Performs Mann-Whitney U-test for Independent-Samples.
This procedure performs a 2-sample rank test (also called the Mann-Whitney U-test for Independent-Samples, or the two-sample Wilcoxon rank sum test) of the equality of two population medians, and calculates the corresponding point estimate and confidence interval. This procedure is a nonparametric alternative to the Independent-Samples t-Test.
The Mann-Whitney U test is used to test whether two samples are drawn from the same population. It is most appropriate when the likely alternative is that the two populations are shifted with respect to each other. The test is performed by ranking the combined data set, dividing the ranks into two sets according the group membership of the original observations, and calculating a two sample z statistic, using the pooled variance estimate. For large samples, the statistic is compared to percentiles of the standard normal distribution. For small samples, the statistic is compared to what would result if the data were combined into a single data set and assigned at random to two groups having the same number of observations as the original samples.
Assumptions of the Mann-Whitney U-test:
•the two samples are independent (unpaired)
•the two populations have the same shape and same variance
•the measurement scale is at least ordinal
When samples are large, a normal approximation is used for the hypothesis test and for the confidence interval.
•Samples in one column:
Choose if the sample data are in a single column, differentiated by factor levels in a second column.
oSamples: Enter the columns containing the sample data.
oFactor and Levels: Enter the columns containing the sample factor, and select the levels.
•Samples in different columns:
Choose if the data of the two samples are in separate columns.
oFirst Sample: Enter the column containing one sample.
oSecond Sample: Enter the column containing the other sample
The display of outputs of VisualStat.
Data can be entered in one of two ways:
•Both samples in a single numeric column with another grouping column (called factor) to identify the population. The grouping column may be categorical, numeric or text.
•Each sample in a separate numeric column.
The sample sizes do not need to be equal. Missing values are ignored.
Check to compute summaries for each sample.
•Adjusted for ties:
Check if the statistic is computed with average ranks used in the case of ties.
Choose to use a continuity correction in the normal approximation to the distribution of the test statistics. This correction is valid only for dichotomous categories.
Enter Two-sided, Upper One-sided, or Lower One-sided. If you choose an One-sided hypothesis test, an upper or lower confidence bound will be constructed, respectively, rather than a confidence interval.
Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.
Two processing systems were used to clean wafers. The data represent the (coded) particle counts. The null hypothesis is that there is no difference between the medians of the particle counts; the alternative hypothesis is that there is a difference.
1.Open the DataBook nonparam.vstz
2.Select the sheet mw
3.Choose the tab Statistics, the group Nonparametric Tests and the command Mann-Whitney
4.Choose Samples in different columns
5.In First Sample, enter Group A
6.In Second Sample, enter Group B
7.Click Statistics. Check Summary Statistics
Report window output
Mann-Whitney U-test for Independent-Samples
Tow-sample rank test of the equality of two population medians
alternative hypothesis: true ETA1 is not equal to ETA2
With continuity correction
N Mean Median Std Dev Mean Rank Rank Sum U
Group A 11 0.5745 0.5500 0.1041 9.6364 106.0000 40.0000
Group B 11 0.6373 0.6500 0.0912 13.3636 147.0000 81.0000
Mann-Whitney U-test for Independent-Samples (adjusted for ties)
Group A ; Group B
Distribution Normal Approximation
Mann-Whitney U 40.0000
Wilcoxon W 106.0000
Z Statistic -1.3152
Critical Value 1.9600
Conclusion Reject the Alternative Hypothesis
VisualStat calculates the sample medians of the ordered data as 0.55 and 0.65 . The test statistic U = 60 has a p-value of 0.1885 . Since the p-value is not less than the chosen a level of 0.05, you conclude that there is insufficient evidence to reject the Null Hypothesis. That means, the two populations have the same median.