Tests of Proportions; Chi-Square and McNemar Test

Question 1

• What is a chi-square test?

- It is used to compare __________ independent groups for their proportions.

Answer 1

• A statistical hypothesis test that uses a test statistic with a known probability distribution of chi-square distribution.
• two or more

Question 2

Example 1:
In a randomized controlled study, 100 hypertensive subjects were recruited, randomly assigned to the experimental group treated with a new medication or the control group with a standard treatment only. As an outcome, their responsiveness to the systolic blood pressure change was measured and recorded with 0 for not being responsive and 1 for being responsive. Among those 50 in the experiment group, 25 subjects were responsive; among those 50 in the control group, 5 subjects were responsive.

• How can you estimate the (lowered) risk of hypertension linked to the use of the new medication?
• How can you test statistically the effect of the new medication over the standard treatment on the hypertensive subjects?

Answer 2

• Compute an epidemiologic measure as an estimate of the lowered risk of hypertension linked to the use of the new medication.
• Run a statistical hypothesis test to compare the proportions of those who were responsive between the experimental group vs. the control group.

Question 3

Example 1:
In a randomized controlled study, 100 hypertensive subjects were recruited, randomly assigned to the experimental group treated with a new medication or the control group with a standard treatment only. As an outcome, their responsiveness to the systolic blood pressure change was measured and recorded with 0 for not being responsive and 1 for being responsive. Among those 50 in the experiment group, 25 subjects were responsive; among those 50 in the control group, 5 subjects were responsive.

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

Answer 3

-χ^2= ∑(O-E)^2/E

Question 4

• What is degree of freedom (df)?

- For chi-square statistic out of the R x C contingency table, the df is what?

Answer 4

• The number of values that are free to vary as you estimate parameters.
• (R-1) x (C-1) (R=rows, C=columns in contingency table)

Question 5

Can a OR be estimated using a 2x2 contingency table? How?

Answer 5

• Yes

- (a/b)/(c/d)

Question 6

Can a RR be estimated using a 2x2 contingency table? How?

Answer 6

• Yes

- (a/(a+b))/(c/(c+d))

Question 7

What are the assumptions for a valid chi-square test?

Answer 7

• The groups are independent (experimental vs control).
• The value of the cell expected count should be 5 or more in at least 80% of the cells.
• No cell should have an expected count of less than 1.

Question 8

MCNEMAR TEST

Answer 8

MCNEMAR TEST

Question 9

• What is a McNemar Test?
• It is a form of the chi-square test used with 2x2 contingency table that involve matched samples, where subjects act as their own __________.

Answer 9

• A statistical hypothesis test used when you want to compare proportions between the two groups that are not independent.
• control

Question 10

What are some examples of when a McNemar Test would be used?

Answer 10

• To look at a subject’s responses to a question and see how many subjects answered correctly or incorrectly before and after exposure to specific information.
• To examine the effects of a particular treatment program by looking at the presence or absence of an outcome result, such as pain, before and after treatment.

Question 11

Example:
In a study about vertebral compression fractures, the researchers looked at the pain reduction and improvement in functional mobility after percutaneous polymethylmethacrylate vertebroplasty. For all 53 subjects, they asked the use of pain medication before the Vertebroplasty and asked again their use of pain medication after the Vertebroplasty.

-How can you test statistically the effect of the Vertebroplasty on the pain reduction in terms of no use of pain meds any more?

Answer 11

-Run a statistical hypothesis test to compare the proportion of those who did not use pain meds vs. the proportion of those who did use pain meds.

Question 12

What is the formula for McNemar Statistic?

Answer 12

x^2 = ((O₃ - O₂)^2)/(O₃ + O₂)

• where O₃ is the observed count of those who change from category 1 to category 2
• where O₂ is the observed count of those who change from categroy 2 to category 1

Question 13

• What is degree of freedom (df)?

- For McNemar statistic out of the R x C contingency table, the df is what?

Answer 13

• The number of values that are free to vary as you estimate parameters.
• (R-1) x (C-1) (R=rows, C=columns in contingency table)

Question 14

Can a OR be estimated using a 2x2 contingency table? How?

Answer 14

• Yes

- b/c

Question 15

• Which test is used to compare two groups or more that are independent?
• Which test is used to compare 2 groups that are paired?
• Which test is used to compare more than 2 groups that are matched?

Answer 15

• Chi-square
• McNemar
• Stuart-Maxwell

Question 16

What is Fishers Exact Test?

Answer 16

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

Question 17

• Which test is used to compare two groups or more that are independent when the data is not sparse?
• Which test is used to compare 2 groups that are paired when the data is not sparse?
• Which test is used to compare more than 2 groups that are matched when the data is not sparse?

Answer 17

• Chi-square
• McNemar
• Stuart-Maxwell

Question 18

• Which test is used to compare two groups or more that are independent when the data is sparse?
• Which test is used to compare 2 groups that are paired when the data is sparse?
• Which test is used to compare more than 2 groups that are matched when the data is sparse?

Answer 18

• Fisher’s Exact Test
• McNemar’’s Exact Test
• Generalized Stuart-Maxwell`

Question 19

Quiz 1:

• A research study was conducted to compare two different screening strategies for colorectal cancer, FOBT and sigmoidoscopy, in their neoplasia detection rates. They assigned 2000 eligible patients to either FOBT or sigmoidoscopy but not both. Since such group assignment forms two _____(a)______ groups, and the data seems to be large enough not being sparse, an appropriate method for comparison of the detection rates between the two group is _____(b)______. Which pair of the following correctly fills the both blanks of (a) and (b)?
  1. independent, chi-square test
  2. independent, Mcnemar’s test
  3. dependent, chi-square test
  4. dependent, Mcnemar’s test
  5. dependent, Fisher’s exact test

Answer 19

1. independent, chi-square test

Question 20

Quiz 2:
-Which of the following is TRUE regarding the statistical hypothesis testing procedures that compare proportions between groups?

1. Chi square test is the most powerful in any study design with no assumptions to check
2. Sample size must be large enough to use a chi square test
3. McNemar’s test is used when the data of the two groups are independent
4. Chi square test is used when the data are matched between two groups
5. Fisher’s exact test must be used when the sample size is large enough

Answer 20

2. Sample size must be large enough to use a chi square test

Question 21

Quiz 3:
-A group of researchers conducted a research about different screening strategies for colorectal cancer. They specifically compared FOBT and sigmoidoscopy in their neoplasia detection rates. They randomly assigned eligible patients to either FOBT or sigmoidoscopy but not both. The sample size was large enough. What statistical test would have been used in this comparison?

1. Chi-square test
2. Student’s t-test
3. McNemar’s test
4. Analysis of variance
5. Kruskal-Wallis test

Answer 21

1. Chi-square test

Question 22

Quiz 4:
-A group of researcher conducted a research about different screening strategies for colorectal cancer. They specifically compared Fecal DNA Panel and Hemoccult II in their detection rates. They had all of eligible patients to complete both procedures. The sample size was large enough. What statistical test would have been used in this comparison?

1. Chi-square test
2. Student’s t-test
3. McNemar’s test
4. Analysis of variance
5. Kruskal-Wallis test

Answer 22

3. McNemar’s test

Question 23

Quiz 5:
-In a study for the depression in Parkinson’s disease (PD) and its relation to a genetic polymorphism of the cannabinoid receptor gene, the researchers compared the two different genotypes frequency between those with and without depression in the group of PD patients. Data were presented in the table below. They noticed that the 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?

1. Chi square test
2. McNemar’s test
3. Student’s t-test
4. Fisher’s exact test
5. Analysis of Variance

Answer 23

4. Fisher’s exact test

Question 24

Summary for Tests of Proportions:
-___________ test is a proper test for testing the proportion between the two or more independent groups
-There are assumptions to check before running a chi-square test including that
than one
-_________ test is available when the factors are not independent
-_______________ test is available when the data is sparse having cell expected count less than 5
-For the data presented in a 2x2 contingency table, odds ratio can be computed for each case of chi-square test and McNemar test

Answer 24

• Chi-square
• the two factors are independent, the value of the cell expected count should be 5 or more in at least 80% of the cells, no cell should have an expected count of less than 1
• McNemar
• Fisher’s Exact