Interpret the key results for Kruskal-Wallis Test

To determine whether any of the differences between the medians are statistically significant, compare the p-value to your significance level to assess the null hypothesis. The null hypothesis states that the population medians are all equal. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.
P-value ≤ α: The differences between some of the medians are statistically significant
If the p-value is less than or equal to the significance level, you reject the null hypothesis and conclude that not all the population medians are equal. Use your specialized knowledge to determine whether the differences are practically significant. For more information, go to Statistical and practical significance.
P-value > α: The differences between the medians are not statistically significant
If the p-value is greater than the significance level, you do not have enough evidence to reject the null hypothesis that the population medians are all equal. Verify that your test has enough power to detect a difference that is practically significant. For more information, go to Increase the power of a hypothesis test.

If your data have ties, Minitab displays a p-value that is adjusted for ties and a p-value that is not adjusted for ties. A tie occurs when the same value is in more than one sample. The adjusted p-value is usually more accurate than the unadjusted p-value. However, because the unadjusted p-value is always greater than the adjusted p-value, it is considered the more conservative estimate. When no ties exist in your data, the two p-values are equal.

Descriptive Statistics Hospital N Median Mean Rank Z-Value 1 11 16 14.0 -1.28 2 11 31 23.3 2.65 3 11 17 13.7 -1.37 Overall 33 17.0
Test Null hypothesis H₀: All medians are equal Alternative hypothesis H₁: At least one median is different
Method DF H-Value P-Value Not adjusted for ties 2 7.05 0.029 Adjusted for ties 2 7.05 0.029
Key Results: Median, P-Value

In these results, the sample estimates of the medians for the three groups are 16.00, 31.00, and 17.00. The null hypothesis states that the population medians for these groups are all equal. Because both p-values are less than the significance level of 0.05, you can reject the null hypothesis and conclude that the medians are not all equal.

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