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One-Sample Sign / One-Sample Wilcoxon.xlsx10.1 KB One-Sample Sign / One-Sample Wilcoxon - Solution.docx

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## Quick reference

### One-Sample Sign / One-Sample Wilcoxon

There are hypothesis tests that can be used when the data is non-normal. One-Sample Sign Test and One-Sample Wilcoxon Test are non-normal hypothesis tests used when there is only one data sample.

### When to use

Both tests compare the data sample median to a target median. The One-Sample Wilcoxon Test is more sensitive and therefore more accurate, but it only works with symmetric data. The One-Sample Sign Test can be used with any non-normal data set, but since it is less sensitive it is more likely to fail to reject the Null hypothesis.

### Instructions

Data is often non-normal. Fortunately, there are many non-normal hypothesis tests that can be used with non-normal data. In some cases, non-normal data may be transformed into normal data. If using Minitab, I would not transform but rather use the non-normal hypothesis test. However Excel does not have non-normal hypothesis tests in its Data Analysis menu, so when using Excel attempt to transform the data. I suggest trying Box-Cox transformations which were discussed in a previous lesson.

The non-normal data hypothesis tests are often “tuned” to a particular type of non-normality. This will be discussed with each test. The table below shows the non-normal data hypothesis test and its normal data test equivalent.

The One-Sample Sign Test compares the median of the non-normal sample data to a target median. It is similar to the One-Sample T Test which compares the sample mean to a target mean. This test is relatively insensitive. It works with any type of non-normality.

- Minitab:
- Stat > Non-parametric – 1 Sample Sign
- Enter the column containing the data
- Set the relationship level (equal, less than, greater than)

The One-Sample Wilcoxon Test compares the median of the non-normal sample data to a target median. The One-Sample Wilcoxon Test is designed for use with symmetric data. When the data is symmetric it is more sensitive and provides a better test than the One-Sample Sign Test. It should not be used with data that is heavily skewed. In all other respects it is similar to the One-Sample Sign Test.

- Minitab:
- Stat > Non-parametric > 1 Sample Wilcoxon
- Enter the column containing the data
- Set the relationship level (equal, less than, greater than)

### Hints & tips

- Check your data to see if it is normal. If it is not, use a non-normal hypothesis test.
- When working with one sample set of data, check your non-normal data to see if it is symmetric. This will determine which test to use.
- Non-normal data uses the median instead of the mean for the measure so central tendency. This reduces the impact or skewed data and outliers.

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