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1-sample Wilcoxon

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QXL Stat Tools Tab > Hypothesis Tests > Tests for Median > 1-Sample Wilcoxon

Test type: Median
Data: Quantitative
Number of Variables: 1
Number of Groups: 1
Assumptions: One sample from continuous, symmetric distribution

A 1-sample Wilcoxon test is a hypothesis test for the significance of the difference between the population median and a hypothesized value. It assumes that data comes from continuous distribution. Distribution should be symmetric but not necessarily normal. If the data is normally distributed, the 1-sample t-Test is more powerful.

Hypothesis tested:

H0 : Median = Median0
H1 : Median ≠ Median0

where Median is the population median, and Median0 is the hypothesized median.

Step #1: Select data source for Wilcoxon test.

Data for the 1-sample Wilcoxon test can come from an Excel spreadsheet or SQL data source.

See source data formats and example data for the 1-sample Wilcoxon test.

Step #2: Options.

  • Standard options

    • 'Not equal to' option. Select this option to run a two tailed test. The null hypothesis is that the population median and hypothesized median are equal.
    • 'Less Than' option. Select this option to run a lower tailed test. The alternative hypothesis is that the population median is smaller than the hypothesized median.
    • 'Greater Than' option. Select this option to run an upper tailed test. The alternative hypothesis is that the population median is greater than the hypothesized median.
    • 'Hypothesized median'. The value of the hypothesized median.

  • Advanced options

    • 'Decision Criteria' option (default = 0.05). The value of the decision criteria (significance or α level).
    • 'Display mode' option. When the 'Verbose (long)' option is on, Quantum XL will display additional text that explains the hypothesis test results.

Example

  • Open 1-sample Wilcoxon worksheet.

  • Run Quantum XL > Hypothesis Tests > Tests for Median > 1-Sample Wilcoxon.

  • In the Options dialog, select 'Not equal to' test, and enter 1.9 for the hypothesized median.

Results 1-sample Wilcoxon

Quantum XL will display test statistics (W), sample size and reduced sample size, estimated median, 95% confidence interval for the median, dataset statistics and p Value.

In this example, the p-Value of 0.4432 is greater than the decision criteria (0.05) so the null hypothesis cannot be rejected. We cannot conclude that the population median is not equal to 1.9.

Update

The 1-sample Wilcoxon test is updatable. After you create an analysis, you can change its data source or add new data to the data source and simply update the analysis.

  • Update: Quantum XL > Statistical Tools > Update Sheet

  • Change settings: Quantum XL > Statistical Tools > Modify Chart/Analysis