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Kruskal-Wallis Nonparametric Tests

Can you explain the conclusions one would come to with this data?

Hypothesis:

Do people who work in sales earn more in wages than people who work in service?
Use the Kruskal-Wallis nonparametric test to answer this question. The K-W test compares the medians of c independent samples (Doane, 2007).

Observation Rank Annual Wage Occupation
1 1 9879 Clerical
2 2 10997 Service
3 3 13312 Service
4 4 13481 Service
5 5 13787 Service
6 6 15013 Service
7 7 15160 Service
8 8 16667 Clerical
9 9 16789 Clerical
10 10 16796 Service
11 11 16817 Clerical
12 12 17626 Clerical
13 13 17694 Service
14 14 18121 Clerical
15 15 18752 Service
16 16 19227 Clerical
17 17 19284 Service
18 18 19452 Service
19 19 19981 Service
20 20 22485 Clerical
21 21 23027 Service
22 22 25166 Service
23 23 25670 Clerical
24 24 28219 Clerical
25 25 28440 Service
26 26 29407 Service
27 27 29736 Service
28 28 29809 Service
29 29 29977 Service
30 30 30006 Clerical
31 31 30308 Service
32 32 31702 Clerical
33 33 31799 Clerical
34 34 32094 Clerical
35 35 32138 Service
36 36 32235 Clerical
37 37 34484 Clerical
38 38 34746 Clerical
39 39 35185 Clerical
40 40 36178 Clerical
41 41 39888 Clerical
42 42 50187 Clerical

Clerical Occupation Rank Service Occupation Rank
9879 1 10997 2
16667 8 13312 3
16789 9 13481 4
16817 11 13787 5
17626 12 15013 6
18121 14 15160 7
19227 16 16796 10
22485 20 17694 13
25670 23 18752 15
28219 24 19284 17
30006 30 19452 18
31702 32 19981 19
31799 33 23027 21
32094 34 25166 22
32235 36 28440 25
34484 37 29407 26
34746 38 29736 27
35185 39 29809 28
36178 40 29977 29
39888 41 30308 31
50187 42 32138 35

Sum of ranks 540 Sum of ranks 363

Step 1
The first step in the researchers hypotheses test is to state both the null hypotheses and the alternative hypotheses numerically and descriptively. After calculating our data these are the two hypotheses:
H0 = All groups have an equal means
H1 = Not all the means are equal
H0 = µ1 = µ2
H1 = µ1 ≠ µ2

Step 2
The researchers will use a significance level of .05 creating a 95% chance of our findings being correct with a 5% chance of them being wrong.

Step 3

The researchers will use a Kruskal-Wallis Test. The Kruskal-Wallis test is a nonparametric test used to compare samples. It is used to test the null hypothesis that all populations have identical distribution functions against the alternative hypothesis that the samples differ only with respect to location (median). The Kruskal-Wallis Test does not assume normal distribution.

Step 4
The decision to reject the null hypothesis is based on the results of the significance test in this case a Kruskal-Wallis Test. The researchers will use the following table:

(p > 0.05) Not significant
(p < 0.05) Significant
(p < 0.01) Highly significant
(p < 0.001) Very highly significant

If the p- value is not significant then the null hypothesis will be accepted but if the p- value is significant the null hypothesis will be rejected.

Step 5
The following chart shows the data set used in determining the researchers hypothesis.

Attached is the Wages and Wage Earners Data Set.

Attachments

Solution Summary

This solution provides answers in Excel for Kruskal-Wallis nonparametric tests.

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