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How to perform Welch's ANOVA in Python?

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Sep 11, 2023 pm 05:21 PM

$如何在Python中执行Welch\'s ANOVA？$

Welch's ANOVA is an extension of the standard ANOVA test that allows for different sample sizes and variances. Often, the samples compared in an ANOVA test may not have comparable variances or sample sizes. In some cases, a Welch's ANOVA should be performed instead of a standard ANOVA test because it is unacceptable. In this article, we will learn more about Welch's Analysis of Variance

What is Welch's analysis of variance?

Welch's analysis of variance is a variation of the ANOVA test used to compare the means of two or more samples. Analysis of variance determines whether the means of two or more samples are significantly different from each other. Welch's ANOVA is an extension of the classic ANOVA test that is used when the variance or sample size of the samples is not uniform.

Unlike usual ANOVA, which assumes equal variance across samples, Welch's ANOVA uses a modified F-statistic to account for uneven variance. Therefore, this is a more robust test that can be used in a wider range of scenarios.

Implementing Welch’s ANOVA in Python

Python’s scipy.stats.f oneway() method can be used to perform Welch’s ANOVA.

grammar

f_statistic, p_value = stats.f_oneway(sample1, sample2, sample3)

This function returns the F statistic and p-value of an ANOVA test that accepts three or more samples as input.

algorithm

Import scipy library.
Create sample data for ANOVA operations.
Perform ANOVA operation.
Print the results.

Example

Instructions on how to use this function to perform a Welch's ANOVA on three samples are provided below -

import scipy.stats as stats

# Sample data
sample1 = [1, 2, 3, 4, 5]
sample2 = [2, 3, 4, 5, 6]
sample3 = [3, 4, 5, 6, 7]

# Perform ANOVA
f_statistic, p_value = stats.f_oneway(sample1, sample2, sample3)

# Print results
print('F-statistic:', f_statistic)
print('p-value:', p_value)

Output

F-statistic: 2.0
p-value: 0.177978515625

In this example, Welch's ANOVA analysis will be performed on three samples, and the f oneway() function will provide the F− statistic and p− value. The ratio of between-group variation to within-group variation was assessed based on the p-value and F-statistic, respectively, assuming that the null hypothesis is true and that such severe results observed are unlikely to occur.

If there is a significant difference between sample means, you can use these numbers to quantify it. If the p-value is less than a preset threshold (usually 0.05), you can reject the null hypothesis and find that there is a significant difference between the sample means.

in conclusion

In summary, Welch's ANOVA test is equivalent to the traditional ANOVA test. If the p-value of the test is less than a preset threshold (usually 0.05), the null hypothesis can be ignored and the sample means are judged to be significantly different. The conclusions of Welch's ANOVA, like the results of any statistical test, are only credible if they are based on the information and assumptions on which they are based. Analysts must carefully consider the test's assumptions and data in order to correctly interpret test results.

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