Chapter 22: Paired Samples and Blocks

Question 1

Define ‘Paired data’.

Answer 1

Data are paired when the observations are collected in pairs or the observations in one group are naturally related to observations in the other. The simplest form of pairing is when we measure each subject twice - often before and after a treatment is applied. More sophisticated forms of pairing in experiments are a form of blocking and arise in other contexts. Pairing in observational and survey data is a form of matching.

Question 2

Define ‘Paired t-test’.

Answer 2

A hypothesis test for the means of the pairwise differences of two groups. It tests the null hypothesis
Ho: μd = 0,
using the statistic
t = (d-bar - 0) / SE(d-bar)
which has a t*(n-1) sampling model under the null hypothesis where SE(d-bar) = sd / sqrt(n) and n is the number of pairs.

Question 3

Define ‘Paired-t confidence interval’.

Answer 3

A confidence interval for the mean of the pairwise differences between independent groups found as
d-bar ± t*(n-1) x SE(d-bar), where SE(d-bar) = sd / sqrt(n) and n is the number of pairs.

Question 4

What are the assumptions and conditions of paired data?

Answer 4

• Paired data condition (quantitative and paired)
• Independence assumption; randomization condition
• Normal population assumption; Nearly normal condition