The Wilcoxon signed-rank test (nonparametric test) used in the case of two related sample. It can also be used as an alternative to the paired student test for example in the case of a population or group that can’t be assumed to be normally distributed. It involves the comparisons of differences between measurements and therefore needs the data to be measured at an interval level of measurement. It therefore should be used whenever the distributional assumptions can’t be met (Utts 2006).
One sample t-test or hypothesis test is an important statistical application that is used to solve real life problems. It is used to determine whether a population parameter is different from a specified value (Ramachandran & Tsokos 2009).
The relationship between the two is such that one test can be used in place of the other. The one sample Wilcoxon signed rank test is a nonparametric alternative to the one sample t-test or hypothesis test as it applies to test whether the location or median, of the measurement is equal to a specific value as described above. Therefore in the absence of certain values that are needed in a one sample hypothesis, the Wilcoxon rank test can fit in properly to generate the same conclusions. This is because the Wilcoxon signed rank test requires no assumptions for the distribution of measurements making it the successful alternative (Ramachandran & Tsokos 2009 and Utts 2006).