How to conduct a one-sample t-test in Python?

introduce

One Sample T-Test is a statistical hypothesis test used to determine whether the population mean is significantly different from the hypothesized value. Python provides us with the resources we need to perform this test. In this article, we will introduce how to perform a one-sample t-test in Python using the SciPy library.

Conduct a sample T test

The first step in conducting a one-sample T-test is to state the null hypothesis and alternative hypothesis. The null hypothesis is the assumption that the population mean is equal to the hypothesized value. The alternative hypothesis is the opposite of the null hypothesis, that is, the population mean is not equal to the hypothesized value.

Assuming that we have a set of data and a hypothesized value for the population mean, we can perform a One Sample T-Test to determine whether the population mean is significantly different from the hypothesized value. Here are the steps to conduct a One Sample T-Test in Python using the SciPy library −

Step 1: Import the required libraries

Importing the essential libraries will be the first step. To perform the One Sample T-Test in Python, we need to import the NumPy and SciPy libraries. While statistical operations are carried out using the SciPy library, mathematical operations are carried out using the NumPy library.

import numpy as np
from scipy.stats import ttest_1samp

Step 2: Load the Data

The data then needs to be loaded into Python. We can use the loadtxt() method of the NumPy module to help us. The file name is passed as a parameter to the loadtxt() function, which generates an array containing the contents.

data = np.loadtxt('data.txt')

Step Three: Define Hypothetical Values

We must specify a hypothetical value for the population mean. This value will serve as a benchmark for assessing whether the population mean deviates significantly from the estimate.

hypothesized_value = 50

Step 4: Perform the One Sample T-Test

We are now prepared to run the One Sample T-Test. The SciPy library's ttest_1samp() function can be used to run the One Sample T-Test. The data and the hypothesized value are the two arguments that the ttest_1samp() function requires.

t_statistic, p_value = ttest_1samp(data, hypothesized_value)

The test statistic and p-value are the results of the ttest_1samp() function. The t-statistic calculates the standard error of the variance of the sample mean under a hypothetical value. Under the null hypothesis, the p-value is the likelihood of generating a t-statistic that is as severe as the observed statistic.

Step 5: Interpret the Results

Finally, we must interpret the results of a sample T-test. We can accomplish this task by comparing p-values ​​and significance levels. The significance level is the critical value for rejecting the null hypothesis. If the p-value is less than 0.05, which is the traditional significance level, then the null hypothesis will be rejected.

if p_value <r; 0.05:
   print('Reject Null Hypothesis')
else:
   print('Fail to Reject Null Hypothesis')

If the p-value is less than 0.05, we reject the null hypothesis and conclude that the population mean is significantly different from the hypothesized value. If the p-value is greater than or equal to 0.05, we fail to reject the null hypothesis and conclude that the population mean is not significantly different from the hypothesized value.

The one-sample T test assumes that the data follows a normal distribution, which is important. If the data does not follow a normal distribution, we may need to use a different statistical test, such as the Wilcoxon signed-rank test. The one-sample T-test also assumes that the data are independent and drawn at random from the population. If certain assumptions are not met, test results may be inaccurate.

Example with code and output

This is an example of performing a one-sample T-test in Python using the SciPy library -

Let's say we have a set of information that includes the weights of a sample of apples. We wish to determine if the population mean apple weight deviates significantly from 100 gramsmes. Using Python, we can perform a One Sample T-Test as follows −

import numpy as np
from scipy.stats import ttest_1samp

# Load the data
data = np.array([98, 102, 95, 105, 99, 101, 97, 103, 100, 98])

# Define the hypothesized value
hypothesized_value = 100

# Perform the One Sample T-Test
t_statistic, p_value = ttest_1samp(data, hypothesized_value)

# Interpret the results
if p_value < 0.05:
   print('Reject Null Hypothesis')
else:
   print('Fail to Reject Null Hypothesis')

Output

Fail to Reject Null Hypothesis

Because the p-value in this instance is higher than 0.05, we are unable to rule out the null hypothesis. We conclude that, at the 0.05 level of significance, there is no difference between the population mean weight of apples and 100 grams.

in conclusion

In summary, performing a one-sample t-test in Python is fairly simple. The SciPy library provides us with the tools we need to conduct this test. Simply import your data, provide the values ​​for your hypothesis, run a one-sample t-test using the ttest_1samp() function, and compare the p-values ​​to the significance level to interpret the results. These steps allow us to evaluate whether the population mean is significantly different from the hypothesized value.

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