Chi-Square Test of Independence
Key Point
The chi-square test is used to determine whether there is a statistically significant association between two categorical variables.
When to Use Chi-Square
The chi-square test of independence is appropriate when:
- 1.
Both variables are categorical (nominal or ordinal)
- 2.
Data are arranged in a contingency table (rows × columns)
- 3.
You want to test the null hypothesis that the two variables are independent
- 4.
Expected frequency in each cell is ≥ 5 (or ≥ 1 in <20% of cells)
Test Statistic
χ2=∑E(O−E)2
where O = observed frequency and E = expected frequency.
Contingency Table Example
| Disease Present | Disease Absent | Total |
|---|
| Exposed | a | b | a+b |
| Not Exposed | c | d | c+d |
| Total | a+c | b+d | n |
High-YieldNEET PG
The chi-square test produces a p-value; if p < 0.05, reject the null hypothesis of independence.
Why Other Options Are Wrong
| Option | Why Incorrect |
|---|
| Paired t-test | Requires continuous data and paired/matched observations |
| One-way ANOVA | Compares means of 3+ groups with continuous outcome |
| Pearson correlation | Measures linear relationship between two continuous variables |
Mnemonic
CAT = Categorical × Another Thing (categorical) → Chi-square
Clinical Pearl
If expected frequencies are too low (<5), use Fisher's exact test (for 2×2 tables) instead of chi-square.
