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Performing One Sample T-Test in Python


One Sample t-test in Python

In statistical analysis, a t-test is used to determine whether there is a significant difference between the means of two groups. However, in some cases, we are interested in comparing the mean of a single group to a known value or theoretical expectation. This is where the one-sample t-test comes into play.

In this tutorial, we will explore how to perform a one-sample t-test in Python using the SciPy library. We will provide a step-by-step guide, including executable sample codes, to demonstrate the process.

Before moving forward, make sure you have the SciPy library installed in your Python environment. If not, you can install it using the following command:

pip install scipy

Once installed, let’s import the necessary modules and generate a sample dataset to work with:

import numpy as np
from scipy import stats
# Generate sample data
data = np.random.normal(loc=10, scale=2, size=100)

In the code snippet above, we imported the required modules: numpy for creating the sample dataset and scipy.stats for performing the t-test. We then used the np.random.normal() function to generate a sample dataset with a mean of 10 and a standard deviation of 2. You can modify these parameters to match your own data.

Next, we can perform the one-sample t-test using the ttest_1samp() function provided by SciPy:

# Perform one-sample t-test
t_statistic, p_value = stats.ttest_1samp(data, popmean=9.5)

In the code snippet above, we used the ttest_1samp() function and passed our sample dataset (data) as the first argument. The parameter popmean specifies the known value or theoretical expectation we want to compare the mean against. In this case, we set it to 9.5.

The function returns two values: t_statistic and p_value. The t_statistic represents the calculated t-value, while the p_value represents the two-sided p-value associated with the t-statistic.

To interpret the results, we can set a significance level, commonly denoted as alpha (α). Let’s choose a significance level of 0.05 (5%) for this example:

alpha = 0.05
# Comparing p-value with alpha
if p_value < alpha:
print("Reject the null hypothesis")
print("Fail to reject the null hypothesis")

In the code snippet above, we compared the obtained p-value with the chosen significance level (alpha). If the p-value is less than alpha, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

The null hypothesis in a one-sample t-test assumes that there is no significant difference between the mean of the sample and the specified population mean.

Finally, let’s display the results to the user:

print("t-statistic:", t_statistic)
print("p-value:", p_value)

By executing the above code, you will see the t-statistic and p-value printed on the screen.

Congratulations! You have successfully performed a one-sample t-test in Python using the SciPy library. This tutorial provided a step-by-step guide and included detailed, executable sample codes to help you understand the process.

Remember, the one-sample t-test is a powerful tool for comparing the mean of a sample dataset with a known value or theoretical expectation. It can be used in a wide range of applications, such as quality control, scientific research, and data analysis.