**How to Conduct Wilcoxon Signed Rank Test**

**Question**

Blood pressure reading of ten patients before and afer medication for reducing the blood pressure are as follows

Patient: 1,2,3,4,5,6,7,8,9,10

Before treatment: 86,84,78,90,92,77,89,90,90,86

After treatment: 80,80,92,79,92,82,88,89,92,83

Test the null hypothesis of no effect agains the alternate hypothesis that medication is effective. Execute it with Wilcoxon test

**Solution Steps**

Get the Excel sheet for this problem here**Step 1: State the null and alternate hypethesis and accptance criteria**

H_{0}: difference between the pairs of observation follows a symetric distribution around 0

H_{1}: difference between the pairs does not follow a symetric distribution around 0

**Step 2: Calculate the differences between the pairsof measurements**

I have done this using Microsof Excel and the result is shown below

**Step 3: Calculate the absolute values of the differences**

In this step, you simply remove the negative signs from the negative differences

An optional addion is to add a column that holds the signs of each of the differences. This is shown in the table below

**Step 4: Rank the differences**

Rank the absolute values of the differences. This is the |X-Y| column.

Values where the differnce is zero is ignored

For values where there is tied ranks, the mid-point of the two ranks is assigned to both values. For example, for values of 1, and 1, the rank of 1.5 is assigned to both values and 3 is assigned to the next rank.

**Step 5: Calculate the signed ranks**

This signed rank is gotten by multiplying the ranks with the corresponding signs in the sign column.

The table would now look like the one below

**Step 6: Calculate Sum of Ranks**

Calculate the sum of ranks for the positive differences as given below

W^{+} = 3+ 5+2+8.5+8.5+6 = 31

Calculate teh sum of ranks for the negative differences

W^{–} = 1+4+7 = 12

The smaller of the two is used as the test statistics.

W = 12

**Step 7: Look up the z-Table and Compare**

Get Statistical table from here