﻿ Wilcoxon Signed Rank Test for Single Group Median

# Wilcoxon Signed Rank Test for Single Group Median

### Statistics > Nonparametric Tests > Wilcoxon Signed Rank Test

Performs Wilcoxon Signed Rank test for Single Group Median

The Wilcoxon signed-rank test is used to test whether the median for a variable has a particular value. Unlike the one- sample t-test, it does not assume that the observations come from a Gaussian distribution.

The Wilcoxon signed rank test hypotheses are

H0: median = hypothesized median

H1: median ≠ hypothesized median

An assumption for the one-sample Wilcoxon test and confidence interval is that the data are a random sample from a continuous, symmetric population. When the population is normally distributed, this test is slightly less powerful (the confidence interval is wider, on the average) than the t-test. It may be considerably more powerful (the confidence interval is narrower, on the average) for other populations.

### Dialog box items

Variables:
Select the column(s) containing the variable(s) you want to test.

Report:
The display of outputs of VisualStat.

### Data

You need at least one column of numeric data. If you enter more than one column of data, VisualStat performs a one-sample Wilcoxon test separately for each column. VisualStat automatically omits missing data from the calculations.

### Options

Test median:
Enter the null hypothesis test value.

Alternative Hypothesis:
Enter Two-sided, Upper One-sided, or Lower One-sided. If you choose an One-sided hypothesis test, an upper or lower confidence bound will be constructed, respectively, rather than a confidence interval.

Confidence Level:
Enter the level of confidence desired. Enter any number between 0 and 100. Entering 90 will result in a 90% confidence interval. The default is 95%.

### Example

In a semiconductor manufacturing process flow, we have a step whereby we grow an oxide film on the silicon wafer using a furnace. In this step, a cassette of wafers is placed in a quartz "boat" and the boats are placed in the furnace. The furnace can hold four boats. A gas flow is created in the furnace and it is brought up to temperature and held there for a specified period of time (which corresponds to the desired oxide thickness). This study was conducted to determine if the process was stable and to characterize sources of variation so that a process control strategy could be developed.

1.Open the DataBook nonparam.vstz

2.Select the sheet oxide

3.Choose the tab Statistics, the group Nonparametric Tests and the command Wilcoxon Signed Rank Test

4.In Variables, enter THICKNESS

5.Click Options page. In Hypothesized median, enter 560.

6.Click OK

Report window output

Wilcoxon Signed Rank test for Single Group Median

Test of median = 560 versus median not = 560

alternative hypothesis: true median is not equal to 560

THICKNESS

N                 168

Estimated median  562.5000

Mean Rank         10.3452

Rank Sum          1738.0000

Z Statistic       1.3765

Distribution      Normal Approximation

p-value           0.1687

alpha-level       0.05

Z Critical        1.9600

Conclusion        Reject the Alternative Hypothesis

### Interpreting the results

There is insufficient evidence to reject the null hypothesis (p > 0.05). The population median is not statistically different from 560. The estimated median is 562.5. This median may be different from the median of the data, which is 560 in this example.