Interpret the key results for Friedman 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.

Friedman Test: Response vs Advtype, Company

Method Treatment = Advtype Block = Company

Descriptive Statistics Advtype N Median Sum of Ranks direct-mail 12 6.1000 16.0 magazine 12 8.1500 24.0 newspaper 12 13.3000 32.0 Overall 36 9.1833

Test Null hypothesis H₀: All treatment effects are zero Alternative hypothesis H₁: Not all treatment effects are zero

DF Chi-Square P-Value 2 10.67 0.005

Key Results: Median, 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 (6.100) and magazine (8.150) are close to the overall median (9.183), but the median response for newspaper advertising (13.300) is substantially higher. These results indicate that newspaper advertising might be more effective than the other types of advertising.