Chi-Square Test: Uncovering Relationships in Categorical Data

Association between two categorical variables: Chi-Square We must apply the chi square test for the association when analyzing relationships between two categorical variables because we cannot utilize the same correlation approach for continuous variables. To determine how likely it is that an observed distribution is the result of chance, researchers use the Chi-square test. The degree to which the observed data distribution resembles the distribution that would be anticipated if the variables were independent is measured. Important Information Let's review a few key aspects before moving on to an example. The Chi-square test is a statistical analysis that assesses the likelihood that the observed data happened by chance by comparing observed and expected data. This test contrasts the values of the observed data with what the model predicts if the data were randomly distributed across the various categories. The chance that the variables are dependent increases whenever the observed data does not fit inside the model of the expected values, disproving the null hypothesis. The Chi-square just indicates that there is a relationship between the two variables. It does not specify what kind of relationship there is. The data analyst must determine the nature of the link between the two variables. Using the Cars Dataset as an Example Let's examine the association between fuel type and aspiration, two categorical variables, using the automobiles dataset. Gas or diesel is the only two options for the vehicle's fuel, and either a normal or turbo engine is desired. We will discover the observed numbers of autos in each group to accomplish this. This may be accomplished by using the pandas package to create a crosstab. A table displaying the relationship between two or more variables is called a crosstab. The crosstab is also referred to as a contingency table when it just displays the association between two category variables. In our case, the crosstab or contingency table displays the counts for each group, including standard cars running on diesel, standard cars running on gas, turbocharged cars running on diesel, and turbocharged cars running on gas. How to Calculate Expected Values The following is the chi-square formula: “The square root of the observed value, or the numbers in each group, multiplied by the predicted value, divided by the observed value”. Expected values are based on the provided totals; in other words, what can we predict the values of individual cells if we were unaware of the observed values? The predicted value of a normal car with diesel is determined by multiplying the row total of 20 by the column total of one 168 and dividing the result by the sum of 205. You will receive 16.39 after doing this. If we apply the same calculation to turbocharged cars running on gas, the result is 33.39. To get at this result, we multiply the row total 185 by the column total 37 and divide it by the sum 250. We may obtain these values by applying the same process to each of them. We will obtain the same values as the totals as the observed values if we add the row totals, column totals, and grand total. Results of the Chi-Square Test Interpreted Returning to the calculation, the chi-square value would be 29.06 if we added up all the observed values and subtracted the predicted values, then divided by the expected value. We check that the degree of freedom equals one row on the chi-square table and locate the value that is most similar to 29.6. Now, we can see that a p-value of less than 0.05 will be between 29.6. As a result, we can state that the p-value is less than 0.05. We may infer from the chi-square test we conducted in the preceding slides that there is a connection between fuel type and ambition. This is because the p-value we found was less than 0.05, which indicates that we reject the idea that the two variables are independent. The chi square contingency function from the SciPy statistics package can be used to run this test in Python. This function will return the degree of freedom, the p-value, and the chi-square test result (29.6, extremely near to 0). (1). Python provides the precise p-value as opposed to the chi-square table, which merely provides a range of p-values. The anticipated values, which we had previously estimated manually, are also visible. We can rule out the null hypothesis because the p-value is so close to zero and draw the conclusion that there is evidence of a link between fuel type and aspiration.