# R - Chi Square Test

Chi-square tests in R are statistical techniques used to assess the association between categorical variables and test whether the observed frequencies differ significantly from expected frequencies. These tests are often employed to explore relationships between variables or to determine if there is a significant deviation from expected patterns. In R, you can perform a chi-squared test using the chisq.test() function.

The chisq.test() function takes three arguments:

1. x: The data set for the first variable.
2. y: The data set for the second variable.
3. correct: A logical value indicating whether to apply Yates' correction. Yates' correction is a small adjustment that is sometimes applied to the chi-squared test to improve the accuracy of the results.

## Types of Chi-Square Tests

There are two primary types of chi-square tests in R:

### Chi-Square Test of Independence (Pearson's Chi-Square Test)

1. This test is used to examine the association or independence between two categorical variables.
2. It compares the observed frequency distribution with the expected frequency distribution under the assumption of independence.

### Chi-Square Goodness-of-Fit Test

1. This test assesses whether the observed data follows a specific theoretical distribution, such as a uniform distribution or a normal distribution.
2. It compares the observed frequencies to the expected frequencies based on the theoretical distribution.
Chi-Square Test of Independence Example:

Suppose you have data on the relationship between two categorical variables: "Smoking Status" (Smoker or Non-Smoker) and "Lung Cancer Diagnosis" (Yes or No). You want to determine if there is an association between smoking status and lung cancer diagnosis.

# Create a contingency table (cross-tabulation) data <- matrix(c(50, 100, 20, 180), nrow = 2, byrow = TRUE) colnames(data) <- c("Smoker", "Non-Smoker") rownames(data) <- c("Lung Cancer", "No Lung Cancer") # Perform a chi-square test of independence chi_sq_result <- chisq.test(data) # Print the result print(chi_sq_result)
#Output: Pearson's Chi-squared test with Yates' continuity correction data: data X-squared = 27.727, df = 1, p-value = 1.397e-07

In this example, the chisq.test() function calculates the chi-square statistic and associated p-value to test the independence of smoking status and lung cancer diagnosis. You can interpret the p-value to make conclusions:

1. If p-value < a (e.g., 0.05), you reject the null hypothesis, indicating that there is a significant association between the two variables.
2. If p-value = a, you fail to reject the null hypothesis, suggesting no significant association.
Chi-Square Goodness-of-Fit Test Example:

Suppose you want to test if the observed distribution of students' favorite colors matches a theoretical distribution based on a survey of color preferences.

# Observed data observed <- c(25, 40, 15, 20) # Expected frequencies based on a theoretical distribution expected <- c(30, 35, 20, 15) # Perform a chi-square goodness-of-fit test chi_sq_fit_result <- chisq.test(observed, p = expected / sum(expected)) # Print the result print(chi_sq_fit_result)
#Output: Chi-squared test for given probabilities data: observed X-squared = 4.4643, df = 3, p-value = 0.2155

In this example, the chisq.test() function is used to test if the observed color preferences match the expected distribution. The test calculates the chi-square statistic and associated p-value. Interpretation is similar to the independence test.

Here are some other things to keep in mind about chi-squared tests:

1. The chi-squared test is a parametric test, which means that it assumes that the data is normally distributed.
2. The chi-squared test is sensitive to the sample size. If the sample size is small, the chi-squared test may not be accurate.
3. The chi-squared test can only be used to test for independence between two categorical variables. It cannot be used to test for other types of relationships, such as causation.

### Conclusion

Chi-square tests in R are statistical methods used to analyze relationships between categorical variables and assess whether observed frequencies differ significantly from expected frequencies. These tests can be applied to test for independence between variables or to evaluate goodness-of-fit to a theoretical distribution. R provides functions like chisq.test() to perform these tests and make statistical inferences based on the results.