Chi-Square Test
The chi-square test is a statistical method used to determine whether there is a significant association between two categorical variables. It is a non-parametric test, meaning it does not rely on assumptions about the distribution of the data. Instead, it assesses whether there is a significant difference between the observed frequencies and the frequencies that would be expected under a specified null hypothesis.
When to Use the Chi-Square Test:
The chi-square test is appropriate when analyzing categorical data to determine if there is a relationship or association between two variables. It is commonly used in various fields, including social sciences, healthcare, marketing, and education, to examine the association between variables such as gender and voting preference, treatment outcomes, or student performance across different groups.
Assumptions and Data Requirements:
The chi-square test has several assumptions and data requirements:
Independence: The observations should be independent of each other.
Categorical Data: The data should be categorical, meaning the variables are divided into distinct categories or groups.
Expected Frequencies: The expected frequencies for each category should be greater than or equal to 5 in most cells of the contingency table.
Formulating Hypotheses for Chi-Square Test:
Null Hypothesis (H0): The null hypothesis states that there is no association between the two categorical variables. In other words, the variables are independent of each other.
H0: There is no association between Variable A and Variable B.
Alternative Hypothesis (H1): The alternative hypothesis contradicts the null hypothesis and suggests that there is an association between the two categorical variables.
H1: There is an association between Variable A and Variable B.
Interpreting the Chi-Square Test:
The chi-square test results in a test statistic (χ²) and a p-value. The test statistic measures the discrepancy between the observed and expected frequencies, while the p-value indicates the probability of observing such a discrepancy by chance alone.
If the p-value is less than a predetermined significance level (e.g., 0.05), the null hypothesis is rejected, and there is evidence of a significant association between the variables.
If the p-value is greater than the significance level, the null hypothesis is not rejected, and there is insufficient evidence to conclude a significant association between the variables.
Sample Situation with Sample Data:
Suppose a researcher wants to investigate whether there is a significant association between students' majors (Science, Arts, Commerce) and their preferences for extracurricular activities (Sports, Music, Debate). The researcher collects data from a random sample of 200 students and tabulates the frequencies in a contingency table.
