Chi-Square Test for Independence Examples

Explore practical examples of the chi-square test for independence across various fields.
By Jamie

Understanding the Chi-Square Test for Independence

The Chi-Square Test for Independence is a statistical method used to determine if there is a significant association between two categorical variables. This test is particularly useful in fields such as social sciences, marketing, and healthcare, where researchers seek to understand relationships between different groups or characteristics. Below are three diverse, practical examples that illustrate how the chi-square test can be applied in real-world contexts.

Example 1: Examining Gender Preference in Movie Genres

In a study conducted by a local cinema, researchers wanted to understand if there was a significant relationship between gender and preferred movie genres. They surveyed 200 individuals, recording their gender and favorite genre from a list that included Action, Comedy, Drama, and Horror.

Survey Results:

Genre Male Female Total
Action 40 20 60
Comedy 30 50 80
Drama 20 30 50
Horror 10 0 10
Total 100 100 200

To test for independence, the researchers formulated the following hypotheses:

  • Null Hypothesis (H0): Gender and movie genre preference are independent.
  • Alternative Hypothesis (H1): Gender and movie genre preference are not independent.

Using the chi-square formula, they calculated the expected counts for each cell and then computed the chi-square statistic. The result showed a chi-square value of 32.4 with a p-value less than 0.01, indicating a significant association between gender and movie genre preference.

Notes:

  • Variations could include testing different age groups or geographic locations.

Example 2: Analyzing Customer Satisfaction Based on Store Type

A retail chain wanted to assess whether customer satisfaction levels were dependent on the type of store (Online vs. Physical). They distributed a satisfaction survey to 300 customers, asking them to rate their satisfaction on a scale of Poor, Fair, Good, and Excellent.

Survey Results:

Store Type Poor Fair Good Excellent Total
Online 20 30 50 40 140
Physical 10 20 80 50 160
Total 30 50 130 90 300

The researchers set up their hypotheses:

  • Null Hypothesis (H0): Customer satisfaction is independent of store type.
  • Alternative Hypothesis (H1): Customer satisfaction is dependent on store type.

After calculating the expected frequencies and the chi-square statistic, they found a chi-square value of 12.7 with a p-value of 0.002. This result suggested that customer satisfaction levels are indeed influenced by the type of store.

Notes:

  • This example can be expanded by including more store types or additional satisfaction metrics.

Example 3: Investigating Health Condition and Exercise Frequency

A public health organization conducted a survey to determine if there was a relationship between individuals’ health conditions (Healthy, Pre-Existing Condition, Chronic Condition) and their frequency of exercise (None, Occasionally, Regularly). They collected data from 250 participants.

Survey Results:

Health Condition None Occasionally Regularly Total
Healthy 20 40 50 110
Pre-Existing Condition 30 50 30 110
Chronic Condition 40 20 10 70
Total 90 110 90 250

The hypotheses were set as follows:

  • Null Hypothesis (H0): Health condition and exercise frequency are independent.
  • Alternative Hypothesis (H1): Health condition and exercise frequency are not independent.

Calculating the expected counts and the chi-square statistic, they found a chi-square value of 25.6 with a p-value of 0.001, indicating a significant relationship between health condition and exercise frequency.

Notes:

  • Future studies could include additional factors such as age or gender to see how they impact the relationship.

These examples of the chi-square test for independence demonstrate its practical application across various fields, helping researchers understand relationships between categorical variables effectively.