Name: single-population sign test for a median
Uploaded: 2025-01-09T15:14:08.000Z
Duration: 1 min 20 s
Channel: JoVE

In a class of 100 students, 60 scored a grade of less than 45 on a test, 15 scored 45, and 25 scored more than 45.
This simple random data, drawn from a single population, allows for the use of the sign test to examine claims about the scores&#39; median.
The null hypothesis posits that the median equals 45, whereas the alternative hypothesis suggests the median is less than 45.
In this scenario, positive signs are assigned to scores above 45 and negative signs to those below 45.
Given that most scores are below 45, the sample data supports the alternative hypothesis.
Since n &#8212; the total number of positive and negative signs &#8212; exceeds 25, the test statistic is calculated using z statistic as follows.
For a one-tailed test at a 0.05 confidence level, the critical z-value is -1.645. As the test statistic falls below the critical value, we reject the null hypothesis, suggesting that the dataset&#39;s median is less than 45.

sign test for median of single population

Sign Test for Median of Single Population

In general, the sign test serves as a nonparametric method to test hypotheses about the median of a single population when the data does not follow a known distribution. This simplicity makes it particularly useful for small sample sizes or when the assumptions of parametric tests cannot be met. The process begins with identifying a null hypothesis, typically stating that the population median equals a specific value. The alternative hypothesis could be that the median is either not equal to, less than, or greater than the tested value, depending on the research question.
The sign test compares each data point to the proposed median under the null hypothesis and uses their differences to calculate the test statistics and obtain conclusions. With this, data points greater than the hypothesized median are labeled with positive signs, and the smaller ones are marked with negative signs. The test then focuses on the count of these signs, ignoring any data points that exactly match the median, as they do not contribute evidence towards either hypothesis.
Unlike other sign tests, such as those for paired samples or matched pairs (often used in before-and-after studies), the single-population sign test does not compare two groups or conditions but focuses solely on assessing the central tendency within a single group relative to a fixed value. This test is useful for determining if a single sample median deviates from a standard, providing a robust alternative when sample sizes are small or distributions are skewed. The test then evaluates the balance between positive and negative signs, which reflects on the median&#39;s true position relative to the hypothesized value. A significant imbalance suggests the sample data contradicts the null hypothesis, indicating an alternative median value for the population.

In a class of 100 students, 60 scored a grade of less than 45 on a test, 15 scored 45, and 25 scored more than 45.
This simple random data, drawn from a ...

sign-test-for-median-of-single-population

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Statistics

Unit 1

Nonparametric Statistics

KEY TERMS AND CONCEPTS

single-population sign test for a median

The single-population sign test checks whether one sample median matches a chosen value. It is a nonparametric method, so it is useful when the data do not follow a known distribution. It is also helpful for small samples or when the usual assumptions for parametric tests are not met.

The test starts with a null hypothesis that the population median equals a specific number. The alternative hypothesis can state that the median is different from, less than, or greater than that number. The choice depends on the research question.

To run the sign test, each data point is compared with the hypothesized median. Values above it receive positive signs, and values below it receive negative signs. Any value that is exactly equal to the median is ignored because it does not support either side.

The test statistic comes from the count of positive and negative signs. It does not compare two groups or a before-and-after change. Instead, it looks at a single group and asks whether its center appears to differ from a fixed value.

A strong imbalance between positive and negative signs suggests the null hypothesis may be false. That result points to a median that is different from the value being tested. This makes the sign test a robust choice for skewed data or other situations where sample median is the main focus.

Single-Population Sign Test for a Median

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key terms and concepts

Learn how the single-population sign test uses positive and negative signs to check whether one sample median differs from a fixed value in nonparametric statistics.

Single-Population Sign Test for a Median | JoVE K12

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Single-Population Sign Test for a Median

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