# Interpret all statistics and graphs for Friedman Test

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

## 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.

## Individual value plot

An individual value plot displays the individual values in each sample. The individual value plot makes it easy to compare the samples. Each circle represents one observation. An individual value plot is especially useful when your sample size is small.

### Interpretation

Use an individual value plot to examine the spread of the data and to identify any potential outliers. Individual value plots are best when the sample size is less than 50.

Skewed data

Examine the spread of your data to determine whether your data appear to be skewed. When data are skewed, the majority of the data are located on the high or low side of the graph. Skewed data indicate that the data might not be normally distributed. Often, skewness is easiest to detect with an individual value plot, a histogram, or a boxplot.

Outliers

Outliers, which are data values that are far away from other data values, can strongly affect your results. Often, outliers are easy to identify on an individual value plot.

Try to identify the cause of any outliers. Correct any data-entry errors or measurement errors. Consider removing data values for abnormal, one-time events (special causes). Then, repeat the analysis.

## 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.

## 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?.

## 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 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.

## S

S is the test statistic for the Friedman test. Under the null hypothesis, the chi-square distribution approximates the distribution of S. 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.

## 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.

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