# Interpret all statistics and graphs for Mann-Whitney Test

Find definitions and interpretation guidance for every statistic that is provided with the Mann-Whitney analysis.

## N

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

### Interpretation

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

Usually, a larger sample size results in 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 the observations are above the value and half the observations are below the value. The median is determined by ranking the observations and finding the observation that are at the number [N + 1] / 2 in the ranked order. If the number of observations are even, then the median is the average value of the observations that are ranked at numbers N / 2 and [N / 2] + 1.

### Interpretation

The median of each sample is an estimate of the population median of each sample.

## Difference

The difference is the difference between the medians of the two samples.

Because this value is based on sample data and not on the entire population, it is unlikely that the sample difference equals the population difference. To better estimate the population difference, use the confidence interval for the difference.

## Confidence interval (CI) and bounds

The confidence interval provides a range of likely values for the population difference. Because samples are random, two samples from a population are unlikely to yield identical confidence intervals. But, if you repeated your sample many times, a certain percentage of the resulting confidence intervals or bounds would contain the unknown population difference. The percentage of these confidence intervals or bounds that contain the difference is the confidence level of the interval. For example, a 95% confidence level indicates that if you take 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the population difference.

An upper bound defines a value that the population difference is likely to be less than. A lower bound defines a value that the population difference is likely to be greater than.

The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size.

## Achieved Confidence

The Mann-Whitney test does not always achieve the confidence interval that you specify because the Mann-Whitney statistic (W) is discrete. Minitab calculates the closest achievable confidence level.

The achieved confidence indicates how likely it is that the population difference is contained in the confidence interval. For example, a 95% confidence level indicates that if you take 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the population difference.

## 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, greater, or different than the hypothesized value in the null hypothesis. The alternative hypothesis is what you might believe to be true or hope to prove true.

## W-Value

The Mann-Whitney statistic (W-Value) is the sum of the ranks of the first sample.

Minitab calculates the Mann-Whitney statistic as follows:
1. Minitab ranks the two combined samples. Minitab gives the smallest observation rank 1, the second smallest observation rank 2, and so on.
2. If two or more observations are tied, Minitab assigns the average rank to both observations.
3. Minitab sums the ranks of the first sample.

### Interpretation

Minitab uses the Mann-Whitney statistic to calculate the p-value, which is a probability that measures the evidence against the null hypothesis.

Because the interpretation of the Mann-Whitney statistic depends on the sample size, use the p-value to make a decision about the test. The p-value has the same meaning for any sample size.

## P-Value

The p-value is a probability that measures the evidence against the null hypothesis. A smaller p-value provides stronger evidence against the null hypothesis.

### Interpretation

Use the p-value to determine whether the difference in population medians is statistically significant.

To determine whether the difference between the medians is statistically significant, compare the p-value to the significance level. 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 difference between the medians is statistically significant (Reject H0)
If the p-value is less than or equal to the significance level, the decision is to reject the null hypothesis. You can conclude that the difference between the population medians is statistically significant. Use your specialized knowledge to determine whether the difference is practically significant. For more information, go to Statistical and practical significance.
P-value > α: The difference between the medians is not statistically significant (Fail to reject H0)
If the p-value is greater than the significance level, the decision is to fail to reject the null hypothesis. You do not have enough evidence to conclude that the difference between the population medians is statistically significantly. You should make sure 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.

A tie occurs when the same value is in both samples. If your data has ties, Minitab displays a p-value that is adjusted for ties and a p-value that is not adjusted. The adjusted p-value is usually more accurate than the unadjusted p-value. However, the unadjusted p-value is the more conservative estimate because it is always greater than the adjusted p-value for a specific pair of samples.

## Boxplot

A boxplot provides a graphical summary of the distribution of each sample. The boxplot makes it easy to compare the shape, the central tendency, and the variability of the samples.

### Interpretation

Use a boxplot to identify any potential outliers. Boxplots are best when the sample size is greater than 20.

Outliers, which are data values that are far away from other data values, can strongly affect the results of your analysis. Often, outliers are easiest to identify on a boxplot.

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 (also called special causes). Then, repeat the analysis. For more information, go to Identifying outliers.

## Individual value plot

An individual value plot displays the individual values in each sample. An individual value plot makes it easy to compare the samples. Each circle represents one observation. An individual value plot is especially useful when you have relatively few observations and when you also need to assess the effect of each observation.

### Interpretation

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

Outliers, which are data values that are far away from other data values, can strongly affect the results of your analysis. Often, outliers are easiest to identify on a boxplot.

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 (also called special causes). Then, repeat the analysis. For more information, go to Identifying outliers.

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