Wilcoxon Signed Rank Test

here we have the nonparametric equivalent to the Paired T-Test. A significant test here confirms that the PAIRED T-test we did earlier caught the differences.

remember we had a mean of 64 at PRE-test and a mean of 76.36 at the POST-test? Just because we know that they are different, we don't kow if that difference happened by chance

wilcox.test(Ttest$PRE, Ttest$POST, alternative='two.sided', paired=TRUE)

## Warning in wilcox.test.default(Ttest$PRE, Ttest$POST, alternative =
## "two.sided", : cannot compute exact p-value with ties

## Warning in wilcox.test.default(Ttest$PRE, Ttest$POST, alternative =
## "two.sided", : cannot compute exact p-value with zeroes

## 
## 	Wilcoxon signed rank test with continuity correction
## 
## data:  Ttest$PRE and Ttest$POST
## V = 109.5, p-value = 5.413e-05
## alternative hypothesis: true location shift is not equal to 0

The results from the Wilcoxon test above have a low probability value, which indicates that the results did not likely happen by chance. We would reject the H:₀ and accept the H:₁ as our most likely scenario