Step 1: Determine whether the differences between group medians are statistically significant
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 group 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 group 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.
N ≤ Overall Median
N > Overall Median
Q3 - Q1
H₀: All medians are equal
H₁: At least one median is different
Key Results: Median, P-value
In these results, the median weights for the four groups are 19, 19, 22, and 18. The null hypothesis states that the population medians are all equal. Because the p-value is greater than the significance level of 0.05, you fail to reject the null hypothesis. The differences between the median weights are not statistically significant.
Step 2: Examine the group medians
An interval plot includes the following components:
The circles represent the median of each group.
The intervals represent the confidence interval of each group. You can be 95% confident that the median for each population is within its confidence interval. However, these confidence intervals do not indicate whether the differences between the medians are statistically significant.