Complete the following steps to interpret a Friedman test. Key output includes the point estimates and the p-value.
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.
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.
Sum of Ranks
H₀: All treatment effects are zero
H₁: Not all treatment effects are zero
Key Results: Median estimates and P-Value
Because the p-value for the advertising data is less than the significance level of 0.05, the analyst rejects the null hypothesis and concludes that at least one of three types of advertising has a different effect. Also, the median responses for direct mail and magazine are close to the overall median, but the median response for newspaper advertising is substantially higher. These results indicate that newspaper advertising might be more effective than the other types of advertising.