the sum of negative ranks, W 

Wilcoxon Signed Rank Test For larger samples, a normal approximation is used

Standard Deviation

Mean  

 

v

 

Z-score

Wilcoxon Signed Rank Test In Excel Sample Data

Difference Calculated

1.Difference is first rank using the excel RANK function 2.R+ & R- is calculated, if difference value is positive, it is R+, else it is R-

Wilcoxon Signed Rank Test In Excel

Sum of positive and negative ranks

Mann Whitney U-Test ASSUMPTIONS: The two samples are random Independent samples and observations Ordinal data type and observations arranged in ranks.

FORMULAE USED: The null and alternate hypotheses:  

Mann-Whitney U-Test The Mann-Whitney U statistic for each sample:  

Verify that:

 

 

The smaller of the two U statistics is the obtained value, U  

Mann-Whitney U-test For large samples (greater than 20), a normal approximation is used

Standard Deviation

Mean

 

   

Ø

 

Z-score

Mann-Whitney U-test In Excel

Sample Data

Sample Data for each year is rank using RANK.AVG Excel Function

Mann-Whitney U-test In Excel

Kruskal Wallis H-Test The null and alternate hypotheses:  

Kruskal Wallis H-statistic:

 

Kruskal Wallis H-Test In Excel

Sample Data

Grouped Sample data is rank using Excel RANK.AVG Function

Rank data values are copied back into the original group and sum of ranks are calculated for each group.

Kruskal Wallis H-Test In Excel

H-Statistics is calculated using following formula :

P- Value is calculated using Excel CHISQ.DIST.RT Function

Sign Test “No difference in medians” Paired Observations: X & Y p=p(X>Y)

H0: p=0.5 H1: p≠0.5 H0: p≤0.5 H1: p>0.5 H0: p≥0.5 H1: p

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