Tukey’s Test For Post-Hoc Analysis Using Python

by | Feb 9, 2023 | Statistics For Machine Learning

Tukey's Test Using Python

What is Tukey’s test for post-hoc analysis?

In one of our previous articles, we discussed the one-way ANOVA test. We looked at an example where a teacher wants to test the effectiveness of three different teaching methods. So, he selects three distinct groups of students, and each group of students is subjected to one teaching method. After that, a test is conducted for each group of students, and the mean marks of each group of students are compared.

Here, our null hypothesis is that there is no difference between the mean marks obtained by three distinct groups of students. And the alternative hypothesis is that there is some difference between the mean marks obtained by the three groups of students.

Now, let’s say we perform a one-way ANOVA test, and as per the p-value obtained, we reject the null hypothesis. So, we can conclude that there is some difference between the mean marks obtained by the three distinct groups of students.

Let’s say the mean marks obtained by three different groups of students are μ1, μ2, and μ3, respectively. So, as we reject the null hypothesis, we can conclude that

\mu_{1}\neq\mu_{2}\ or\ \mu_{2}\neq\mu_{3}\ or\ \mu_{1}\neq\mu_{3}\

But which of the above three statements is/are true? To know that, we need to perform Tukey’s test for post-hoc analysis.

How to calculate the test statistic for Tukey’s post-hoc analysis?

Tukey statistic between the first and the second group is calculated using the following formula:

q_{12}=\frac{(\bar{X}_{2}-\bar{X}_{1})}{\sqrt{\frac{s^{2}}{2}\times (\frac{1}{n_{1}}+\frac{1}{n_{2}})}}\\ \bar{X}_{1}=the\ mean\ marks\ obtained\ by\ the\ first\ group\\ \bar{X}_{2}=the\ mean\ marks\ obtained\ by\ the\ second\ group\\ n_{1}=the\ number\ of\ observations\ in\ the\ first\ group\\ n_{2}=the\ number\ of\ observations\ in\ the\ second\ group\\ s^{2}=the\ mean\ squared\ error\ for\ the\ ANOVA\ test=MSE

We know that in a one-way ANOVA test, the F-statistic is calculated in the following way: …

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Amrita Mitra

Author

Ms. Amrita Mitra is an author, who has authored the books “Cryptography And Public Key Infrastructure“, “Web Application Vulnerabilities And Prevention“, “A Guide To Cyber Security” and “Phishing: Detection, Analysis And Prevention“. She is also the founder of Asigosec Technologies, the company that owns The Security Buddy.

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