Comparing Two Means

Paired data or two independent samples?

12 problems · about 22 minutes · UNC-4.Y, DAT-3.G

What this lesson teaches

The student distinguishes paired from two-sample designs and carries out the matching procedure.

Straightforward practice. Get the method working first.

5 problems

Paired data with 12 subjects. What are the degrees of freedom?
Answer 11
Why 11.
How do you decide whether a design is paired?
Answer Ask whether each value in one group has a natural partner in the other.
Why The natural pairing of individual observations.
Two unrelated groups of 30 and 40 people. Paired or two-sample? 1 or 2?
Answer 2
Why Different sizes and no partners.
Left and right hand strength on the same people. 1 paired, 2 two-sample.
Answer 1
Why Same person, two measurements.
Paired data with 15 subjects. Degrees of freedom for the t procedure?
Answer 14
Why n − 1 on the differences.

The same ideas with more to keep track of.

3 problems

Can two-sample groups have different sizes? 1 yes, 0 no.
Answer 1
Why They are unrelated.
Can paired groups have different sizes? 1 yes, 0 no.
Answer 0
Why Every value needs a partner.
Differences 2, 4, 6. What is their mean?
Answer 4
Why 12 ÷ 3.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Sort each study by its design.
Answer Paired: Before and after on the same subjects, Matched twins, one in each condition · Two-sample: A treatment group and a separate control group, Two unrelated schools compared
Why Ask whether each value has a natural partner.
Paired data with 25 subjects. Degrees of freedom?
Answer 24
Why n − 1.
The Design: Before and after readings on the same 20 patients. Paired or two-sample? 1 paired, 2 two-sample.
Answer 1
Why Paired.
The Count: 20 patients measured twice. How many differences are analysed?
Answer 20
Why 20.