A two sample t-test is used to test whether or not the means of two populations are equal. Show This tutorial explains how to conduct a two sample t-test in Python. Researchers want to know whether or not two different species of plants have the same mean height. To test this, they collect a simple random sample of 20 plants from each species. Use the following steps to conduct a two sample t-test to determine if the two species of plants have the same height. Step 1: Create the data. First, we’ll create two arrays to hold the measurements of each group of 20 plants: import numpy as np group1 = np.array([14, 15, 15, 16, 13, 8, 14, 17, 16, 14, 19, 20, 21, 15, 15, 16, 16, 13, 14, 12]) group2 = np.array([15, 17, 14, 17, 14, 8, 12, 19, 19, 14, 17, 22, 24, 16, 13, 16, 13, 18, 15, 13]) Step 2: Conduct a two sample t-test. Next, we’ll use the ttest_ind() function from the scipy.stats library to conduct a two sample t-test, which uses the following syntax: ttest_ind(a, b, equal_var=True) where:
Before we perform the test, we need to decide if we’ll assume the two populations have equal variances or not. As a rule of thumb, we can assume the populations have equal variances if the ratio of the larger sample variance to the smaller sample variance is less than 4:1. #find variance for each group
print(np.var(group1), np.var(group2))
7.73 12.26
The ratio of the larger sample variance to the smaller sample variance is 12.26 / 7.73 = 1.586, which is less than 4. This means we can assume that the population variances are equal. Thus, we can proceed to perform the two sample t-test with equal variances: import scipy.stats as stats #perform two sample t-test with equal variances stats.ttest_ind(a=group1, b=group2, equal_var=True) (statistic=-0.6337, pvalue=0.53005) The t test statistic is -0.6337 and the corresponding two-sided p-value is 0.53005. Step 3: Interpret the results. The two hypotheses for this particular two sample t-test are as follows: H0: µ1 = µ2 (the two population means are equal) HA: µ1 ≠µ2 (the two population means are not equal) Because the p-value of our test (0.53005) is greater than alpha = 0.05, we fail to reject the null hypothesis of the test. We do not have sufficient evidence to say that the mean height of plants between the two populations is different. Additional ResourcesHow to Conduct a One Sample T-Test in Python In this article, we are going to see how to conduct a two-sample T-test in Python. This test has another name as the independent samples t-test. It is basically used to check whether the unknown population means of given pair of groups are equal. tt allows one to test the null hypothesis that the means of two groups are equal AssumptionsBefore conducting the two-sample t-test using Python let us discuss the assumptions of this parametric test. Basically, there are three assumptions that we can make regarding the data groups:
Note that even if our data groups don’t follow the three assumptions discussed above. This is because there is an alternate test present if our data do not fall in the normal distribution or we can transform the dependent data group using different techniques like square root, log, etc Two sample T-Test in PythonLet us consider an example, we are given two-sample data, each containing heights of 15 students of a class. We need to check whether two different class students have the same mean height. There are three ways to conduct a two-sample T-Test in Python. Method 1: Using Scipy libraryScipy stands for scientific python and as the name implies it is a scientific python library and it uses Numpy under the cover. This library provides a variety of functions that can be quite useful in data science. Firstly, let’s create the sample data. Now let’s perform two sample T-Test. For this purpose, we have ttest_ind() function in Python.
Note that by default equal_var is True Before conducting the two-sample T-Test we need to find if the given data groups have the same variance. If the ratio of the larger data groups to the small data group is less than 4:1 then we can consider that the given data groups have equal variance. To find the variance of a data group, we can use the below syntax,
Python3
Output:  Two sample T-Test Here, the ratio is 12.260 / 7.7275 which is less than 4:1. Performing Two-Sample T-Test Python3
Output: Performing Two-Sample T-Test Analyzing the result: Two sample t-test has the following hypothesis:
Here, since the p-value (0.53004) is greater than alpha = 0.05 so we cannot reject the null hypothesis of the test. We do not have sufficient evidence to say that the mean height of students between the two data groups is different. Method 2: Two-Sample T-Test with PingouinPingouin is a statistical-type package project that is based on Pandas and NumPy. Pingouin provides a wide range of features. The package is used to conduct the T-Test but also for computing the degree of freedoms, Bayers factor, etc. Firstly, let’s create the sample data. We are creating two arrays and now let’s perform two sample T-Test. For this purpose, we have ttest() function in the pingouin package of Python. The syntax is given below,
Note that by default equal_var is True Example: Python3
Output: Two-Sample T-Test with Pingouin Interpreting the result This is the time to analyze the result. The p-value of the test comes out to be equal to 0.523, which is greater than the significance level alpha (that is, 0.05). This implies that we can say that the average height of students in one class is statistically not different from the average height of students in another class. Also, the Cohen’s D that is obtained in a t-test is in terms of the relative strength. According to Cohen:
It implies that even if the two data groups’ means don’t differ by 0.2 standard deviations or more then the difference is trivial, even if it is statistically significant. Method 3: Two-Sample T-Test with StatsmodelsStatsmodels is a python library that is specifically used to compute different statistical models and for conducting statistical tests. This library makes use of R-style modules and dataframes. Firstly, let’s create the sample data. We are creating two arrays and now let’s perform the two-sample T-test. Statsmodels library provides ttest_ind() function to conduct two-sample T-Test whose syntax is given below,
Example: Python3
Output: Two-Sample T-Test with Statsmodels Interpreting the result: This is the time to analyze the result. The p-value of the test comes out to be equal to 0.521, which is greater than the significance level alpha (that is, 0.05). This implies that we can say that the average height of students in one class is statistically not different from the average height of students in another class. How do you code a two sample tThere are three ways to conduct a two-sample T-Test in Python.. data_group1: First data group.. data_group2: Second data group.. equal_var = “True”: The standard independent two sample t-test will be conducted by taking into consideration the equal population variances.. What is ttest_ind () in Python?Calculates the T-test for the means of TWO INDEPENDENT samples of scores. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances.
How do you do a 2 tTwo Sample t-test: Example. Step 1: Gather the sample data. Suppose we collect a random sample of turtles from each population with the following information:. Step 2: Define the hypotheses. ... . Step 3: Calculate the test statistic t. ... . Step 4: Calculate the p-value of the test statistic t. ... . Step 5: Draw a conclusion.. |
