Transcript IndvsDepDesigns

Inference for Two Population Means
Goal: Hypothesis Test or Confidence interval for the “average
difference” between two populations
There are two designs possible:
Independent samples design – the data values gathered from
one sample are unrelated to the data values gathered
from the second sample.
Dependent samples design (matched/paired) – subjects are
paired (matched) so they are as much alike as possible in
terms of characteristics other than the variable of interest
before measurements on that variable are made.
Examples of Independent Samples
Independent samples design: (samples sizes can be different)
•
Independently select a different sample from each of the
two populations
Example: Randomly select 35 males and 35 females.
Measure their diastolic blood pressures to see if there is a
significant difference based on gender.
The two populations of interest are (1) blood pressures for
males and (2) blood pressures for females.
Notice the two samples were selected from the populations
without trying to match people based on family or
personal history in terms of health.
Examples of Independent Samples
Independent samples design: (samples sizes can be different)
•
Independently select a different sample from each of the
two populations
Example: Randomly select 40 NKU athletes and 35 nonathletes (not on NKU teams). Measure GPA’s to see if
there is a difference.
The two populations of interest are (1) GPAs for athletes
and (2) GPAs for non-athletes.
Notice the two samples were selected from the populations
without trying to match people based on prior academic
performance, number of hours enrolled, etc.
Examples of Independent Samples
Independent samples design: (samples sizes can be different)
•
Another way to use the independent samples design is to
take a large sample (say 100 subjects) and randomly
assign them to two “treatment” groups. Again, sample
sizes may be different
Example: For testing 2 drugs, randomly assign 50 people
to drug A and 50 people to drug B. No matching based
on health, income level, etc. is assumed in this case.
Then measure reactions based on the drug taken (time
until relief, reduction in blood pressure, etc.).
Examples of Independent Samples
Independent samples design: (samples sizes can be different)
Example: Take a sample of 500 incoming students, and
randomly assign them to one of two “learning
communities” (a group of classes all students take
together). Measure outcomes (GPAs for these classes)
to determine if one set of classes seems to work better
as a collection than another.
Again, there is no matching stated in this case, so this
would be independent samples.
Examples of Dependent Samples
Dependent samples design (matched/paired):
•
subjects are measured twice – apply both “treatments” to
the same subject.
Example: Examine pretest and posttest scores for the
same person. Do this for a total of 50 students. This
can be used to examine how much a student learned in
the class. Now a student who already knew the
material would not show much improvement or
increase in knowledge, while a student with little
knowledge of the subject should show vast increases.
This eliminates comparisons between students who
have prior knowledge and those who do not for a given
subject.
Examples of Dependent Samples
Dependent samples design (matched/paired):
•
subjects are measured twice – apply both treatments to
the same subject.
Example: Measure reactions to two medicines for the same
person. Again examine this pair of measurements for
several patients. This will allow a better measurement
of effectiveness since you no longer need to worry
about “health” and “lifestyle” since the same person is
measured twice. High blood pressure, high cholesterol,
active vs. sedimentary lifestyle patients, etc are all
accounted for in this scenario.
Examples of Dependent Samples
Dependent samples design (matched/paired): (another way)
•
subjects are paired in some way before the experiment is
conducted – measure differences between subjects
Example: Pair patients based on blood pressure, then
measure different reactions (blood pressure reduction)
for two types of medicine, one given to each patient in
each pair. This eliminates differences between pairs of
patients, which hopefully gives a much better measure
of how different the two medications are, regardless of
other health characteristics.
Examples of Dependent Samples
Dependent samples design (matched/paired):
•
subjects are paired in some way before the experiment is
conducted – measure differences between subjects
Example: Match children based on socio-economic status;
then assign to two types of teaching methods and
measure learning (test scores).
So children with more support at home and more
educational opportunities are matched. Also children
from homes where both parents have to work fulltime
(or maybe multiple jobs) are matched. The only
difference should be the two teaching methods.
Examples of Dependent Samples
Dependent samples design (matched/paired):
•
subjects are paired in some way before the experiment is
conducted – measure differences between subjects
Example: Dr. Agard and Dr. Miller both claim to be the
better Statistics professor. (not really, but let’s pretend)
To determine who is better, match students based on
ACT Math scores (one student with ACT Math = 20
from Dr. Agard’s class and one student with ACT
Math = 20 from Dr. Miller’s class; repeat for various
scores), then measure their performances in STA 205.
This eliminates differences based on math ability, as
measured by ACT, from making one teacher look
better, if it is the prior ability instead of instruction.
Independent Versus Dependent Designs
You will need to be able to distinguish between these
two methods.
Once you determine whether the design is
independent samples or dependent samples, the
remaining analysis is straight-forward.
Actually, for dependent samples designs, we take
differences of the pairs and then use exactly the
same methods as we covered in t-tests before.