LEC 8 Categorical Data Analysis

Question 1

Statistical test for

• nominal data
• 2 groups
• independent

Answer 1

Chi-square test
or
Fisher’s exact test

To test the null hypothesis that the population proportions corresponding to the random samples are equal
OR
To test the null hypothesis that there is no association between the ‘exposure’ and the ‘outcome’

Question 2

Statistical test for

• nominal data
• 2 groups
• paired

Answer 2

McNemar’s test

To test the null hypothesis that the population proportions of ‘outcome’ corresponding to the paired random samples are equal
OR
To test the null hypothesis that there is no association between the ‘exposure’ and ‘outcome’

Question 3

Statistical test for

• nominal data
• > = 2 groups
• independent

Answer 3

Chi-square test
or
Fisher-Freeman-Halton test (extension of Fisher’s exact test)

Question 4

Arrangement of the data for nominal data (Chi-square and Fisher’s exact test)

Answer 4

RxC contingency table
Rows (horizontal) : exposure
Column (vertical) : outcome

Question 5

Chi-square test & Fisher’s exact test assumptions (4)

Answer 5

1. The samples are random samples of their populations
2. All observations are independent
3. For 2x2 contingency table, the expected count for each cell has to be at least 5
4. For larger contingency table,
   - the expected count for each cell has to be at least 1
   - no more than 20% of the cells have <5

3&4, if not fulfilled then do Fisher’s exact test

Question 6

Observed count for Chi-square

Answer 6

= (row total x column total)/grand total

Question 7

Chi-square test & Fisher’s exact test hypothesis types (2)

Answer 7

1. Association

2. Proportion

Question 8

Chi-square test & Fisher’s exact test hypothesis (Association)

Answer 8

Ho :
- There is no association between __ and __

H1 :
- There is an association between __ and ‘__

Question 9

Chi-square test & Fisher’s exact test hypothesis (Proportion)

Answer 9

Ho :
- There is no significant difference in proportion of __ and __

H1 :
- There is significant difference in proportion of __ and __

Question 10

McNemar’s test assumptions (2)

Answer 10

1. The samples are random samples of their populations

2. Each observation in the first sample has a corresponding observation in the second sample (paired samples)

Question 11

Concordant pairs

Answer 11

Outcome is the same for each member of the pairs

• provide no information about differences in __ and __
• ignored and not used in the analysis

eg test A +ve and test B +ve

Question 12

Discordant pairs

Answer 12

Outcome is different for each member of the pairs

eg test A +ve and test B -ve

Question 13

Arrangement of the data for nominal data in table (McNemar’s test)

Answer 13

Need to take into account the paired nature of the data

Row :

• exposure 1
• split into 2 outcomes

Columns :

• exposure 2
• split into 2 outcomes

Question 14

McNemar’s test hypothesis types (3)

Answer 14

1. Proportion
2. Association
3. Discordant pairs

Question 15

McNemar’s test hypothesis (Proportion)

Answer 15

Ho :
- There is no difference between the proportions of subjects with __ and __

eg There is no difference between the proportions of subjects with test A positive results and test B positive results

H1 :
- There is a difference between the proportions of subjects with __ and __

Question 16

McNemar’s test hypothesis (Association)

Answer 16

Ho :
- There is no association between __ and __

eg There is no association between the test used and the reaction observed

H1 :
- There is an association between __ and __

Question 17

McNemar’s test hypothesis (Discordant pairs)

Answer 17

Ho :
- There is no difference between the number of pairs in __ and the number of pairs in __

eg There is no difference between the number of pairs in which reaction to test A is positive and the matched reaction to test B is negative (n1) and the number of pairs in which reaction to test B is positive and the matched reaction to test A is negative (n2)

H1 :
- There is a difference between the number of pairs in __ and the number of pairs in __

Question 18

Criteria to use McNemar’s test

Answer 18

Total discordant pairs >=20

but if using software, it is ok to use if <20

Question 19

If >2 independent groups with nominal data

Answer 19

Use Chi-square test or Fisher’s Freeman Halton test

Usually no need to do post-hoc test cos only want to check for association

Question 20

McNemar’s test

Answer 20

To test the null hypothesis that the population proportions of “outcome” corresponding to the paired random samples are equal
eg Testing Ho that there is no difference between the proportion of persons with positive reaction to test A and proportion of persons with positive reaction to test B

OR

To test the null hypothesis that there is no association between “exposure” and “outcome”