Both paired sample sign test and paired sample Wilcoxon signed rank test are alternative non-parametric methods of paired sample t-test. When the normality assumption is not satisfied or the sample size is too small, t-test is not valid. In this case, paired sample sign test or paired sample Wilcoxon signed rank test should be used to test their means.
While paired sample sign test only uses the sign of paired difference ranks, paired sample Wilcoxon signed rank test uses magnitude and sign of the paired difference ranks.
As an example, suppose researchers want to test whether a new antihypertension drug is more effective than a traditional one. They collected the reduced value of blood pressure by these two antihypertension drugs in 10 hypertensive patients.
Since the normality is not satisfied, paired sample t-test is not valid. Now we use these two nonparametric methods to test whether their means are equal.
At first, we use paired sample Wilcoxon signed rank test.
Here we use paired-sample sign test.