# Simple Chi-Square

This is a simple test of assication

This test involves only four cells and is often referred to as a 2 x 2 contingency table.

This table contains two samples and both are divided into two values of a second variable.

This test tells us whether there is an association between the 2 variables

This test works by taking each of the values and comparing it with what would have been there is the null hypothesis were true. (The null hypothesesis table - no association)

We find the difference between the four values and the large the differences, the more our distributions differ from one another.

Note: The 2 sample sizes do not have to be the same size.

X2 (X squared) value is then looked up in a stats table

The degrees of freedom is the number of categories.

### Accuracy

When calculating simple chi-square the value is 0.5 is subtracted from the observed frequenceis

The incorporation of this step is known as **Yates correction**.

It is the correlation for continuity which is sometimes omitted

However it improves the accuracy of the test and produces a slightly more conservative estimate for X2

It should always be included in calculation from 2x2 contingency tables and is essential when samples are small (less than 25)

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