Suppose the following data are in C1, and C2 and C3 are empty:

24 12 24 19 12 21 23 11 17 19 23 14 23 15 14 6

- Calculate W
_{(i)}= (X_{i}+ X_{j})/2 = all pairwise averages for i j.- Choose .
- In Variable, enter
*C1*. - In Store averages
in, type
*C2*. Click OK.

- Calculate the estimated median
- Choose .
- In Variables, enter
*C2*. - Click Statistics and check only Median.
- Click OK in each dialog box

The resulting stored value (17.5) is the Estimated Median for the 1-Sample Wilcoxon test.

Suppose the following data are in C1, and C2 and C3 are empty:

24 12 24 19 12 21 23 11 17 19 23 14 23 15 14 6

- Calculate W
_{(i)}= (X_{i}+ X_{j})/2 = all pairwise averages for i j.- Select .
- In Variable, enter
*C1*. - In Store averages
in, type
*C2*. Click OK.

- Put the pairwise averages in numerical order from lowest to highest.
- Select .
- In Columns to sort by, enter
*C2*under Column. - In Columns to sort select Specified columns.
- In Columns, enter
*C2*. - Under Storage location for the sorted columns, select In the original columns. Click OK.

The sorted pairwise averages are in C2. - To get the endpoints of the (1-α)*100% confidence interval, first solve for Z
_{(1-α/2)}. For a 95% confidence interval:- Select .
- Select Inverse cumulative probability.
- Select Input constant and enter
`0.975`. Click OK.

- Next, calculate d, which is approximately
- Select .
- In Store
result in variable, enter
`C3`. - in Expression, enter
`16*17/4-.05-1.96*sqrt(16*17*33/24)`. Click OK.

- Using the notation above, the lower endpoint of the confidence interval is W(d+1) and the upper endpoint is W(n
_{w}-d), where n_{w}is the number of pairwise averages.W(d+1) = W(31). The 31

^{st}pairwise average in C2 is 14.5.W(n

_{w}-d) = W(136-30) = W(106). The 106^{th}pairwise average in C2 is 21.### Wilcoxon Signed Rank CI: C1

Method η: median of C1Descriptive Statistics Achieved Sample N Median CI for η Confidence C1 16 17.5 (14.5, 21) 94.75%###### Note

Because d (which approximates the Wilcoxon test statistic) is positive, it will seldom be possible to achieve the specified confidence. The procedure prints the closest value, which is computed using a normal approximation with a continuity correction.