Week 9: Tests of Proportions - Chi-square test; McNemar test

Question 1

What tests used for tests of differences?

Answer 1

1. Parametric tests
   - Student’s t-test
   - Paired t-test
   - ANOVA
   - Repeated measures ANOVA
2. Non-parametric tests
   - Mann-Whitney U
   - Wilcoxon signed-rank test
   - Kruskal-Wallis H test
   - Friedman test

Question 2

What tests used for tests of proportions?

Answer 2

1. chi-square test
2. McNemar test
3. Fisher’s Exact test

Question 3

Chi-square test for comparing proportions -

Answer 3

• a statistical hypothesis test that uses a test statistic with a known probability distribution of chi-square distribution
• used to compare two or more independent groups for their proportions

Question 4

How can you estimate the (lowered) risk of hypertension linked to the use of the new medication?

Answer 4

Compute an epidemiologic measure as an estimate of the lowered risk of hypertension linked to the use of the new medication = odds ratio

Question 5

How can you test statistically the effect of the new medication over the standard treatment on the hypertensive subjects?

Answer 5

Run a statistical hypothesis test to compare the proportions of those who were responsive between the experimental group vs. the control group

Question 6

Expected data contingency table is calculated using what?

Answer 6

Computed based on the marginal sums:
ex: (a*c/T) = expected 1
a*d/T = E3
b*c/T = E2
b*d/T = E4

Question 7

Degrees of freedom -

Answer 7

The number of values that are free to vary as you estimate parameters

Question 8

For chi-square statistic out of the R x C contingency table, df=

Answer 8

(df) is (R - 1) x (C - 1)

R= number rows/ C=number columns

Question 9

OR [(a/b)/(c/d)] (RCT) calculated using 2x2 contingency table = 9, interpret.

Answer 9

OR = 9 > 1.0; the rate of being responsive is 9 times higher with the new medication than the standard treatment only

Question 10

RR [(a/a+b)/c/c+d)} (cohort study) estimated using a 2x2 contingency table = 0.5, interpret.

Answer 10

OR = 0.5 < 1.0; the risk of hip fracture is lower by a factor of ½ in those physically active than those not

Question 11

Assumptions for valid chi-square test:

Answer 11

1. the groups are independent (e.g. experimental vs. control; physically active vs. not active)
2. the value of the cell expected count should be 5 or more in at least 80% of the cells (All of E1, E2, E3, and E4 must be greater than 5)
3. no cell should have an expected count of less than one (Any of E1, E2, E3, or E4 must not be less than 1)

Question 12

McNemar test -

Answer 12

• a statistical hypothesis test used when you want to compare proportions between the two groups that are not independent (pretest/posttest design)
• a form of the chi-square test used with 2x2 contingency table that involve matched samples, where subjects act as their own controls or where they are matched

Question 13

OR for matched data can be estimated using a 2x2 contingency table (b/c), interpret OR = 5

Answer 13

OR = 5 > 1.0; the rate of becoming not to use pain meds is 5 times higher than those becoming to use pain meds.

Question 14

What test of proportions used for independent groups of two group comparison and multi group comparison?

Answer 14

Chi-square test

Question 15

What test of proportions used for paired (matched) groups of two group comparison?

Answer 15

McNemar test

Question 16

What test of proportions used for paired (matched) groups of multi group comparison?

Answer 16

Stuart-Maxwell test

Question 17

Fisher’s Exact test -

Answer 17

• test used when you want to compare proportions between the two independent groups when the data are sparse
• test resulting in the exact probability of the occurrence of the observed frequencies, given the marginal totals

Question 18

Test of proportions when independent groups, 2 group comparison or multi group comparison when data are sparse.

Answer 18

Fisher’s Exact test

Question 19

Test of proportions when paired (matched) groups for 2 groups when data is sparse?

Answer 19

McNemar’s exact test

Question 20

Test of proportions when paired (matched) groups for multi groups when data is sparse?

Answer 20

Generalized stuart-maxwell

Question 21

Ex: assigned 2000 eligible patients to either FOBT or sigmoidoscopy but not both and data is large enough, what test?

Answer 21

independent, chi-square test

Question 22

T/F Chi square test is used when the data are matched between two groups

Answer 22

False, data independent

Question 23

T/F Sample size must be large enough to use a chi square test

Answer 23

True

Question 24

T/F McNemar’s test is used when the data of the two groups are independent

Answer 24

False, dependent

Question 25

T/F Fisher’s exact test must be used when the sample size is large enough

Answer 25

Sparse

Question 26

Ex: all of eligible patients to complete both procedures. The sample size was large enough. What statistical test would have been used in this comparison?

Answer 26

McNemar’s test

Question 27

Ex: compared the two different genotypes frequency between those with and without depression in the group of PD patients. sample size is very limited being sparse. Which statistical test would be best to compare the proportions of having one genotype against the other between those with depression and no depression in the group of PD patients?

Answer 27

Fisher’s exact test