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# Anova test, Kruskai-Wallis test, t-test, and Wilkoxon Rank Sum

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Random samples of populations (in thousands) of U.S. cities in three sections of the country are listed. Is there evidence to conclude a difference in means at the 0.001 level of significance?

Eastern Third Middle Third Western Third
187 217 276
146 478 110
362 277 177
186 113 122
174 128 134
248 150 137
335 198 338
255

A) Solve using a one-way ANOVA test

B) Solve using a Kruskal-Wallis test

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The expert examines Anova test, Kruskai-Wallis test, t-test, and Wilkoxon Rank Sum.

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Random samples of populations (in thousands) of U.S. cities in three sections of the country are listed. Is there evidence to conclude a difference in means at the 0.001 level of significance?

Eastern Third Middle Third Western Third
187 217 276
146 478 110
362 277 177
186 113 122
174 128 134
248 150 137
335 198 338
255

A) Solve using a one-way ANOVA test

B) Solve using a Kruskal-Wallis test

Solution:

A) ANOVA Analysis:

Null Hypothesis: All the three sections have the same mean population.
Alternate Hypothesis: At least one of the sections has a different mean population.

ANOVA: Single Factor

SUMMARY
Groups Count Sum Average Variance
Eastern Third 7 1638 234 7106.33
Middle ...

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• MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
• BSc, Banaras Hindu University
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