The Chi-square independence test is used to test whether 2 categorical variables, each having 2 or more categories, are dependent or independent of each other.

- The
*null hypothesis H*states that the 2 variables are independent (i.e. knowing the value of one does not tell us anything about the other)_{0} - The
*alternative hypothesis H*states that the 2 variables are dependent (i.e. knowing the distribution of one helps us predict the other)_{1}

So after running the Chi-square independence test:

**If the p-value is < 0.05:**then we reject the null, so the data provide convincing evidence that the 2 variables are associated.**If the p-value is > 0.05:**then we cannot reject the null hypothesis, so we cannot rule out the possibility that the 2 variables are independent.

## Information that should be reported

### Reporting the use of a Chi-square independence test

When reporting a Chi-square independence test, the following information should be mentioned in the METHODS section:

- the
**assumptions**of the Chi-square test (the observations should be drawn independently from the population, and each cell must have at least 5 cases in 80% of the cells and no cell should have less than 1) - the
**objective**of the test - the
**threshold for statistical significance**(generally set at 0.05).

#### Example:

In order to examine the relationship between Gender (Male, Female) and Sunscreen use (Never, Sometimes, Always), we used a Chi-square independence test after verifying its assumptions (the sample consisted of independent observations, and the count in each cell was larger than 5).

A p-value less than 0.05 will indicate statistical significance.

### Reporting the output of a Chi-square independence test

And the following should be mentioned in the RESULTS section:

- the results of the Chi-square test:
- the value of the
**Chi-square statistic** - the
**degrees of freedom**(equal to (the number of categories of the first variable – 1) * (the number of categories of the second variable -1)) - and the
**p-value**

- the value of the
- the
**consequence/interpretation**of these results **Cramer’s V**or any other strength test, if used.

#### Example:

The Chi-square independence test showed that gender proportions differed significantly between different levels of sunscreen use (

χ^{2}= 12.3; df = 2; p = 0.02), which means that males and females showed different behavior regarding the application of sun protection.

## Further reading

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