Mann-Whitney
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What is the Mann-Whitney U test?
The Mann-Whitney U test is a non-parametric statistical technique used when we have one independent categorical variable with two groups and one dependent quantitative, continuous variable. In other words, the Mann-Whitney U test examines differences between two independent groups on a continuous scale. Instead of comparing the means of two groups, the Mann-Whitney U test compares their medians. The Mann-Whitney U test is a non-parametric alternative to the parametric independent samples t-test.
When Should a Mann-Whitney U test be Used?
The Mann-Whitney is used when you have two separate groups of individuals or cases in a between-participants design.
An Example Of the Mann-Whitney U test
For example, a researcher wants to examine whether there are differences in statistics test scores between students who have prior knowledge of statistics and students who do not. Thus, we have one dependent variable – statistics test scores and one categorical variable with two groups (previous knowledge of statistics or not).
What are the use of null and alternative hypothesis for the Mann-Whitney U test?
Therefore, we test the following hypotheses:
Null hypothesis: There is no difference in statistic exam scores between students who have previous knowledge of statistics and students who do not.
Alternative hypothesis: There is a difference in statistic exam scores between students who have previous knowledge of statistics and students who do not.
R function to Compute Mann-Whitney U Test
The code to run a Mann-Whitney U Test using R is as follows:
wilcox.test(DV~ IV, data = dataframe, exact = FALSE)
DV: dependent variable
IV: Independent variable
In this section, we will show you how to run the Mann-Whitney U test using the r studio program and how to interpret the test results after we obtain the result of the test. In the first part, we present the r program code and function for the Mann-Whitney u test. Next, you will see the outputs as a result of running the r codes. In the last section, you can find the interpretation of the Mann-Whitney U test in APA format.
# LOAD DATA
library(readxl)
Data <- read_excel(“Data.xlsx“)
# VIEW DATA
View(Data)
# NAME VARIABLES
data <- Data
knowledge <- data$knowledge
exams <- data$exams
# SHOW LEVELS OF CATEGORICAL VARIABLE
levels(knowledge)
# SHOW THE MEDIAN OF THE DEPENDENT VARIABLE BY CATEGORICAL VARIABLE
library(dplyr)
group_by(data, knowledge) %>% summarise(count = n(), median = median(exams, na.rm = TRUE))
# PERFORM MANN WHITNEY U TEST
res <- wilcox.test(exams ~ knowledge, data = data, exact = FALSE)
res
> group_by(data, knowledge) %>% summarise(count = n(), median = median(stress, na.rm = TRUE))## # A tibble: 2 × 3
## knowledge count median
## <chr> <int> <dbl>
## 1 NO 46 50.5
## 2 YES 53 80.0> res <- wilcox.test(exams ~ knowledge, data = data, exact = FALSE)
> res##
## Wilcoxon rank sum test with continuity correction
##
## data: exams by knowledge
## W = 635.5, p-value = 4.252e-05
## alternative hypothesis: true location shift is not equal to 0Reporting Mann-Whitney U Test in R
Mann-Whitney U test was conducted to determine whether there is a difference in statistic exam scores between students who have previous knowledge of statistics and students who do not.The results indicate a significant difference, W = 635.5, p < 0.001. We therefore must reject the null hypothesis and conclude that there is a difference in statistic exam scores between students who have previous knowledge of statistics and students who do not. The median statistic exam score for students who did not have previous knowledge of statistics is 50.5 is lower than the median statistic exam score for students who had previous knowledge of statistics (80.0).
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