Name: testing paired data with wilcoxon signs
Uploaded: 2025-01-09T15:14:08.000Z
Duration: 1 min 9 s
Channel: JoVE

Consider the dataset of fasting blood sugar levels of patients for two consecutive months. How does one test the claim that there is no difference between the May and June blood sugar levels?
For testing the null hypothesis, the Wilcoxon signed-ranks test can be performed using ranks along with signs.
To test the claim, first obtain the difference in blood sugar levels between the two months.
Then, the signs of the differences are ignored to arrange them in ascending order.
After that, rank with the appropriate sign is assigned to each number.
The absolute value of the sum of the positive and negative ranks is obtained separately. The smaller of the two values is taken as T, which in this case is five.
With an n equal to nine and a significance level of 0.05, the critical value comes out to be six.
Since T is less than the critical value, six, the null hypothesis is rejected, meaning that the May and June blood sugar levels are apparently not the same.

wilcoxon signed-ranks test for matched pairs

Wilcoxon Signed-Ranks Test for Matched Pairs

The Wilcoxon signed-rank test for matched pairs evaluates the null hypothesis by combining the ranks of differences with their signs. It essentially tests whether the median of the differences in a population of matched pairs is zero. Since the test incorporates more information than the sign test, it generally yields more trustable conclusions. This test also does not require the data to follow a normal distribution, but two conditions must be met for it to be applicable: (1) the data must consist of matched pairs; and (2) the distribution of the differences between these pairs should be approximately symmetric.
The difference, d, for each data pair is calculated by subtracting the second value from the first. In the Wilcoxon signed-rank test, the signs of these differences are initially ignored, and their absolute values are ranked in ascending order, and ranks are then assigned to each difference. After that, the original signs are reapplied to the ranks, creating signed ranks. The sum of the positive and negative signed ranks is calculated separately. With this, the sample size, n, is the number of pairs with non-zero differences, which determines the test statistic used.
<ol style="list-style-type: circle;">
	<li>If n is less than equal to 30, the test statistic, T, is taken as the smallest of the two sums obtained;</li>
	<li>If n is higher than 30, the test statistic, Z, is calculated using the formula: 14160_Equation_PT_1</li>
</ol>
<img alt="Equation statistical analysis, formula for z-score, diagram of mathematical expression." src="/files/ftp_upload/14160/PT_14160_Equation_1.jpg" style="text-align: center; height: 74px;" data-altupdatedat="1761830439000" data-alt="Equation 1">
In both cases, the critical z-value is also up from its table. If the test statistic, T, is less than the critical value, z,  the null hypothesis is rejected.

Consider the dataset of fasting blood sugar levels of patients for two consecutive months. How does one test the claim that there is no difference between ...

wilcoxon-signed-ranks-test-for-matched-pairs

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Statistics

Unit 1

Nonparametric Statistics

KEY TERMS AND CONCEPTS

testing paired data with wilcoxon signs

The Wilcoxon signed-rank test checks paired data by using both the size and the direction of the differences. It is a nonparametric test, which means it does not require the data to follow a normal distribution. It tests whether the median of the differences in a population of matched pairs is zero.

This test works best when the data come in matched pairs, such as two measurements from the same subject or linked observations. The differences between each pair should also have an approximately symmetric distribution. Because it uses more information than the sign test, the Wilcoxon signed-rank test often gives more reliable conclusions.

To carry out the test, find each difference by subtracting the second value from the first. Then ignore the signs at first and rank the absolute values in ascending order. After the ranks are assigned, put the original signs back on the ranks to make signed ranks.

Next, add the positive signed ranks and the negative signed ranks separately. The sample size, n, is the number of pairs with non-zero differences, and it determines which test statistic to use. If n is 30 or less, use T, the smaller of the two rank sums. If n is greater than 30, calculate Z with the given formula.

In both cases, compare the test statistic with the critical z-value from the table. If T is less than the critical value, reject the null hypothesis. This means the data do not support the claim that the median difference is zero.

Testing Paired Data with Wilcoxon Signs

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key terms and concepts

Learn how the Wilcoxon signed-rank test analyzes matched pairs, ranks differences, and uses T or Z to decide whether to reject the null hypothesis.

Testing Paired Data with Wilcoxon Signs | JoVE K12

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Testing Paired Data with Wilcoxon Signs

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