What happens if two groups have the same median?

If two groups have an identical or similar distribution of scores shape AND have identical medians then you can be sure that there is no significant difference between them.

Does the Wilcoxon test compare medians?

The wilcox. test( ) function will perform the Wilcoxon signed rank test comparing medians for paired samples. The paired data must be represented by two data vectors with the same number of subjects.

Why is the Mann Whitney significant when the medians are equal?

The reason the Mann-Whitney-Wilcoxon is significant for the above data is the ranks for group 1 (other than those at the median) are lower than the ranks for group 2 (again, other than those values at the median). The difference in the sum of ranks is large enough to be statistically significant at the alpha equals .

How do you know if a Wilcoxon test is significant?

With the Wilcoxon test, an obtained W is significant if it is LESS than or EQUAL to the critical value. Our obtained value of 13 is larger than 11, and so we can conclude that there is no significant difference between the number of words recalled from the right ear and the number of words recalled from the left ear.

What does it mean if two groups have the same mean?

Two groups of means are equal means that both are equal and no need to apply any statistical test.

Are two medians significantly different?

If you accept the assumption of identically shaped distributions, then a small P value from a Mann-Whitney test leads you to conclude that the difference between medians is statistically significant.

How do you find the significant difference between two medians?

Perform a chi-square test of independence. If p-value < α then there is a significant difference between the medians of the populations from which the two samples are derived; otherwise no significant difference between the medians is found.

What does Wilcoxon test compare?

The Wilcoxon test compares two paired groups and comes in two versions, the rank sum test and the signed rank test. The goal of the test is to determine if two or more sets of pairs are different from one another in a statistically significant manner.

What is one difference between the Mann-Whitney U and the median test?

The Mann-Whitney test is a test of both location and shape. Given two independent samples, it tests whether one variable tends to have values higher than the other. One distribution is shifted 0.75 units to the right: the medians differ by 0.75 units but the shapes are identical.

Does Mann-Whitney U compare medians?

But since the Mann-Whitney test analyzes only the ranks, it does not see a substantial difference between the groups. The Mann-Whitney test compares the mean ranks — it does not compare medians and does not compare distributions.

What is the difference between Mann-Whitney and Kruskal-Wallis?

The major difference between the Mann-Whitney U and the Kruskal-Wallis H is simply that the latter can accommodate more than two groups. Both tests require independent (between-subjects) designs and use summed rank scores to determine the results.

Why use Mann-Whitney U test instead of t test?

Unlike the independent-samples t-test, the Mann-Whitney U test allows you to draw different conclusions about your data depending on the assumptions you make about your data’s distribution. These different conclusions hinge on the shape of the distributions of your data, which we explain more about later.

Is the difference in ranks significant when medians are equal?

With sufficient sample size the difference in ranks will be large enough to be significant even though the medians are equal. The table below gives the sum of the ranks for each group for the full sample of 120 observations. Group 2 clearly has a much larger sum of ranks than group 1.

What is the Mann-Whitney-Wilcoxon test?

Basically, the Mann-Whitney-Wilcoxon test ranks all of the observations from both groups and then sums the ranks from one of the groups which is compared with the expected rank sum. It is possible, although not very common, for groups to have different rank sums and yet have equal or nearly equal medians.

When should you use the Wilcoxon rank sum test?

When assumptions #2 and #3 (equal variance and normality) are not satisfied but the samples are large (say, greater than 30), the results are approximately correct. But when our samples are small and our data skew or non-normal, we probably shouldn’t place much faith in the two-sample t-test. This is where the Wilcoxon Rank Sum Test comes in.

Is the Mann-Whitney test a median or rank sum test?

The answer is that the Mann-Whitney and the equivalent Wilcoxon test (hereafter called the Mann-Whitney-Wilcoxon test) are rank sum tests and not median tests. Basically, the Mann-Whitney-Wilcoxon test ranks all of the observations from both groups and then sums the ranks from one of the groups which is compared with the expected rank sum.