The sample size (N) is the total number of observations in the sample.
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?.
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.
The median of each sample is an estimate of the population median of each sample.
The difference is the difference between the medians of the two samples.
Because the difference 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.
Confidence interval (CI for Difference) 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.
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.
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.
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.
The Mann-Whitney statistic (W-Value) is the sum of the ranks of the first sample.
Minitab calculates the Mann-Whitney statistic as follows:
Minitab ranks the two combined samples. Minitab gives the smallest observation rank 1, the second smallest observation rank 2, and so on.
If two or more observations are tied, Minitab assigns the average rank to both observations.
Minitab sums the ranks of the first sample.
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.
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.
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.
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.