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Feb 12, 2024 · We can use the following formula to calculate our test statistic: t = (x – μ) / (s/√n) Where: x: the sample mean. μ0: a hypothesized population mean. s: the sample standard deviation. n: the sample size. We then need to calculate the p-value using degrees of freedom equal to n – 1.
Jul 25, 2023 · A t-test is a statistical method that’s used to determine whether there is a significant difference between the means of two groups. Here’s how to do it in Python.
- Machine Learning Engineer
- 20 min
Feb 24, 2010 · I'm looking to generate some statistics about a model I created in python. I'd like to generate the t-test on it, but was wondering if there was an easy way to do this with numpy/scipy. Are there any good explanations around? For example, I have three related datasets that look like this: [55.0, 55.0, 47.0, 47.0, 55.0, 55.0, 55.0, 63.0]
- Terminology Explained
- T-test Assumptions
- One-Sample t-test
- How to Perform Two-Sample t-test in Python
- How to Perform Paired t-test in Python
- How to Perform Welch's t-test in Python
- Conclusion
- References and Recommended Resources
Before we delve deeper into the details of the t-test, let us quickly understand some of the associated terminologies that will help strengthen your conceptual grasp of this statistical test.
Understanding the assumptions of a statistical test is crucial to ensure accurate and reliable results. The t-test is no exception. Any violation of its assumptions could lead to misleading conclusions, which would be counterproductive. Let's explore the four assumptions of the t-test in detail:
The one-sample t-test is a statistical hypothesis test that helps determine if an unknown population mean (mu) does not equal a claimed value. Where, x = sample mean 𝝁 = population mean S = sample standard deviation n = number of examples in the sample t = t-statistic Let’s understand this by using an example. A company claims to produce ball bear...
Let’s extend our example by assuming that the company sets up another factory to produce identical ball bearings. We need to find out if the ball bearings from the two factories are of different sizes. For such a scenario, we use the two-sample test. Here the t-statistic is defined as below. Where, X1= first sample mean X2 = second sample mean S1= ...
Upon sharing these results with the company, it decides to improve its manufacturing technology by introducing a new casting machine. It starts this pilot from one of the factories and conducts a test to identify if the new casting machine leads to a change in the diameter of the bearings by comparing two samples of 25 bearings – one before the new...
After a successful pilot from the new casting machine at one factory, the company wants to try another pilot at its second factory with a new rubbing machine. This machine is known to produce highly accurate ball bearings but is affected by temperature changes and power fluctuations. The company needs to identify if the ball bearings from the two f...
Data has the power to uncover the true underlying phenomenon impacting business decisions only if interrogated rightly. It requires a robust understanding of different statistical tests to know which one to apply and when. This tutorial focuses on t-tests and explains their underlying assumptions, such as independent and identically distributed obs...
- Independent Two Sample t-Test in Pandas. An independent two sample t-test is used to determine if two population means are equal. For example, suppose a professor wants to know if two different studying methods lead to different mean exam scores.
- Welch’s t-Test in Pandas. Welch’s t-test is similar to the independent two sample t-test, except it does not assume that the two populations that the samples came from have equal variance.
- Paired Samples t-Test in Pandas. A paired samples t-test is used to determine if two population means are equal in which each observation in one sample can be paired with an observation in the other sample.
T-tests are parametric tests for determining correlations between two samples of data. T-tests require data to be distributed according to the following assumptions about unknown population parameters:
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What is a t-test in Python?
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How do you calculate a t-statistic?
The test statistic is the t value and can be calculated using the following formula: $t = \frac{(\bar{x}_1 - \bar{x}_2) - D_0}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}$ Where $s_p$ is the pooled standard deviation and is calculated as $s_p = \sqrt{\frac{(n_1 - 1)s_1^2 + (n_2 - 1)s_2^2}{n_1 + n_2 - 2}}$
