I have a question about using wilcox.test in R.
I have the following code/data:
a <- c(1,1,1,1,1,2,2,2,2) b <- c(1,1,1,1,1,1,1,1) results <- wilcox.test(a,b, conf.int = T, exact = F) print(results)
The code above returns the following:
> Wilcoxon rank sum test with continuity correction > > data: a and b W = 52, p-value = 0.04271 alternative hypothesis: true > location shift is not equal to 0 95 percent confidence interval: 0 1 > sample estimates: difference in location > 9.415723e-05
As you can see the p-value is less than 0.05 but is not exact. In fact, when I make exact parameter TRUE then I get the warning message that exact p-value cannot be computed:
1: In wilcox.test.default(a, b, conf.int = T, exact = T) : cannot compute exact p-value with ties
Here are my questions:
Even though the p-value is less than 0.05, the confidence interval includes 0. How am I supposed to interpret such data? Is the statistical test significant?
After performing two-tailed Wilcoxon test in R, what is the correct way to interpret which group's distribution is significantly higher/lower? Do you look at the confidence interval or the difference in location?
How do you interpret the test result when the confidence interval cannot be computed because all observations are tied?