Hypothesis Testing Explained

1. Introduction

Goal of this Tutorial

This tutorial aims to provide a comprehensive understanding of Hypothesis Testing: a statistical method used to make inferences or draw conclusions about a population based on a sample.

What You Will Learn

By the end of this tutorial, you will learn about the concept of Hypothesis Testing, its types, steps, and how to implement it using Python.

Prerequisites

Familiarity with Python programming and basic knowledge of Statistics are needed to follow along with this tutorial.

2. Step-by-Step Guide

Hypothesis testing is a statistical method that helps you make decisions about a population parameter. It involves the following steps:

1. Formulate the null hypothesis (H0) and the alternative hypothesis (H1). Null hypothesis assumes no effect or relationship between the variables. Alternative hypothesis is what you might believe to be true or hope to prove true.

2. Choose the significance level (α), the probability that you will reject the null hypothesis even when it is true. Common choices are 0.05 and 0.01.

3. Calculate the test statistic based on your sample data.

4. Determine the critical value from the statistical distribution of your test statistic.

5. Compare your test statistic to the critical value to decide whether to reject or fail to reject the null hypothesis.

3. Code Examples

Let's go through an example using Python's SciPy library. Suppose you have a sample data of weights (in kg) of 20 people:

import numpy as np
from scipy.stats import ttest_1samp

weights = np.array([60, 62, 63, 65, 66, 68, 69, 70, 72, 73, 75, 76, 78, 80, 82, 84, 85, 87, 89, 90])

You want to test if the average weight is 70 kg. So, your null hypothesis is that the mean weight is 70 kg and alternative hypothesis is that the mean weight is not 70 kg.

# Null hypothesis: mean = 70
# Alternative hypothesis: mean ≠ 70

# Perform t-test
t_statistic, p_value = ttest_1samp(weights, 70)

print("T-Statistic:", t_statistic)
print("P-Value:", p_value)

The output will be the t-statistic and p-value. If p-value is less than your chosen significance level, you reject the null hypothesis.

4. Summary

We learned about Hypothesis Testing, its types, steps, and how to implement it using Python. We used the SciPy library to perform a t-test on a sample data.

Next, you can learn about other types of hypothesis tests like two-sample t-test, paired t-test, chi-square test, etc. You can also explore how to perform hypothesis testing using other Python libraries like statsmodels.

5. Practice Exercises

1. Perform a one-sample t-test on the following data with a null hypothesis that the mean is 50.

data = np.array([45, 47, 49, 51, 53, 55, 57, 59, 61, 63])

1. Perform a one-sample t-test on the following data with a null hypothesis that the mean is 30.

data = np.array([25, 27, 29, 31, 33, 35, 37, 39, 41, 43])

Use a significance level of 0.05 for both tests.

Solutions

t_statistic, p_value = ttest_1samp(data, 50)
print("T-Statistic:", t_statistic)
print("P-Value:", p_value)

You can conclude based on the p-value whether to reject or fail to reject the null hypothesis.

t_statistic, p_value = ttest_1samp(data, 30)
print("T-Statistic:", t_statistic)
print("P-Value:", p_value)

Again, you can conclude based on the p-value whether to reject or fail to reject the null hypothesis.

Keep practicing with different data and hypotheses to become more comfortable with hypothesis testing!