Kruskal-Wallis Test |
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The Kruskal-Wallis Test is a version of the independent measures (One-Way) ANOVA that can be performed on ordinal(ranked) data. |

Ordinal data is displayed in the table below. Is there a difference between Groups 1, 2, and 3 using alpha = 0.05?

Figure 1. |
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Let's test to see if there are any differences with a hypothesis test.

Steps for Kruskal-Wallis Test |
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1. Define Null and Alternative Hypotheses 2. State Alpha 3. Calculate Degrees of Freedom 4. State Decision Rule 5. Calculate Test Statistic 6. State Results 7. State Conclusion |

1. Define Null and Alternative Hypotheses

Figure 2. |
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2. State Alpha

alpha = 0.05

3. Calculate Degrees of Freedom

df = k – 1, where k = number of groups

df = 3 – 1 = 2

4. State Decision Rule

We look up our critical value in the Chi-Square Table and find a critical value of plus/minus 5.99.

Figure 3. |
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5. Calculate Test Statistic

First, we must rank every score we have:

Figure 4. |
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We then replace our original values with the rankings we've just found:

Figure 5. |
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An "H" score (think of it as a Chi-Square value) is then calculated using the sums of the ranks of each group:

Figure 6. |
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6. State Results

Figure 7. |
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Do not reject the null hypothesis.

7. State Conclusion

There is no significant difference among the three groups, H = 2.854 (2, N=18), p > .05.