Chi-squared tests

A Chi-squared test, ?2 test (pronounced “kai squared”, notice that the letter is not an X, but the Greek letter ? ) is a statistical method to estimate the variability between observed data from an experiment and the expected data (or theoretical data).

We look at how close the observed data are to the expected ones.

The test is always carried out based on a hypothesis, called the null hypothesis, H0. An alternative hypothesis, H1should also be stated.

The null hypothesis normally states that 1) “data follows the expected distribution” (chi-squared Goodness-of-fit), or 2) “there is no correlation between the two variables” (chi-squared test of independence). See later in this paper for an explanation of the two different types of tests.

Expected data must be calculated, based on the assumption that the null hypothesis is correct.

To make sure that the sample size, n is big enough the expected value in each category must be equal to or greater than 5

Deviations between the observed data and the expected data must be calculated, using the formula: observed data-expected data2expected data. The sum of these deviations, ?2 gives the test statistic.

The degrees of freedom must be calculated – this is the number of independent values, which are free to vary when estimating statistical parameters.