5.1. Chi-square Distribution

Question 1

Chi-squared distribution to calculate…

Answer 1

Confidence interval estimates of the population variance.

Compare actual observations with expected values.

Test for an association between two variables.

Question 2

Has set properties…

Answer 2

Defined by degrees of freedom.

Is always negative.

Is skewed to the right.

Becomes more symmetric as the degrees of freedom (the sample size - 1) increases.

Question 3

Goodness of fit test used to…

Answer 3

Test whether outcome frequencies follow a specified distribution.

Compare observed values with expected values.

Question 4

Test for independence…

Answer 4

If the cross-tabulation of the frequency of two variables is available, the chi-square tests can also be used to test for the association between two variables.

For example, boys and girls and their preferences on soft drinks.

Question 5

Issues with chi-square testing…

Answer 5

Expected values must be greater than 5 and therefore we may need to combine rows and / or columns to generate a result.

The test should not be carried out using proportions or percentages, otherwise important information on sample size would be lost.