Two-sample t-test using Python

by | Feb 9, 2023 | Statistics For Machine Learning

Two-sample t-Test Using Python

What is the two-sample t-test?

The two-sample t-test is used to determine whether the difference in means of two different independent groups are statistically significant. For example, Let’s say there are two distinct species of rabbits. We want to know whether the mean weights of the two species of rabbits are different.

Now, there are thousands of rabbits in each species. It is time-consuming and expensive to collect the weights of each rabbit in each species and then compare the mean weights of each species of rabbits.

So, instead, we can collect random samples from two distinct species of rabbits and take the mean weight of each species of rabbit. After that, we can perform a two-sample t-test to determine whether the difference in mean weights of two different species of rabbits is statistically significant.

Please note that for a two-sample t-test, the following assumptions should be satisfied:

  • The samples should be collected using the random sampling method.
  • The observations in one sample should be independent of the observations in another sample.
  • The data should be approximately normally distributed.
  • And the variance of the two samples should be approximately the same.

The two-sample t-test is also known as the independent samples t-test.

How to calculate the test statistic in a two-sample t-test?

The test statistic in a two-sample t-test can be calculated using the following formula:

t=\frac{\bar{X_{1}}-\bar{X_{2}}}{s_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}} \\ \bar{X_{1}}=the\ mean\ of\ the\ first\ sample \\ \bar{X_{2}}=the\ mean\ of\ the\ second\ sample \\ n_{1}=the\ sample\ size\ of\ the\ first\ sample \\ n_{2}=the\ sample\ size\ of\ the\ second\ sample \\s_{p}=the\ pooled\ standard\ deviation\\ s_{p}=\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2}} \\ s_{1}=the\ standard\ deviation\ of\ the\ first\ sample \\ s_{2}=the\ standard\ deviation\ of\ the\ second\ sample

Two-sample t-test using Python

We can use the following Python code to perform a two-sample t-test. …

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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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