week 11 - Chi-Squared test

Question 1

What is the Chi-Square?

Answer 1

• a test of association
• needed when the variables of interest are categorical

Question 2

Correlations are used with scale variables, what variable is Chi-Square used with?

Answer 2

used with categorical variables

Question 3

A correlation is a parametric statistic, what statistic is chi-square?

Answer 3

Chi-square is a non-parametric statistic

• does not make assumptions about a distribution

Question 4

How are Chi-square data represented?

Answer 4

• contingency tables
• shows how the data is distributed across the variables
• the numbers in the cells are known as observed frequencies
• they represent the frequency of people who fall in each combination of levels of the variable

Question 5

How do we describe contingency tables?

Answer 5

_ x _ design

e.g. 2 variables, and 2 levels of each category

so we have a 2 x 2 design

Question 6

What can we conclude if there is no association?

Answer 6

if there is no association, the observed values 0 the frequencies in each cell.

• they do not differ from what we would expect to happen merely by chance

Question 7

What can we conclude if there is an association?

Answer 7

• if the observed values are significantly different from the expected values, we can conclude there is an association between the variables that differs from what we would expect by chance

Question 8

How do we know what the expected values are?

Answer 8

• expected values are the values you would expect to see in each cell if no association existed between the 2 variables (null hypothesis is true)

Question 9

What is the equation for the expected value?

Answer 9

(Row total x column total) / Grand total

Question 10

What is O-E?

Answer 10

observed value - Expected value

Question 11

What is the Chi-square (X²) equation?

Answer 11

X² = sum of ((O - E)² / E)

Question 12

How do we calculate Chi-square?

Answer 12

The chi-square statistic measures the degree of difference between the observed and expected frequencies

1. square each O-E value
2. divide each result by its own expected value
3. sum all the results

Question 13

How do we interpret the Chi-square value?

Answer 13

Chi-square should ALWAYS be either zero or a positive number

• if not zero, then an association exists
• is the association statistically significant?
  • we figure this out with the p value
• we also want to know how strong the association is
  • for this we need an effect size

Question 14

How do we calculate the degrees of freedom for a chi-square?

Answer 14

• R = number of rows
• C = number of columns
  • df = (R - 1) (C - 1)

Question 15

What are the two effect sizes for chi-square?

Answer 15

• Phi-coefficient
• Cramer’s V
• both give n a value between 0 (complete independence) and 1 (perfect association)

Question 16

what effect size do we use for 2x2 contingency tables?

Answer 16

Phi-coefficient

Question 17

what effect size do we report for contingency tables that are NOT 2x2?

Answer 17

Cramer’s V

Question 18

what are the values for small, medium and large effect size’s for Phi and Cramer’s V?

Answer 18

• small: 0.10
• medium: 0.30
• large: 0.50

Question 19

how do we report the results of a chi-square test?

Answer 19

X² (1, N = 180) = 30.13, p < .001, φ = .4

X² (df, N) = chi square statistic, p value, phi (effect size)

Question 20

What assumptions must be met before running a chi-square test?

Answer 20

1. both variables are categorical
2. categories are mutually exclusive (participants cannot be in more than one category of each variable)
3. number of cells in the frequency table should have an expected frequency lower than 1
4. more than 80% of the cells in the contingency table should have an expected frequency of 5 or more

note: 2x2 tables only have 4 cells, so each cell is 25% of the total. that means that if you have a 2x2 table, even one cell with an expected frequency or more means the assumption is violated

Question 21

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

Answer 21

• if this happens and the table is 2x2, read the significance value from Fisher’s exact test line
• if this happens and the table is larger
  • consider pooling categories
  • use exact p-value for the Pearson’s chi-square
  • use other analysis such as likelihood ratio