Week 4- Associations between categorical variables

Question 1

What is a categorical variable

Answer 1

Categorical variables represent types of data which may be divided into groups. Examples of categorical variables are race, sex, age group, and educational level

Question 2

What is chi-square- definition

Answer 2

Non-parametric tests or inference for categorical data

Question 3

What is chi-square

Answer 3

• Measures the relationship between 2 or more nominal variables, questioning whether observations are contingent upon another categorical variable
• Tests whether frequency counts can be expected by chance or whether there’s a relationship between the categorical variables

Question 4

Examples of chi-square. Testing whether2 nominal variables are associated

Answer 4

• Is gender associated with preferred subject?
• Is ownership of a dog associated with residence?
• Is smoking associated with drinking

Question 5

Hypothesis testing

Answer 5

• Null- there is no association between the 2 variables
• Alternative- the two variables are associated

Question 6

Steps for constructing chi-squared by hand

Answer 6

1. Note the observed frequencies in each cell in a contingency table
2. Calculate the expected frequency for each cell by multiplying the two relevant
   marginal totals (the row total and the column total) for that cell and divide by the
   total number of participants in the sample.
3. Calculate chi-square (see formula above) by:
   a. Calculating the difference between the observed and the expected frequency
   for each cell and squaring that number;
   b. Dividing the result by the expected frequency for that cell.
4. Add up the results for all cells to acquire chi-square.
5. Determine the degrees of freedom by multiplying the number of columns minus 1
   by the number of rows minus 1 (see formula above).
6. Look up the significance of chi-square in the table below

Question 7

Assumptions of chi-squared

Answer 7

-Independence
> Data cannot be related (must use distinct nominal categories)- cannot fall into both categories. Between subjects
- Raw frequencies
> Should be conducted on raw frequencies not percentages
- Sample/ cell size
> No expected cell frequencies should be less than 1 and no more than 20% should be less than 5
- If don’t meet this can collapse categories

Question 8

Other important things to note when reporting chi-squared

Answer 8

• Percentages
  > Chi-square should be conducted on raw frequencies not percentages. But percentages are useful to report in addition to these raw frequencies
• Cramer’s V
  > Measure of effect size
• Variance accounted for
  > We can square the effect size to see how much variance one variable can be accounted for by other variables

Question 9

What are standardised residuals

Answer 9

• Help determine which cells are contributing to the ‘significant association’
• They’re z scores indicating how many SD’s above or below an expected count an observed count is

Question 10

What are degrees of freedom?

Answer 10

-the number of independent pieces of info that went into calculating the estimate
e.g. 9, 10 and mean of 30, other number must be 11

Question 11

Issues with chi-square

Answer 11

• raw frequency counts NOT percentages
  AND
• Larger contingency tables can be difficult to interpret
• So can use
  > Standardised residuals to determine main contributors
  > Partitioning- carry out multiple 2 times 2 chi-squares
  > Combine categories