T Wilcoxon Matched Pairs Signed Ranks Test

Reference:Marin R Tutorial 4.5

Data set: BloodPressure

Read the data set in to R and attach it. As always, it is a good idea to produce a graphic so we can better visualize our data. A box plot is appropriate in this case.

boxplot(Before, After)

We may also want to see a summary of the data. I renamed it “BP” to save some typing.

summary(BP)

##     Subject       Before          After      
##  Min.   : 1   Min.   :117.0   Min.   :119.0  
##  1st Qu.: 7   1st Qu.:131.0   1st Qu.:125.0  
##  Median :13   Median :137.0   Median :130.0  
##  Mean   :13   Mean   :138.3   Mean   :130.3  
##  3rd Qu.:19   3rd Qu.:147.0   3rd Qu.:135.0  
##  Max.   :25   Max.   :158.0   Max.   :147.0

The actual Wilcoxon matched pairs signed ranks test is as follows.

wilcox.test(Before, After, mu = 0, alt = "two.sided", paired = T, conf.int = T, conf.level = 0.99, exact = F)

## 
##  Wilcoxon signed rank test with continuity correction
## 
## data:  Before and After
## V = 267, p-value = 0.0008655
## alternative hypothesis: true location shift is not equal to 0
## 99 percent confidence interval:
##   2.000012 14.000038
## sample estimates:
## (pseudo)median 
##       7.500019

All are defaults except paired and exact. “paired = T” is necessary in this case so R knows to run the Wilcoxon T rather than the Rank Sums test. “exact = T” will generate warnings due to the ties.

The small p value suggests that whatever manipulation we performed between the Before and After readings were taken must have been successful.