# What is Chi-Square Test? Formula, Examples & Characteristics

Are you curious about the role of the Chi-Square test in machine learning and how it can improve your models? Feature selection is a crucial aspect of machine learning, as it involves choosing the best features out of a large set to build a model.

One effective method for tackling feature selection problems is through the use of the Chi-Square test. By examining the relationship between elements, the Chi-Square test can help you select the most important features for your model.

In this tutorial, we will dive into the Chi-Square test and its application in machine learning. Get ready to learn how to use this powerful tool to improve your models and achieve better results.

## What is Chi-Square Test?

What is Chi-Square test? or also known as Pearson’s chi-square test or the chi-squared test, is a statistical procedure used to determine the difference between observed and expected data.

It is a commonly used test in fields such as statistics, data analysis, and machine learning. The test is used to determine whether there is a correlation between two categorical variables in our data and whether the difference between these variables is due to chance or a real relationship.

This test is particularly useful for feature selection in machine learning, where it helps identify the most relevant features for a model. The Chi-Square test can also be used for hypothesis testing, where it helps determine if a relationship between variables is statistically significant.

Overall, the Chi-Square test is a powerful tool for understanding and interpreting data, and it is widely used in various fields of research and analysis.

## Chi-Square Test Formula

In a Chi-Square test, the degrees of freedom (c) represent the number of variables that can vary in the calculation. These calculations are used to determine the statistical validity of a chi-square test.

The test compares observed data with data that would be expected if a particular hypothesis were true. The degrees of freedom can be calculated to ensure that the test is statistically valid.

The observed values are the data collected during the study, while the expected values are the frequencies that are predicted based on the null hypothesis.

It is important to note that the difference between observed and expected values is used to determine if the data is due to chance or if there is a correlation between the variables.

c = Degrees of freedom

O = Observed Value

E = Expected Value

## General Requirements of Chi-Square Test

The general requirements for the Chi-Square test are: the frequency of respondents or samples used is enormous, because several Chi Square conditions can be used, namely:

1. There are no cells with a real frequency value, called the Actual Count (F0) of 0 (Zero).

2. If the form of the contingency table is 2 X 2, then there cannot be only 1 cell with an expected frequency or an expected count (“Fh”) of less than 5.

3. If the form of the table is more than 2 x 2, for example, 2 x 3, then the number of cells with an expected frequency of less than 5 cannot be more than 20%.

#### Characteristics of Chi-Square

• The Chi-Square value is always positive.
• There are several families of Chi-Square distributions, viz
• Chi-Square distribution with DK=1, 2, 3, etc.
• The shape of the Chi-Square distribution is positively skewed.

## Why Do You Use Chi-Square Test?

Chi-square is a statistical test that compares categorical variables from a random sample to assess whether the observed results align with the expected results. The test can be used for various purposes, including:

1. Evaluating whether the data follows a known probability distribution such as Normal or Poisson
2. Assessing the goodness of fit of a trained regression model on different data sets such as training, validation, and test data. The Chi-squared test helps to determine if the model is suitable for the data and if it can be used to make accurate predictions.

## What’s Results You Get from Chi-Square Test?

A Chi-Square test ( 2 ) is a statistical method used to analyze data and compare it to a model. The test calculates the difference between the observed data and the expected data.

To be valid, the data used in the test must be raw, randomly drawn from independent variables, and a representative sample of the population.

The Chi-Square test was introduced by Karl Pearson in 1900 for analyzing categorical data and distributions. It is also known as Pearson’s Chi-Squared Test.

Chi-Square Tests are commonly used in hypothesis testing, which involves making assumptions about a condition and then testing to see if it is true.

The test measures the discrepancy between the expected results and the actual results when the sample size and number of variables in the relationship are known.

The test uses degrees of freedom to determine if a null hypothesis can be rejected based on the number of observations made in the experiment.

The larger the sample size, the more reliable the results. It is important to note that the Chi-Square test is a powerful tool for understanding and interpreting data, and it is widely used in various fields of research and analysis.

There are two main types of Chi-Square tests namely –

### 1. Independence

The Chi-Square Test of Independence is a statistical method used to determine if there is a relationship between two sets of categorical variables.

This test is often used when the data consists of counts of values for two nominal or categorical variables and is considered a non-parametric test. A large sample size and independent observations are necessary to conduct this test.

For example:

In a movie theater, if we were to create a list of movie genres as the first variable and whether or not the movie-goers bought snacks at the theater as the second variable, we can use the Chi-Square Test of Independence to determine if there is a relationship between the movie genre and snack sales.

The null hypothesis in this case would be that there is no relationship between the movie genre and snack sales. If the test shows that the null hypothesis is true, it means that the movie genre does not have an impact on snack sales.

### 2. Goodness-of-Fit

In statistical hypothesis testing, the Chi-Square Goodness-of-Fit test is used to determine if a set of data values conforms to a specific distribution.

This test is applied when we have value counts for categorical variables. It is used to evaluate if the data is a “good enough” fit for the proposed distribution or if it is a representative sample of the entire population.

#### For example:

if we have a bag of balls with five different colors in each bag, and we know that the bag should contain an equal number of balls of each color. We can use the Chi-Square Goodness-of-Fit test to test the idea that the proportions of the five colors of balls in each bag must be exact. This test will help us determine if the data aligns with the expected distribution or not.