A one sample t-test is used to determine whether or not the mean of a population is equal to some value. Show
This tutorial explains how to conduct a one sample t-test in Python. Example: One Sample t-Test in PythonSuppose a botanist wants to know if the mean height of a certain species of plant is equal to 15 inches. She collects a random sample of 12 plants and records each of their heights in inches. Use the following steps to conduct a one sample t-test to determine if the mean height for this species of plant is actually equal to 15 inches. Step 1: Create the data. First, we’ll create an array to hold the measurements of the 12 plants: data = [14, 14, 16, 13, 12, 17, 15, 14, 15, 13, 15, 14] Step 2: Conduct a one sample t-test. Next, we’ll use the ttest_1samp() function from the scipy.stats library to conduct a one sample t-test, which uses the following syntax: ttest_1samp(a, popmean) where:
Here’s how to use this function in our specific example: import scipy.stats as stats #perform one sample t-test stats.ttest_1samp(a=data, popmean=15) (statistic=-1.6848, pvalue=0.1201) The t test statistic is -1.6848 and the corresponding two-sided p-value is 0.1201. Step 3: Interpret the results. The two hypotheses for this particular one sample t-test are as follows: H0: µ = 15 (the mean height for this species of plant is 15 inches) HA: µ ≠15 (the mean height is not 15 inches) Because the p-value of our test (0.1201) 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 for this particular species of plant is different from 15 inches. Additional ResourcesHow to Conduct a Two Sample T-Test in Python In this Python tutorial, we will learn about the “Python Scipy Ttest_ind” to evaluate one or more populations’ means through hypothesis testing and how to implement it using Python Scipy. Additionally, cover the following topics. Nội dung chính
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What is a T-test in the StatisticWhen comparing the means of two groups and their relationships, a t-test is an inferential statistic used to assess whether there is a significant difference. When data sets have a normal distribution and unknown variances, t-tests are utilized. When evaluating a hypothesis, the t-test uses the t-statistic, the values of the t-distribution, and the degrees of freedom to assess statistical significance. The t-test establishes the problem statement mathematically by taking a sample from each of the two sets. The two means being equal is taken as the null hypothesis. Three essential data values are needed to calculate a t-test. They consist of the mean difference, the standard deviation of each group, and the total number of data values for each group, as well as the difference between the mean values from each data set. The difference’s effect on chance and whether it is outside that range of chance are both determined by this comparison. The t-test investigates if the difference between the groups is a genuine difference in the study or merely a chance difference. In this tutorial, we will compute the T-test of the independent samples using the method of Python Scipy. Also, check: Python Scipy Stats Norm To compute the T-test using the means of two independent scoring samples. The Python Scipy has a method The syntax is given below.
Where the parameters are:
The method Let’s take an example and compute the T-test of the independent samples by following the below steps: Import the required libraries using the below python code.
Define random number generator using
Now perform the T-test on the samples with the same means using the below code. Python Scipy ttest_indHere the ttest_ind returns two values, a statistic = 0.295 and pvalue = 0.76. Read: Python Scipy Mann Whitneyu Python Scipy ttest_ind alternativeThe parameter The alternative parameter accepts the following options.
Let’s understand with an example how to perform the T-test with an alternative hypothesis by following the below steps: Import the required libraries or methods using the below python code.
Create a sample using the below code.
Apply the T-test with an
alternative hypothesis equal Python Scipy ttest_ind alternative two sided Again apply the T-test with an alternative hypothesis equal to Now again, perform the T-test with an alternative hypothesis equal to This is how to use the alternative hypothesis with the help of Python SciPy ttest_ind. Read: Python Scipy Eigenvalues Python Scipy ttest_ind nanThe method
Let’s see with examples how to handle the nan values in arrays or samples while performing the T-test. Import the required methods or libraries using the below python code.
Generate data with nan values using the below code.
Perform the T-test on the data with nan_policy equal to Python Scipy ttest_ind nan raise Again perform the T-test with nan_policy equal to
Python Scipy ttest_ind nan omitAt last, perform the T-test with nan_policy equal to Python Scipy ttest_ind nanThis is how to handle the nan values within the sample while computing the T-test using the method Read: Python Scipy Stats Mode Python Scipy ttest_ind outputThe method Using these two values, we determine the significance of the means of two samples. To know about the method Let’s see with an example and compute the T-test by following the below steps: Import the required libraries or methods using the below python code.
Generate two sample data using the below code.
Perform the T-test to get the two values that we have discussed above. Python Scipy ttest_ind outputThis is how to perform the T-test on the sample and get the output to determine the significance of the sample. Read: Python Scipy Minimize Python Scipy ttest_ind axisThe The provided 2-dimensional array has two axes, one that runs vertically across rows is axis 1 and the other that runs horizontally across columns is axis 0. Here we will see an example of how to compute the T-test along the specified axis of data by following the below steps: Import the required libraries or methods using the below python code.
Generate sample data using the below code.
Perform the T-test on the whole array which is by default.
Now compute the T-test on the specified axis of the data using the below code. Python Scipy ttest_ind axisThis is how to compute the T-test along the specified axis of the given array or sample using the method Read: Python Scipy Exponential Python Scipy ttest_ind equal_varIf we have data samples with equal variances, then what we will do in that case?, We will use the
parameter When there is the same number of samples in each group or when the variance of the two data sets is comparable, the identical variance t-test, an independent t-test, is used. The parameters accept two values Import the required libraries or methods using the below code.
Generate data with equal variance using the below code.
Compute the T-test on the above sample with equal variances using the below code. Python Scipy ttest_ind equal_var This is how to compute the T-test of the sample with equal means using the method Read: Scipy Find Peaks Python Scipy ttest_ind statisticThe method Let’s do an example by following the below steps: Import the required libraries or methods using the below python code.
Generate sample data using the below code.
Compute the T-test and get the Python Scipy ttest_ind statisticIn the above output, Read: Python Scipy Special Module Python Scipy ttest_ind degrees of freedomFirst, we are going to know about “What are degrees of freedom?“, The number of independent data points used to calculate an estimate is referred to as the degree of freedom of the estimate. It’s not the same as the sample’s sample size. We must deduct 1 from the total number of items to obtain the degrees of freedom for the estimate. Imagine we were looking for the average weight loss for a diet. One option is to utilise 50 persons with df = 49, or 10 people with 9 degrees of freedom (10 – 1 = 9). The amount of values in a data collection that is free to change is another way to think about degrees of freedom. “Free to change” – what does that mean? The mean (average) is used in the following example: Choose a group of numbers with an average (mean) of 10, Like we could choose from the following sets of numbers: 7, 9, 11, 2, 10, 9, or 4, 8, 12. The third number in the set is fixed once we’ve selected the first two. In other words, we are unable to select the third piece from the group. The first two numbers are the only ones that can change. We can choose 7 + 9 or 2 + 10, but once we’ve made our choice, we must select a specific number that will yield the desired mean. Therefore, a set of three numbers has TWO degrees of freedom. Also, take a look at some more Python SciPy tutorials.
So, in this tutorial, we have learned about the “Python Scipy ttest_ind” and covered the following topics.
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