Chi-square

Question 1

What is chi-square?

Answer 1

Test of association - variables of interest are categorical
Non-parametric

Question 2

What are contingency tables?

Answer 2

Shows how data are distributed across variables
- observed frequencies are the numbers in the cells - represent the frequency of people who fall in each combination of levels of the variable.
Column and row totals should add up to N

Question 3

What kind of contingency table has 2 variables and 2 levels?

Answer 3

2x2 design

Question 4

How can the association between variables be eyeballed?

Answer 4

Descriptive statistics
- do we observe roughly the frequencies we would expect if there were no association
OR
Are our observed frequencies different from expected frequencies?
Need to look at percentage, rather than N of ppts in each category (what % of each category would we expect to fall into each category if there is no association between each variable?)

Question 5

What are expected values?

Answer 5

Values you expect to see in each cell if no association exists between the 2 variables (null hypothesis = true)
Want to know these for each individual cell

Question 6

What is the equation for expected values?

Answer 6

(row total x column total) / grand total

Question 7

What is the equation for chi-square?

Answer 7

X2= ∑ (O-E)squared/E
Square each O-E value in contingency table
Divide each result by expected value
Add up all results

Question 8

What value should Chi-square always be?

Answer 8

0+ - if not 0, an association exists
- Check for stat sig

Question 9

How do you check statistical significance?

Answer 9

p-value
need to know df
df = (R-1)(C-1)
R = number of rows
C - number of columns

Question 10

What is an effect size?

Answer 10

Strength and association

Question 11

What are the two effect size measures for chi-square?

Answer 11

Phi-coefficient
Cramer’s V
- both give values between 0-1
and take sample size into account

Question 12

When should you report phi?

Answer 12

2x2 contingency tables

Question 13

When should you report Cramer’s V?

Answer 13

For anything other than 2x2 contingency tables

Question 14

How should you interpret effect size? (Phi and Cramer’s V)

Answer 14

• check value against standardised cutoffs to judge magnitude of effect
• value should be equal to or greater than that given on table to fall into that category
• Values answer the question: what is the association between the 2 variables as a percentage of their max possible variation?

Question 15

How should you report chi-square?

Answer 15

eg. χ2 (1, N = 180) = 30.13, p < .001, φ = .4

df = degrees of freedom

χ2= chi-square statistic

p= significance value

φ = Phi OR V = Cramer’s V (effect size)

Question 16

What assumptions should be met before running chi-square?

Answer 16

1. Both variables are categorical
2. Categories are mutually exclusive
3. No cells in contingency table should have expected frequency of lower than 1
4. More than 80% of cells should have an expected frequency of 5+

Question 17

What does it mean for categories to be mutually exclusive?

Answer 17

Ppts cant be in more than 1 category of each variable

Question 18

What if the expected count is less than 5? (4th assumption is not met)

Answer 18

• If table is 2x2, read significance from Fisher’s exact test (corrects the fact that there is an expected count of less than 5 in one of the cells) - calculates exact probability.
• If not met for larger tables, consider pooling categories, use exact p-value for persons chi-square, or use other analyses such as likelihood ratio