Section 6: Basic analysis for Determining Associations with numeric outcomes I: T-test and ANOVA

Question 1

What is the IV & DV for “A study finds that reading levels are affected by whether a person is born in the U.S. or in a foreign country”?

Answer 1

• Independent: Country of birth
• Dependent: Reading level

Question 2

What is the IV & DV if “A large cohort study has shown that men who smoke have more than 30 times the risk of developing lung cancer, compared to non-smoking males”?

Answer 2

• Independent: Smoking,
• Dependent: Lung Cancer

Question 3

What is the IV & DV if “A researcher studies how different drug doses affect the progression of a disease and compares the intensity and frequency of symptoms when different doses are given”?

Answer 3

• Independent: Drug dose, Dependent: Intensity of symptoms
• Independent: Drug dose, Dependent: Frequency of symptoms

Question 4

What are the types of analysis of a categorical exposure and a numeric outcome?

Answer 4

1. Independent samples T-test (Student’s T-test)
2. Paired samples T-test (matched pairs T-test)
3. One-way ANOVA analysis

Question 5

What is the null hypothesis for an independent samples t-test?

Answer 5

• population means from two unrelated groups are equal
• alternatively mean diff=0
• H0 : μ1 = μ2 or H0: diff = 0

Question 6

What are the assumptions for independent samples t-tests?

Answer 6

1. DV should follow normal distribution for each of 2 pops being compared
2. DV shouldn’t have outliers
3. 2 pops being compared should have same variance
4. data used to carry out test should be sampled independently from 2 pops being compared

Question 7

How can normality be tested for independent samples t-test?

Independent samples T-test Assumptions

Answer 7

Using Shapiro-wilk or Shapiro-Francia tests using the if == options

Question 8

How do we test 2 pops being compared should have same variance for indepenedent samples t-tests?

Independent samples T-test Assumptions

Answer 8

Testable using Two Group Variance Comparison Test (sdtest) in STATA

Question 9

Why does the data used to carry out test be sampled independently from 2 pops being compared for independent samples t-tests?

Independent samples T-test Assumptions

Answer 9

If the data were dependently sampled, the t-tests may give misleading results

Question 10

What are the assumptions for one-way anova?

Answer 10

• Normal distribution in each group.
• No outliers.
• Equal variances (tested with Bartlett’s test).
• Independent samples.

Question 11

What does a independent samples t-test compare?

Answer 11

Comparison of outcome mean between two independent/different groups

Question 12

What are the five types of bivariate analyses?

Answer 12

1. Categorical independent – Numeric dependent
2. Numeric independent – Numeric dependent
3. Categorical independent – Categorical dependent
4. Categorical independent – Dichotomous dependent
5. Numeric independent – Dichotomous dependent

Question 13

Which tests are used when the exposure is categorical and the outcome is numeric?

Answer 13

• Independent samples t-test
• Paired samples t-test
• One-way ANOVA.

Question 14

What does an independent samples t-test compare?

Answer 14

The means of two independent groups.

Question 15

What p-value indicates statistical significance at α=0.05?

Answer 15

A p-value less than 0.05 means we reject the null hypothesis.

Question 16

What does a paired samples t-test compare?

Answer 16

Two sets of measurements from same group (e.g., before and after an intervention).

Question 17

What are the assumptions of the paired t-test?

Answer 17

• Normal distribution for both sets of observations.
• No extreme outliers.
• Equal variances between sets of observations.
• 2 sets of observations need to be dependent (from the same, or matched individuals).

Question 18

What does the one-way ANOVA test do?

Answer 18

• Comparison of the outcome mean between the independent/different category groups
• > 2 groups

Question 19

What happens if Bartlett’s test is significant (p<0.05)?

Answer 19

The variances are unequal, and ANOVA results may be unreliable.

Question 20

What is Bartlett’s test used for in ANOVA?

Answer 20

To test the assumption of equal variances across groups.

Question 21

What does a 95% confidence interval (CI) that does not include 0 indicate?

Answer 21

The difference between means is statistically significant

Question 22

What Stata command tests for equal variances?

Answer 22

sdtest variable, by(group).

Question 23

What Stata command tests for normality?

Answer 23

swilk variable (Shapiro–Wilk test).

Question 24

What Stata command performs an independent samples t-test?

Answer 24

ttest outcome, by(exposure).

Question 25

What Stata command performs a paired t-test?

Answer 25

ttest variable1 == variable2

Question 26

What Stata command performs a one-way ANOVA? | not sure if this is correct

Answer 26

oneway outcome group, bonferroni sidak tabulate.