Interpret the key results for 1-Sample Wilcoxon

Complete the following steps to interpret a 1-sample Wilcoxon test. Key output includes the estimate of the median, the confidence interval, and the p-value.

Step 1: Determine a confidence interval for the population median

First, consider the sample median, and then examine the confidence interval.

The median of the sample data is an estimate of the population median. Because the median is based on sample data and not on the entire population, it is unlikely that the sample median equals the population median. To better estimate the population median, use the confidence interval.

The confidence interval provides a range of likely values for the population median. For example, a 95% confidence level indicates that if you take 100 random samples from the population, you could expect approximately 95 of the samples to produce intervals that contain the population median. The confidence interval helps you assess the practical significance of your results. Use your specialized knowledge to determine whether the confidence interval includes values that have practical significance for your situation. If the interval is too wide to be useful, consider increasing your sample size.

Because of the discreteness of the Wilcoxon statistic, it is not always possible to achieve a confidence interval at the requested confidence level. Minitab calculates the closest achievable value using a normal approximation with a continuity correction.

Note

To get both the confidence interval and the test results you must perform the analysis twice because Minitab only calculates one item at a time.

Wilcoxon Signed Rank CI: Time

Method η: median of Time
Descriptive Statistics Achieved Sample N Median CI for η Confidence Time 16 11.55 (9.2, 12.6) 94.75%
Key Results: Median, CI for η

In these results, the estimate of the population median for reaction time is 11.55. You can be 94.75% confident that the population median is between 9.2 and 12.6.

Step 2: Determine whether the test results are statistically significant

To determine whether the difference between the population median and the hypothesized median is statistically significant, compare the p-value to the significance level. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.
P-value ≤ α: The difference between the medians is significantly different (Reject H0)
If the p-value is less than or equal to the significance level, the decision is to reject the null hypothesis. You can conclude that the difference between the population median and the hypothesized median is statistically significant. Use your specialized knowledge to determine whether the difference is practically significant. For more information, go to Statistical and practical significance.
P-value > α: The difference between the medians is not significantly different (Fail to reject H0)
If the p-value is greater than the significance level, the decision is to fail to reject the null hypothesis. You do not have enough evidence to conclude that the population median is significantly different from the hypothesized median. You should make sure that your test has enough power to detect a difference that is practically significant.
Note

To get both the confidence interval and the test results you must perform the analysis twice because Minitab only calculates one item at a time.

Wilcoxon Signed Rank Test: Time

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

The null hypothesis states that the median reaction time is 12 minutes. Because the p-value is 0.227, which is greater than the significance level of 0.05, you fail to reject the null hypothesis and cannot conclude that the median reaction time is less than 12 minutes.

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