How to do a t-test in Python?

Do you want to know what T-tests are and how to run them? This tutorial simplifies the steps of running a T-test.

Data scientists often use T-tests to determine if there is a significant difference between the means of two groups or samples. This statistical test helps assess whether the observed differences are likely to have occurred by chance or if they are statistically significant.

For example, a pharmaceutical company is testing a new drug to reduce blood pressure. They conduct a clinical trial with two groups: one group receives the new drug, and the other gets a placebo. After the trial, the company wants to determine if the two groups significantly differ in blood pressure reduction. Here's where the T-test comes in. The data scientists would collect blood pressure measurements from both groups and calculate each group's mean blood pressure reduction. Then, they would use a T-test to compare these means. If the T-test shows a significant difference between the two groups' mean blood pressure reduction, the company can conclude that the new drug is effective in lowering blood pressure compared to the placebo.

Making critical decisions requires hypothesis testing to support actions using statistical analysis. One such testing method is the T-test. In this data science tutorial, we will learn about T-tests and how to perform them to gain a solid understanding and efficiently apply them to our data.

What is a T-test?

The t-test or check (Student’s T-Test) compares two averages (means) and tells you if they're entirely or partially different. It examines two data groups and tells you how significant the variations are. In other words, it enables you to understand if those variations may have happened unintentionally.

What are the Pre-Requisites for a T-test?

The essential prerequisites for the T-test are:

  1. Hypothesis Testing: This process starts with an assumption or null hypothesis and finds evidence for or against it.

  2. P-value: It is the probability of obtaining data as extreme as the observed results, given that the null hypothesis (assumption) is true.

  3. Degree of Freedom: This signifies the number of data points free to vary after considering the statistical constraints.

  4. Significance Level: It is the probability of acceptance or rejection of the null hypothesis.

  5. T-Score: The t-score measures the standardized difference between two group means relative to the within-group variability. A larger absolute t-score indicates greater dissimilarity between the groups, while a smaller t-score suggests higher similarity. 

How to calculate T-test in Python?

For t-test calculations, we need the T-statistic or T-value, which is calculated using the formula

T-value Formula

where,

μ= Mean of sample 1

μ= Mean of sample 2

σ2= Variance of sample 1

σ22 = Variance of sample 2

 n1  = Sample Size of Sample 1

 n2  = Sample Size of Sample 1

How to perform T-Test In Python?

Let's look at a step-by-step t-test for Python code to do T-tests in Python. The California Housing Dataset is the T-test Python example used for the same.

Step 1: Importing Libraries

Importing Python Libraries

Step 2: Reading Datasets

Reading dataset in Python from csv file

Step 3: Defining two sample rows

Sample rows to measure Statistics and p-values from t-test

Step 4: Performing the T-test

Performing T-test on the sample

The test statistic is -233.0345623005931, and the corresponding p-value is 0.0. If the p-value is less than 0.05, we reject the null hypothesis. We have sufficient evidence that this data has skewness and kurtosis, which is different from a normal distribution.

How to interpret T-test in Python?

The next step is to interpret the T-test result. If the p-value is less than the significance specified(alpha= 0.05), then the null hypothesis is rejected, and it is thus concluded that there is a significant difference in the median income between the groups; else, there is no significant difference between the median income between the groups.

The T-test Code in Python for the same is-

Interpreting T-test of the sample

How to prepare a Dataframe for Correlation Analysis In Python?

For this example, let us consider a dataframe containing columns such as median income, median house value, total rooms, and population. To prepare my dataframe for correlation in Python, we will follow the following steps:

Step 1: Import the necessary libraries

import pandas as pd

Step 2: Load the dataset into the Pandas Dataframe

# Load the dataset into a DataFrame

df = pd.read_csv('your_dataset.csv')

Step 3: Select the variables for correlation analysis

# Select the variables for correlation analysis

variables_of_interest = ['median_income', 'median_house_value']

Step 4: Create a new Dataframe with selected variables

# Create a new DataFrame with selected variables

selected_df = df[variables_of_interest]

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ProjectPro allows learners to deepen their understanding of statistical concepts like the T-test in a practical, real-world context. By working on projects that involve applying T-tests to analyze data and draw meaningful conclusions, learners can sharpen their statistical analysis skills and gain valuable experience that prepares them for tackling complex data challenges at an enterprise level. ProjectPro offers 250+ solved end-to-end project templates designed by industry experts on data science and big data topics. It is the perfect platform for aspiring data scientists and analysts to grow their data skills.

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