Example of 1-Sample Wilcoxon

A chemist for a pharmaceutical company wants to determine whether the median reaction time for a newly developed antacid is less than 12 minutes. The chemist measures the reaction time for 16 samples of the antacid.

The chemist performs a 1-sample Wilcoxon test to determine whether the median reaction time is less than 12 minutes.

Open the sample data, AntacidReactionTime.MTW.
Choose Stat > Nonparametrics > 1-Sample Wilcoxon.
In Variables, enter Time.
Select Test median and enter 12.
From Alternative, select less than.
Click OK.

Interpret the results

The null hypothesis states that the median reaction time is 12 minutes. Because the p-value is approximately 0.23, which is greater than the significance level of 0.05, the chemist fails to reject the null hypothesis and cannot conclude that the median reaction time is less than 12 minutes.

Method

η: median of Time

Descriptive Statistics

Sample	N	Median
Time	16	11.55

Test

Null hypothesis	H₀: η = 12
Alternative hypothesis	H₁: η < 12

Sample	N for Test	Wilcoxon Statistic	P-Value
Time	16	53.00	0.227