L10: Categorical Data Analysis

Question 1

What test to use when comparing data between two independent groups with nominal data?

Answer 1

chi-square test or fisher’s exact test

Question 2

What are the assumptions for the chi-square test?

Answer 2

• all observations are independent (each subject contributes data to only one cell)
• for 2x2 contingency table, expected count of each cell must be at least 5
• for larger contingency tables, expected count of each cell must be at least 1 and no more than 20% of the cells be less than 5

Question 3

When do we use fisher’s exact test?

Answer 3

When the expected count assumption for chi square test are not met.

Question 4

How to construct a contingency table?

Answer 4

Exposure in rows and outcome in columns

Question 5

How to calculate expected count?

Answer 5

( row total x column total ) / grand total

Question 6

How to formulate hypotheses for chi square test/fisher’s exact test?

Answer 6

Based on association:
H0: There is no association between exposure and outcome
H1: There is an association between exposure and outcome

OR based on proportions:
H0: There is no difference in the proportion of outcome in the two exposure groups
H1: There is a difference in the proportion of outcome in the two exposure groups

if >2 independent groups,
H0: All the proportions of outcome in the exposure groups are the same
H1: Not all the proportions of outcome among the exposure groups are the same.

Question 7

What test to use when comparing data between >2 independent groups with nominal data?

Answer 7

Chi square or fisher-freeman halton test

Question 8

If not all the proportions in the >2 independent groups are the same, what do we do?

Answer 8

Do different pairwise comparisons (2x2 contingency table) and do bonferroni adjustment

Question 9

What test do we use to compare data between two paired groups with nominal data?

Answer 9

McNemar’s test

Question 10

How do we arrange data for the McNemar’s test

Answer 10

• must take into account the paired nature of the data

- e.g. drug x (with and without outcome) and drug y (with and without outcome) `

Question 11

What are concordant and discordant pairs?

Answer 11

Concordant pairs: outcome is the same for each member of the pair
Discordant pair: outcomes differ for members of the pair

Question 12

How to formulate hypotheses for McNemar’s Test?

Answer 12

Based on association:
H0: There is no association between outcome and exposure
H1: There is an association between outcome and exposure

Based on proportions:
H0: There is no difference in the proportion of outcome for the groups
H1: There is a difference in the proportion of outcome for the groups

Based on no of discordant pairs:
H0: n1 = n2
H1: n1 not equal to n2

Question 13

What is a requirement for McNemar’s test?

Answer 13

n1 + n2 should be at least 20