Name: using the sign test for paired data
Uploaded: 2025-01-09T15:14:08.000Z
Duration: 1 min 10 s
Channel: JoVE

The sign test is a nonparametric method for evaluating claims about simple random data from matched pairs, nominal data, or assertions regarding the population median.
It transforms data into positive and negative signs based on predetermined assumptions and assesses if the difference in the total counts of each sign is statistically significant.
The null hypothesis of the sign test proposes that the population characteristics align with the claims, whereas the alternative hypothesis suggests the opposite.
For data sets where the total count of signs does not exceed 25, the test statistic, denoted by x, corresponds to the quantity of the less frequent sign.
In cases where the total exceeds 25, the test statistic, represented by z, is computed.
Specific tables are used to ascertain the critical values. The null hypothesis is dismissed if the test statistic value is less than or equal to the critical value. Otherwise, there is a failure to reject the null hypothesis.

introduction to the sign test

Introduction to the Sign Test

The sign test is an important tool in nonparametric statistics, offering a straightforward yet effective method for analyzing matched pairs, nominal data, or hypotheses concerning the median of a population. It transforms data points into positive or negative signs, avoiding the need for assumptions about data distribution and instead focusing on the direction of change. It is particularly valuable when data does not conform to the normal distribution requirements of many parametric tests. For instance, researchers might employ the sign test to evaluate pre- and post-treatment effects in a medical study, determining whether the treatment correlates with an improvement (positive sign) or deterioration (negative sign) in patient outcomes. The null hypothesis proposes no difference in medians between two populations, while a predominance of one sign over the other may suggest a statistically significant effect.
As the name suggests, the sign test compares data in terms of the signs of their differences.&#160; For each pair of observations, we compare their&#160; values and:
<ol style="list-style-type: circle;">
	<li>If the value in sample A is greater than in sample B, assign a &#34;+&#34; sign.</li>
	<li>If the value in sample A is less than in sample B, assign a &#34;&#8722;&#34; sign.</li>
	<li>If the values are equal, discard the pair (no sign is assigned).</li>
</ol>
With this, we can count the number of positive and negative signs and follow on with the test. In analyzing small datasets with up to 25 observations, the test statistic (x) represents the count of the less frequent sign. A z-score is computed for larger datasets, facilitating a comparison against critical values from standard statistical tables. If the test statistic is less than or equal to these critical values, the null hypothesis is rejected, indicating a significant difference. If the opposite happens, the null hypothesis cannot be dismissed, reflecting insufficient evidence of a significant effect.

The sign test is a nonparametric method for evaluating claims about simple random data from matched pairs, nominal data, or assertions regarding the ...

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Nonparametric Statistics

KEY TERMS AND CONCEPTS

using the sign test for paired data

The sign test is a nonparametric statistics method for paired data, nominal data, and claims about a population median. It uses only the direction of change, so it does not rely on assumptions about the data distribution. That makes it useful when data do not fit the normal distribution requirements of many parametric tests.

Researchers can use the sign test to compare two related measurements, such as pre- and post-treatment results in a medical study. In that example, a positive sign can show improvement, while a negative sign can show deterioration in patient outcomes. The null hypothesis states that there is no difference in medians between the two populations.

To run the test, each pair of observations is compared. If sample A is greater than sample B, a plus sign is assigned. If sample A is less than sample B, a minus sign is assigned. If the two values are equal, the pair is discarded and no sign is given.

After the signs are counted, the test uses the less frequent sign as the test statistic for small datasets with up to 25 observations. For larger datasets, a z-score is calculated and compared with critical values from standard statistical tables. If the test statistic is less than or equal to the critical value, the null hypothesis is rejected. If not, there is not enough evidence to reject it.

Using the Sign Test for Paired Data

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The sign test is a nonparametric statistics method for paired data, nominal data, and claims about a population median. It uses only the direction of change, so it does not rely on assumptions about the data distribution. That makes it useful when data do not fit the normal distribution requirements of many parametric tests. Researchers can use the sign test to compare two related measurements, such as pre- and post-treatment results in a medical study. In that example, a positive sign can...

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key terms and concepts

Learn how the sign test compares paired data, counts positive and negative signs, and uses a test statistic or z-score to test median differences.

Using the Sign Test for Paired Data | JoVE K12

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Using the Sign Test for Paired Data

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