1
STA2023  Chapter 25 (Paired Samples)
Like chapter 24, chapter 25 addresses inferences for comparing two sets of sample data, but now the groups
being compared are not independent groups.
Chapter 24:
Comparing the means of two independent
groups by taking random samples from each
group.
Inferences of this type are called a
2sample inferences
.
Chapter 25:
Comparing two sets of sample data, where the observations between the groups are
dependent
observations.
Beware: within each group the observations are independent…but
the groups themselves are not independent.
The outcome of an observation in the 2
nd
group
is somehow related to an observation in the 1
st
group.
Inferences of this type are called
MatchedPairs inferences
(aka. Paired Differences).
See the Assumptions and Conditions
on page 653.
* A typical matched pairs setting involves some “before” and “after” measurement on
each subject in the study.
(ex:
change in weight before and after an exercise
program)
* Another typical example is where there is some relationship between the subjects in
each group (husband & wife, roommates, siblings, friends, etc).
For example,
suppose we are measuring something like time spent on a particular leisure activity
for a group of married couples…the time spent on this activity by a husband is
probably somewhat related to the time spent on this activity by his wife.
Inferences for MatchedPairs studies (paired differences) are almost exactly the same as 1sample
inferences from chapter 23.
The only new concept is that we must first find the paired difference for each
matched pair in the sample data.
In other words, match up each observation in the first sample with it’s
corresponding observation in the second sample, and find the difference (
d
= y
1
– y
2
or
d
= y
2
– y
1
)
between the observations for each pair.
Now, ignore the original y
1
and y
2
data values and use the
d
data
values as the set of sample data (see highlights at bottom of page 652).
So, there is now only one set of
data values (
d
).
Enter those values into a list of your calculator (as you did in chapter 23).
Use STAT/CALC/1Var Stats to find the mean of the paired differences in the sample (
_
d
) and the
standard deviation of the paired differences (
s
d
).
From here it’s business as usual…use these
_
d
and
s
d
values to find a 1Sample TInterval or run a 1Sample TTest to determine what differences might exist
between the groups…remembering that tprocedures are only estimates and best used when the sample size
is large and/or the distribution of the sample data is close to symmetric with no outliers (see page 592)
Confidence Interval Formula:
_
*
d
s
d
t
n
±
⋅
where
_
( )
d
s
SE d
n
=
Degrees of freedom:
df = n
d
– 1
Test Statistic Formula:
_
d
d
d
t
s
n
μ

=
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
2
Activity 1 (guided activity)
The example presented in the chapter 24 lesson involved comparing the stretching ability of two
independent groups (Gainesville women versus Gainesville men).
Furthermore, the sample data included
35 Gainesville women and 45 Gainesville men.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Ripol
 Statistics, Statistical hypothesis testing, researcher

Click to edit the document details