## 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.

#### Data

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.

Source: http://www.itl.nist.gov/div898/handbook/ppc/section5/ppc511.htm

#### Analysis

- Open the DataBook
*nonparam.vstx* - Select the sheet
*oxide* - Choose the tab
**Advanced Statistics**, the group**Nonparametric Tests**and the command**Wilcoxon Signed Rank Test** - In
**Variables**, enter*THICKNESS* - Click Options page. In Hypothesized median, enter 560.
- Click
**OK**

#### Output

Wilcoxon Signed Rank Test for Single Group MedianTest 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.