Week 9 - Chi-Square Tests

Question 1

What are the types of contingency tables?

Answer 1

1-way - one categorical variable
2-way - two categorical variables
multi way - more than two categorical variables

Question 2

What is a chi-squared test used for?

Answer 2

To test a hypothesis for categorical data
They compare what we observed in data to what is expected based on the contingency table so see if the frequencies of the sample differ significantly from the hypothetical population

Question 3

Is a chi-square test parametric or non-parametric?

Answer 3

Non-parametric

Question 4

What is the notation for the null and alternative hypotheses for chi-square tests?

Answer 4

Null: There is no association beteeen the two groups; they are independent
H0: P11 = P21
H0: P12 = P22
H0: P13 = P23

Alternative: There is an association between the two groups; they are dependent
HA: P11 ≠ P21
HA: P12 ≠ P22
HA: P13 ≠ P23

Question 5

What does the chi-square distribution look like?

Answer 5

Continuous probability distribution
Only positive values
Shape varies based on df
There is a positive skew, especially when df are low
No directionality

Question 6

How do you calculate df for chi-square tests?

Answer 6

Df= (row-1)(column-1)

Question 7

What is the rejection region called?

Answer 7

tcrit
found from the t-distribution table

Question 8

What are the assumptions for chi-square tests?

Answer 8

Both variables are categorical
No cell counts are less than 5 (if they are the Fisher’s Exact Test should be used)

Question 9

When do we reject the null hypothesis for chi-square tests?

Answer 9

X^2 observed > tcrit and p < alpha