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# Hypothesis Testing: Kruskal Wallis test & ANOVA

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Use a nonparametric test (attached) to see whether current salaries for clerical employees differ for the four gender/race groups. Compare results from those from a parametric analysis. Summarize conclusions.

Part 1 output

NPar Tests

Kruskal-Wallis Test

Ranks
SEX & RACE CLASSIFICATION N Mean Rank
CURRENT SALARY WHITE MALES 194 329.23
MINORITY MALES 64 244.55
WHITE FEMALES 176 163.64
MINORITY FEMALES 40 106.28
Total 474

Test Statisticsa,b
CURRENT SALARY
Chi-Square 175.068
df 3
Asymp. Sig. .000
a. Kruskal Wallis Test
b. Grouping Variable: SEX & RACE CLASSIFICATION

Part 2 Output

Oneway

ANOVA
CURRENT SALARY
Sum of Squares df Mean Square F Sig.
Between Groups 5.688E9 3 1.896E9 54.405 .000
Within Groups 1.638E10 470 3.485E7
Total 2.207E10 473

Post Hoc Tests

Multiple Comparisons
CURRENT SALARY
Bonferroni
(I) SEX & RACE CLASSIFICATION (J) SEX & RACE CLASSIFICATION Mean Difference (I-J) Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
WHITE MALES MINORITY MALES 4891.727* 850.965 .000 2637.12 7146.34
WHITE FEMALES 7107.449* 614.521 .000 5479.29 8735.60
MINORITY FEMALES 8565.165* 1025.109 .000 5849.17 11281.16
MINORITY MALES WHITE MALES -4891.727* 850.965 .000 -7146.34 -2637.12
WHITE FEMALES 2215.722 861.692 .063 -67.31 4498.75
MINORITY FEMALES 3673.438* 1189.843 .013 520.98 6825.89
WHITE FEMALES WHITE MALES -7107.449* 614.521 .000 -8735.60 -5479.29
MINORITY MALES -2215.722 861.692 .063 -4498.75 67.31
MINORITY FEMALES 1457.716 1034.031 .956 -1281.92 4197.35
MINORITY FEMALES WHITE MALES -8565.165* 1025.109 .000 -11281.16 -5849.17
MINORITY MALES -3673.438* 1189.843 .013 -6825.89 -520.98
WHITE FEMALES -1457.716 1034.031 .956 -4197.35 1281.92
*. The mean difference is significant at the 0.05 level.

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https://brainmass.com/statistics/nonparametric-tests/310880

#### Solution Summary

The solution provides step by step method for the calculation of Kruskal Wallis test and ANOVA. Formula for the calculation and Interpretations of the results are also included.

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## Hypothesis testing: ANOVA, Kruskal Wallis test

1 There are four McDonalds restaurants in a particular area. The numbers of burgers sold at the respective restaurants for each of the last 4 days are shown below.

Restaurant
1 2 3 4
Day 1 81 79 55 36
2 83 69 65 45
3 67 59 58 62
4 77 69 73 58

Restaurant sum of squares= 1793.25
Day sum of squares= 250.25
Total sum of squares= 2841.75

i) Construct ANOVA table for the above data.
ii) Test at the 5% significance level to determine if differences exist among the restaurants
iii) Test at the 5% significance level to determine if differences exist among the four days
iv) Calculate Tukey's criticalnumber w at the 5% level of significance and perform the comparison between Restaurant 1 and 2
2 Bank A is interested in determining how long it takes one of its tellers to complete a transaction as compared to two other banks B and C. The following results were obtained.
Time to complete transaction
Bank A Bank B Bank C
12 23 15
14 8 20
11 17 21
16 9 7
10 13 22
24

Using Kruskal- wallis test, determine whether there is any difference in the completion time of these banks. Use alpha = 5%

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