Select the analysis options for Mann-Whitney Test (Options tab)

On the Options tab of the Mann-Whitney Test dialog box, specify the confidence level for the confidence interval or define the alternative hypothesis.

Alternative hypothesis

From Alternative hypothesis, select the hypothesis that you want to test.
Difference < 0

Use this one-sided test to determine whether the difference between the population medians of sample 1 and sample 2 is less than 0, and to get an upper bound. This one-sided test has greater power, but it cannot detect when the median of the first sample is greater than the median of the second sample.

For example, an analyst uses this one-sided test to determine whether the median strength of one type of steel is statistically less than the median of a second type. This one-sided test has greater power to detect whether the strength of the first type of steel is less than the second type of steel, but it cannot determine whether the first type is greater than the second type.

Difference ≠ 0

Use this two-sided test to determine whether the population medians differ, and to get a two-sided confidence interval. This two-sided test can detect differences that are less than or greater than 0, but it has less power than a one-sided test.

For example, a transportation analyst tests whether the lengths of time that two brands of paint persist on a road differ. Because any difference in the length of time is important, the analyst uses this two-sided test to determine whether the time that one paint persists is greater than or less than the time that the other paint persists.

Difference > 0

Use this one-sided test to determine whether the population median of the first sample is greater than the population median of the second sample, and to get a lower bound. This one-sided test has greater power, but it cannot determine when the median of the first sample is less than the median of the second sample.

For example, a technician uses this one-sided test to determine whether the median difference between the speeds of two filling machines is greater than 0 seconds per box. This one-sided test has greater power to detect whether the difference in speed is greater than 0, but it cannot determine whether the difference is less than 0.

Confidence level

From Confidence level, select the level of confidence for the confidence interval.

Usually, a confidence level of 95% works well. A 95% confidence level indicates that, if you take 100 random samples from the population, the confidence intervals for approximately 95 of the samples will contain the population difference.

For a given set of data, a lower confidence level produces a narrower confidence interval, and a higher confidence level produces a wider confidence interval. The width of the interval also tends to decrease with larger sample sizes. Therefore, you may want to use a confidence level other than 95%, depending on your sample size, as follows:
• If your sample size is small, a 95% confidence interval may be too wide to be useful. Using a lower confidence level, such as 90%, produces a narrower interval. However, the likelihood that the interval contains the population difference decreases.
• If your sample size is large, consider using a higher confidence level, such as 99%. With a large sample, a 99% confidence level may still produce a reasonably narrow interval, while also increasing the likelihood that the interval contains the population difference.
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