In statistical analysis, the chi-square test is a powerful tool that helps us determine the relationship between categorical variables. It is used to compare observed frequencies with expected frequencies and assess whether there is a significant association between the variables. However, it is important to understand which type of data is suitable for chi-square analysis.

## Qualitative Data

Chi-square analysis is most commonly used for qualitative or categorical data. This includes variables that can be divided into distinct categories or groups. For example, data on gender (male/female), occupation (doctor/engineer/teacher), or preferred mode of transportation (car/bus/train) are all examples of qualitative data.

## Independence Assumption

One of the key assumptions for conducting a chi-square test is independence. This means that the observations in each category should be independent of each other.

In other words, the frequency in one category should not be influenced by the frequency in another category. If this assumption is violated, then chi-square analysis may not provide accurate results.

### Example 1:

Suppose we want to study the relationship between smoking habits (smoker/non-smoker) and lung cancer diagnosis (diagnosed/not diagnosed). We collect data from a sample of individuals and create a contingency table that shows the number of individuals falling into each category.

Lung Cancer Diagnosed | Lung Cancer Not Diagnosed | |
---|---|---|

Smoker | 50 |
150 |

Non-Smoker | 30 |
170 |

In this example, we can use chi-square analysis to determine whether there is a significant association between smoking habits and lung cancer diagnosis. Since both variables are qualitative, they are suitable for chi-square analysis.

### Example 2:

Now let’s consider a different scenario where we want to analyze the relationship between age groups (18-25/26-40/41-60) and preferred social media platform (Facebook/Twitter/Instagram).

‘

18-25 | 100 |
80 |
120 |

26-40 | 80 |
100 |
90 |

41-60 | 70 |
50 |