Chapter 8 - Hypothesis Testing (Two-Sample)

Question 1

Two-sample hypothesis testing

Answer 1

• in a two-sample hypothesis-testing problem, the underlying parameters of two different populations, neither of whose values are known, are compared
• different tests are available, depending on study design

Question 2

Longitudinal or follow-up study

Answer 2

• the same group of people is followed over time

- also, this represents a paired-sample design because each person is used as his or her own control

Question 3

Cross-sectional study

Answer 3

• the participants are seen at only one point in time
• this study represents an independent sample design because two completely different groups of people are being compared
• a cross-sectional study is also less expensive than a follow-up study

Question 4

Types of two-sample data

Answer 4

• paired samples

- independent samples

Question 5

Paired samples

Answer 5

• when each data point in the first sample is matched and is related to a unique data point in the second sample
• may represent two sets of measurements on the same people
• or, on different people who are chosen on an individual basis using matching criteria

Question 6

Independent samples

Answer 6

• when the data points in one sample are unrelated to the data points in the second sample

Question 7

Two-sample t-test for independent samples

Answer 7

• the two-sample t-test for independent samples is used to test hypotheses of independent samples

Question 8

F distribution

Answer 8

• not a symmetric distribution
• positively skewed
• family of distributions that depend on degrees of freedom

Question 9

Two-sample t-test for independent samples with unequal variances

Answer 9

• since variances are unequal, we shouldn’t use a pooled estimate of variance
• instead, the traditional estimates for variances are used

Question 10

Estimation of sample size for two-sample hypothesis tests

Answer 10

• sample size estimation is more difficult for two-sample tests of hypotheses because there are two samples sizes to consider
• for some study designs, estimating equal sample sizes is appropriate, but some health conditions (eg. a rare disease), it may be unrealistic to obtain equal sample sizes