2. Paired Data
• Two data sets are paired when there is a 1-1 relationship between
the values in the two data sets, meaning…
– Each data set has the same number of data points
– Each data point in one data set is related to one and only one
data point in the other data set
– Must use a matched pairs t-test to see if there is a significant
difference in the means from paired data.
EX: Matching the times of a group of runners sprinting a mile at
the start of their training, and then a month after their training.
3. CI for a difference between Paired Means
Estimation Requirements
1. The data set is a Simple random sample of observations from the population
of interest
2. Each element of the population includes data on two paired variables, such
that the paired difference between them is: d= a-b
3. Sampling distribution of mean difference between the data pairs (d) is
approximately normally distributed
4. Data sets are not independent
How to find the CI for the mean difference with Paired Data
1. Sample statistic (use mean difference between sample data pairs, d, to
estimate the mean difference between population data pairs, μd)
2. Confidence Level
3. Margin of error: use t-score where the DF= n-1
4. Specify the CI- sample statistic + ME
written as: (Sample Stat – ME, Sample Stat + ME)
4. Variability of the Mean difference
between Matched Pairs
• If d is the mean difference between sample data
pairs, we need to compute the SE of the sampling
distribution for d.
• When the population is at least 10 times larger than the
sample size, SE can be approximated:
