A Chi-Square Goodness of Fit Test is used to determine whether or not a categorical variable follows a hypothesized distribution.
This tutorial explains how to perform a Chi-Square Goodness of Fit Test in Python.
Example: Chi-Square Goodness of Fit Test in Python
A shop owner claims that an equal number of customers come into his shop each weekday. To test this hypothesis, a researcher records the number of customers that come into the shop in a given week and finds the following:
- Monday: 50 customers
- Tuesday: 60 customers
- Wednesday: 40 customers
- Thursday: 47 customers
- Friday: 53 customers
Use the following steps to perform a Chi-Square goodness of fit test in Python to determine if the data is consistent with the shop owner’s claim.
Step 1: Create the data.
First, we will create two arrays to hold our observed and expected number of customers for each day:
expected = [50, 50, 50, 50, 50] observed = [50, 60, 40, 47, 53]
Step 2: Perform the Chi-Square Goodness of Fit Test.
Next, we can perform the Chi-Square Goodness of Fit Test using the chisquare function from the SciPy library, which uses the following syntax:
chisquare[f_obs, f_exp]
where:
- f_obs: An array of observed counts.
- f_exp: An array of expected counts. By default, each category is assumed to be equally likely.
The following code shows how to use this function in our specific example:
import scipy.stats as stats #perform Chi-Square Goodness of Fit Test stats.chisquare[f_obs=observed, f_exp=expected] [statistic=4.36, pvalue=0.35947]
The Chi-Square test statistic is found to be 4.36 and the corresponding p-value is 0.35947.
Note that the p-value corresponds to a Chi-Square value with n-1 degrees of freedom [dof], where n is the number of different categories. In this case, dof = 5-1 = 4. You can use the Chi-Square to P Value Calculator to confirm that the p-value that corresponds to X2 = 4.36 with dof = 4 is 0.35947.
Recall that a Chi-Square Goodness of Fit Test uses the following null and alternative hypotheses:
- H0: [null hypothesis] A variable follows a hypothesized distribution.
- H1: [alternative hypothesis] A variable does not follow a hypothesized distribution.
Since the p-value [.35947] is not less than 0.05, we fail to reject the null hypothesis. This means we do not have sufficient evidence to say that the true distribution of customers is different from the distribution that the shop owner claimed.
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In this article, we are going to see how to Perform a Chi-Square Goodness of Fit Test in Python
The Chi-Square Goodness of fit test is a non-parametric statistical hypothesis test that’s used to determine how considerably the observed value of an event differs from the expected value. it helps us check whether a variable comes from a certain distribution or if a sample represents a population. The observed probability distribution is compared with the expected probability distribution.
null hypothesis: A variable has a predetermined distribution.
Alternative hypotheses: A variable deviates from the expected distribution.
Example 1: Using stats.chisquare[] function
In this approach we use stats.chisquare[] method from the scipy.stats module which helps us determine chi-square goodness of fit statistic and p-value.
Syntax: stats.chisquare[f_obs, f_exp]
parameters:
- f_obs : this parameter contains an array of observed values.
- f_exp : this parameter contains an array of expected values.
In the below example we also use the stats.ppf[] method which takes the parameters level of significance and degrees of freedom as input and gives us the value of chi-square critical value. if chi_square_ value > critical value, the null hypothesis is rejected. if chi_square_ value