analysing categorical data (chi-squared)

Question 1

How do we analyse categorical data?

Answer 1

-Predict category that someone falls into
-Create contingency table and perform chi-squared test of the data

Question 2

What is a contingency table?

Answer 2

-Table of frequencies for how often an observation occurs in a category
-Categories have to be mutually exclusive and exhaustive

Question 3

Describe the use of a chi-squared test

Answer 3

-Calculates how often an observation falls into a category based on how many were expected by chance

Question 4

What is the use of the null hypothesis in this situation?

Answer 4

-Means that the frequencies observed were expected by chance

Question 5

What is the use of the experimental hypothesis in this situation?

Answer 5

-Means that the frequencies observed reflect real differences in categories

Question 6

What 2 assumptions can be made?

Answer 6

1: Independence
-Each person can only contribute to one cell of a contingency table
2: Expected frequencies
-All expected counts should be greater than 1 and no more than 20% of expected counts should be less than 5-If violated, power can be lost

Question 7

What can we do to prevent loss of power?

Answer 7

-Use an exact test instead e.g. fisher’s or MLR
-Collapse/remove data across one variable
-Collapse levels of one variable
-Collect more data

Question 8

What are the 3 steps for a chi-squared formula?

Answer 8

1: Calculate expected frequencies
2: Calculate chi-squared value based on observed and expected
3: Compare chi-squared value against critical value

Question 9

What differs if you have 2 IV’s?

Answer 9

-Difference will be calculating the expected values in each case
-Have to calculate expected frequencies of specific cells

Question 10

What is a binomial test?

Answer 10

-Compares observed and expected frequencies for variable with only 2 levels
-E.g. Are there more people in the sample from USA than what we would expect by chance?