Chi-square tests are statistical methods used to determine whether there is a significant association between categorical variables. They are particularly useful in analyzing frequency data and can help researchers draw conclusions from sample data to infer about the larger population. Below are three practical examples of chi-square tests in inferential statistics.
In a marketing study, a company wants to understand whether there is a relationship between gender and preference for a new beverage. They survey a sample of 200 individuals, recording their gender and their preferred beverage type.
To determine if there is a significant association between gender and beverage preference, a chi-square test can be applied. The null hypothesis (H0) states that gender and beverage preference are independent, while the alternative hypothesis (H1) posits that they are not.
The test calculates the expected frequencies based on the assumption of independence and compares them with the observed frequencies. After performing the calculations, the chi-square statistic is found to be 6.45 with a p-value of 0.04.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis, indicating that there is a significant association between gender and beverage preference.
A sociologist is interested in whether educational attainment affects employment status. They collect data from a sample of 300 individuals categorized by their highest education level (high school, bachelor’s, master’s) and their employment status (employed, unemployed).
To analyze this data, the sociologist conducts a chi-square test where the null hypothesis states that educational attainment and employment status are independent. After calculating the expected frequencies and performing the test, the chi-square statistic is determined to be 15.23 with a p-value of 0.001.
Given that the p-value is significantly lower than the 0.05 threshold, we reject the null hypothesis. This indicates a strong association between educational attainment and employment status, suggesting that higher education tends to correlate with higher employment rates.
A digital marketing firm wants to analyze whether there’s a difference in social media platform preference across various age groups. They survey 400 individuals categorized into age groups (18-24, 25-34, 35-44) and their preferred platform (Facebook, Instagram, Twitter).
Using a chi-square test, the null hypothesis claims no relationship between age group and platform preference. After performing the necessary calculations, the chi-square statistic comes out to be 22.58 with a p-value of 0.0001.
Since the p-value is much lower than the established significance level, we reject the null hypothesis, concluding that age significantly influences social media platform preference.