Chi-squared test

Question 1

What is a chi test?

Answer 1

• Test for an association between 2 categorical variables
• Based on the chi-squared distribution with n degrees of freedom
  where n is given by (no. of rows-1) x (no. of columns-1)
• Equivalent to the z test for two proportions (where each variable
  has only 2 categories)
• Gives a P value but no direct estimate or confidence interval for
  the estimates

Question 2

What is the null hypothesis?

Answer 2

In the population where the samples come, there is no association between the two variables

Question 3

What can be calculated by the Chi test?

Answer 3

• Calculates the expected frequencies if there were no association (i.e. null hypothesis is true)
• Compares the observed frequencies with these expected values
• If the observed frequencies are very different to the expected values this provides evidence that there is an association
• The test uses a formula based on the chi-squared distribution to
  give a P value

Question 4

What are the assumptions of chi test?

Answer 4

• ‘Large sample’ test
  Rule of thumb for test to be valid:
• at least 80% of expected frequencies must be greater than 5
• For 2x2 test this will be true if all frequencies >5

If assumptions don’t hold, consider collapsing the table if multi-category, or using Fisher’s exact test

Question 5

Rules of chi squared

Answer 5

• Always use with frequencies, never use percentages for calculations
• Chi-squared test works for all size tables
• The test is usually done with a computer program – the following
  calculations are done to show how the test works

Question 6

What does the small p value mean?

Answer 6

This has degrees of freedom (3-1) x (2-1) = 2 and the P value is <0.0001
* The very small p-value provides
* strong evidence to suggest that there is an association between gender and ice cream flavour preference
* strong evidence to suggest that men and women tend to have different preferences for ice cream flavours