Biology Fieldwork

A Level

Chi squared

Sleeping in the sunshine

4. Chi squared

Chi-squared test

Chi squared is a statistical test that is used either to test whether there is a significant difference, goodness of fit or an association between observed and expected values.

`chi^2 = ∑ (O-E)^2 / E`

The chi squared test can only be used if

  • the data are in the form of frequencies in a number of categories (i.e. nominal data).
  • there are more than 20 observations in total
  • the observations are independent: one observation does not affect another

There are 3 steps to take when using the chi squared test

Step 1. State the null hypothesis

There is no significant association between _______ and _______

Step 2. Calculate the chi squared statistic

`chi^2 = ∑ (O-E)^2 / E`

`chi^2` = chi squared statistic

`O` = Observed values

`E` = Expected values

Step 3. Test the significance of the result

Compare your calculated value of `chi^2` against the critical value for `chi^2` at a confidence level of 95% / significance value of P = 0.05, and appropriate degrees of freedom.

`"Degrees of freedom" = ("number of rows" – 1) xx ("number of columns" – 1)`

If Chi Squared is equal to or greater than the critical value REJECT the null hypothesis. There is a SIGNIFICANT difference between the observed and expected values.

If Chi Squared is less than the critical value, ACCEPT the null hypothesis. There is NO SIGNIFICANT difference between the observed and expected values.