I have 2 data sets, each N=10, that I would like to compare. They fail Levene's test for homogeneity of variances, and for this reason, I can't use the t-test. I believe that the Mann-Whitney-Wilcoxon nonparametric test is my proper alternative.

Here are the data:

X1 = [90.4 96.0 94.8 90.4 96.0 90.4 96.0 94.8 94.4 96.4];

X2 = [29.6 40.0 44.4 29.6 40.0 29.6 40.0 44.4 44.0 31.6];

I have performed the MWW test, and I get the following results:

MANN-WHITNEY-WILCOXON TEST

--------------------------------------------------------------------------------

Sample size is good enough to use the normal distribution approximation

T: 155.0000

U: 100.0000

mT: 105.0000

sT: 13.2245

zT: 3.7431

p-value (1-tailed): 0.0001

From the p-value (as well as boxplot visualization), the difference between the two groups appears to be significant. However, from the reading I've done about the MWW U statistic, my U value should be *less than* or equal to the following values in order to achieve significance:

for N = 10,

~ at the 5% significance level, the U value must be less than or equal to 23 in order for the result to be significant.

~ at the 1% significance level, the U value must be less than or equal to 16 in order for the result to be significant.

Clearly, my U value of 100 is significantly larger than either of these values.

I would appreciate any clarification about how these 2 seemingly very different data sets can still have a U value that seems to indicate a lack of significant difference. (Also, if there is a better test to use for these data, that would be great to know.) Thanks a lot!

Here are the data:

X1 = [90.4 96.0 94.8 90.4 96.0 90.4 96.0 94.8 94.4 96.4];

X2 = [29.6 40.0 44.4 29.6 40.0 29.6 40.0 44.4 44.0 31.6];

I have performed the MWW test, and I get the following results:

MANN-WHITNEY-WILCOXON TEST

--------------------------------------------------------------------------------

Sample size is good enough to use the normal distribution approximation

T: 155.0000

U: 100.0000

mT: 105.0000

sT: 13.2245

zT: 3.7431

p-value (1-tailed): 0.0001

From the p-value (as well as boxplot visualization), the difference between the two groups appears to be significant. However, from the reading I've done about the MWW U statistic, my U value should be *less than* or equal to the following values in order to achieve significance:

for N = 10,

~ at the 5% significance level, the U value must be less than or equal to 23 in order for the result to be significant.

~ at the 1% significance level, the U value must be less than or equal to 16 in order for the result to be significant.

Clearly, my U value of 100 is significantly larger than either of these values.

I would appreciate any clarification about how these 2 seemingly very different data sets can still have a U value that seems to indicate a lack of significant difference. (Also, if there is a better test to use for these data, that would be great to know.) Thanks a lot!

Last edited: