The chi-square test for contingency tables is a statistical method used to determine if there is a significant association between two categorical variables. It compares the observed frequencies in each category of a contingency table to the frequencies expected if there were no association. This test is widely used in fields such as social sciences, marketing, and health research.
In a study investigating the relationship between education level and job satisfaction among employees at a large corporation, researchers collected data from 400 employees, categorizing them by their education level (High School, Bachelor’s, Master’s) and their job satisfaction (Satisfied, Neutral, Dissatisfied).
| Education Level | Satisfied | Neutral | Dissatisfied | Total |
|---|---|---|---|---|
| High School | 50 | 30 | 20 | 100 |
| Bachelor’s | 80 | 60 | 20 | 160 |
| Master’s | 70 | 30 | 40 | 140 |
| Total | 200 | 120 | 80 | 400 |
To perform the chi-square test, the observed frequencies are compared to the expected frequencies calculated under the null hypothesis of no association. After calculating the chi-square statistic, researchers found a significant association between education level and job satisfaction.
Note: Variations of this study could include different job sectors or additional demographic factors to explore further correlations.
A cinema chain conducted a survey to understand if there is a relationship between gender and preference for different movie genres (Action, Comedy, Drama). They surveyed 300 individuals, resulting in the following contingency table:
| Gender | Action | Comedy | Drama | Total |
|---|---|---|---|---|
| Male | 70 | 50 | 30 | 150 |
| Female | 40 | 80 | 30 | 150 |
| Total | 110 | 130 | 60 | 300 |
By applying the chi-square test to this table, researchers could determine if gender influences movie preferences. The results indicated a significant relationship, suggesting that males tend to prefer action films more than females.
Note: This example could be expanded by adding age groups or geographic locations to analyze trends across different demographics.
A company launched two different marketing strategies (Social Media and Email Campaign) for two products (Product A and Product B). They tracked the sales over a month, resulting in the following data:
| Marketing Strategy | Product A | Product B | Total |
|---|---|---|---|
| Social Media | 120 | 80 | 200 |
| Email Campaign | 100 | 100 | 200 |
| Total | 220 | 180 | 400 |
Using the chi-square test, the company assessed if the marketing strategy had a significant effect on the sales of the two products. The analysis revealed that the social media campaign significantly outperformed the email campaign for Product A but not for Product B.
Note: Further analysis could involve testing different marketing channels or seasonal effects to refine the marketing strategy.