Interpret all statistics for Friedman Test

Find definitions and interpretation guidance for every statistic that is provided with the Friedman test.

In This Topic

N
Median
Sum of Ranks
Null hypothesis and alternative hypothesis
DF
Chi-Square
P-Value

N

The sample size (N) is the total number of observations in each group.

Interpretation

The sample size affects the confidence interval and the power of the test.

Usually, a larger sample yields a narrower confidence interval. A larger sample size also gives the test more power to detect a difference. For more information, go to What is power?.

Median

The median is the midpoint of the data set. This midpoint value is the point at which half of the observations are above the value and half of the observations are below the value. The median is determined by ranking the observations and finding the observation at the number [N + 1] / 2 in the ranked order. If your data contain an even number of observations, the median is the average value of the observations that are ranked at numbers N / 2 and [N / 2] + 1.

Interpretation

The sample median is an estimate of the population median of each group. The overall median is the median of all observations.

Sum of Ranks

Minitab ranks the data separately within each block and then sums the ranks for each treatment. Higher data values receive higher ranks.

Interpretation

A higher sum of ranks indicates that a treatment is associated with higher ranks. Minitab uses the sum of ranks to calculate S, the test statistic for Friedman test.

Null hypothesis and alternative hypothesis

The null and alternative hypotheses are two mutually exclusive statements about a population. A hypothesis test uses sample data to determine whether to reject the null hypothesis.

Null hypothesis: The null hypothesis states that a population parameter (such as the mean, the standard deviation, and so on) is equal to a hypothesized value. The null hypothesis is often an initial claim that is based on previous analyses or specialized knowledge.
Alternative hypothesis: The alternative hypothesis states that a population parameter is smaller, larger, or different from the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.

DF

The degrees of freedom (DF) equals the number of groups in your data minus 1. Under the null hypothesis, chi-square distribution approximates the distribution of the test statistic, with the specified degrees of freedom. Minitab uses the chi-square distribution to estimate the p-value for this test.

Chi-Square

The chi-square statistic is the test statistic for the Friedman test. Under the null hypothesis, the chi-square distribution approximates the distribution of the test statistic. The approximation is reasonably accurate when either the number of blocks or the number of treatments in the randomized block design is greater than 5.

Interpretation

Minitab uses the test statistic to calculate the p-value, which you use to make a decision about the statistical significance of the terms and the model. The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.

A sufficiently high test statistic indicates that at least one difference between the medians is statistically significant.

You can use the test statistic to determine whether to reject the null hypothesis. However, using the p-value of the test to make the same determination is usually more practical and convenient.

P-Value

The p-value is a probability that measures the evidence against the null hypothesis. Lower probabilities provide stronger evidence against the null hypothesis.

Interpretation

Use the p-value to determine whether any of the differences between the 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 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.