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Kruskal wallis test
- 1. KRUSKAL-WALLIS TEST Student: Dr. Yasmeen Chaudhari Dr. Kalyani Ekre Teacher: Dr. R. Mankeshwar Dr. M. Baviskar
- 2. SYNONYMS RANK SUM TEST KRUSKAL- WALLIS ONE- WAY ANOVA BY RANKS H - TEST
- 3. CONTENT • HISTORY • KRUSKAL-WALLIS TEST • PRE-REQUISITES • ASSUMPTIONS MADE • LIMITATIONS • USES • ADVANTAGES • DRAWBACK • EXAMPLES • REFERENCES
- 4. HISTORY • Described for the first time by William Henry Kruskal & Wilson Allen Wallis • They used this test for quantitative data & it tests the equality of population medians among group
- 5. KRUSKAL-WALLIS TEST WHAT Non parametric Analysis Of Variance in one way classification (data replaced by their ranks) Extension of Mann-Whitney U test for three or more groups
- 6. WHY To Test Homogeneity of samples drawn from the same population To test the equality of population medians among groups
- 7. WHEN When there are three or more comparable groups The number of observations in each comparable group is 5 or more The distribution approximates the chi-square distribution When the assumptions of one-way ANOVA are not met When there is one nominal variable & one measurement/ ranked variable
- 9. PRE REQUISITES There must be three or more groups of observations The observations should be measured on a ratio or interval scale Number of observations in each group should be 5 or more
- 10. ASSUMPTIONS MADE The groups are comparable but independent of each other Within each group, the observations are independent of each other but identically distributed
- 11. LIMITATION When we substitute ranks for the original values, we lose information which makes KW test somewhat less powerful than one-way ANOVA
- 12. USES For small sample size Distribution of population from where the sample is drawn, is not normal
- 13. ADVANTAGES Simple to understand & easy to calculate Based on observations No information is deleted or omitted Totally numerical based & quantitative test
- 14. DRAWBACK Can not be performed for very large data
- 15. EXAMPLE • The serum protein levels in gm/dl of 15 cases with Grade I, II, & III under nutrition are given below: Test whether differences in serum protein levels are statistically significant at 5% l.o.s. Grade I Grade II Grade III 6.8 6.2 5.6 7 6.3 5.5 7.2 6.5 5.4 7.1 6.7 5.7 7.4 7.3 6.9
- 16. SOLUTION • H0 - There is no difference in the serum protein levels of the 3 groups • H1- There is significant difference in the serum protein levels of the 3 groups
- 17. Serum Protein (gm/dl) Rank Grade 5.4 1 III 5.5 2 III 5.6 3 III 5.7 4 III 6.2 5 II 6.3 6 II 6.5 7 II 6.7 8 II 6.8 9 I 6.9 10 III 7 11 I 7.1 12 I 7.2 13 I 7.3 14 II 7.4 15 I
- 18. Grade I Grade II Grade III 9 5 1 11 6 2 12 7 3 13 8 4 15 14 10 R1 = 60 R2 = 40 R3 = 20 (R1)2 = 3600 (R2)2 = 1600 (R3)2 = 400 (R1)2/ n1 = 720 (R2)2/ n2 = 320 (R3)2 = 80 Sum the Ranks
- 19. REFERENCES • J. Dixit, text book of Principles and Practice of Biostatistics, edition 7 pg. 257 • K. S. Negi, text book of methods in biostatistics, pg. 204 to 210 • S. Kartikeyan, comprehensive text book of biostatistics & research methodology, 1st edition pg. 365 to 367 • W. Daniel, text book of Biostatistics basic concepts and methodology for the health sciences, 10th edition pg.704 to 709 • http://www.statisticssolutions.com/kruskal-wallis-test/ • https://www.ncbi.nlm.nih.gov/pubmed/9413454
- 20. THANK YOU
Editor's Notes
- *William Henry Kruskal was an American mathematician and statistician. He is best known for having formulated the Kruskal–Wallis one-way analysis of variance, a widely used nonparametric statistical method & The Wilson Allen Wallis was an American economist and statistician who was the companion of Kruskal…..
- Here I’m trying to explain this particular statistical test in a different way like ….. What is the test is???? Why we use this test???? When we use the test???? How it is Being used??? *It is a non parametric counterpart of one way anova……. * It resembles one way anova , only that , the data is replaced by their ranks………
- **e.g. for Ranked……Dominance hierarchies (in behavioral biology) and developmental stages are the ranked variables…….
- Step 1: state the null hypothesis…………… which will be,, there is no significant difference between the medians of the groups………. Step 2: state the altenative hypothesis…….. Step 3: assigning of ranks to all the observations…….. 1st arrange all observations in ascending order & then give the rank from smallest one……….xxx Step 4: calculate the sum of ranks of each group………. Step 5: calculate Kruskal-wallis statistic from the given formula……… n. = total no. of observations in all samples together………. Ri = sum of ranks in the ith sample. Step.6: compare the calculated value of KW with Tabulated value from chi-square table……. Where degree of freedom is equal to (k – 1) where ‘k’ is the no. of groups……. With the level of significance 0.05….. Inference: if the calculated value of KW statistic (H) is less than the tabulated value from chi-square table accept the H0……. & if it is more then reject the H0…………
- There are some pre-requesites for application of this test
- There are some assumptions like…….
- Like all other tests this test also have some limitations……….. 2. Being a non parametric test it is less powerfull than one way anova if population follows normal distribution…….
- Used when the sample size is small & the sample is drawn from a population that does not have a normal distribution.
- We can not perform this test for very large data…… Now Dr. Kalyani will explain the test with examples…..
- Grades of under nutrition are comparable but independent of each other & the no. of observations in each group is 5 hence KW test can be used…………..