1. A special type of t-inference
Matched Pairs Test
A special type of
t-inference

2. Matched Pairs – two forms
Pair individuals by certain characteristics
Randomly select treatment for individual A
Individual B is assigned to other treatment
Assignment of B is dependent on assignment of A
Individual persons or items receive both treatments
Order of treatments are randomly assigned before measurements are taken
The two measures are dependent on the individual

3. Is this an example of matched pairs?
1)A college wants to see if there’s a difference in time it took last year’s class to find a job after graduation and the time it took the class from five years ago to find work after graduation. Researchers take a random sample from both classes and measure the number of days between graduation and first day of employment
No, there is no pairing of individuals, you have two independent samples

4. Is this an example of matched pairs?
2) In a taste test, a researcher asks people in a random sample to taste a certain brand of spring water and rate it. Another random sample of people is asked to taste a different brand of water and rate it. The researcher wants to compare these samples
No, there is no pairing of individuals, you have two independent samples – If you would have the same people taste both brands in random order, then it would be an example of matched pairs.

5. Is this an example of matched pairs?
3) A pharmaceutical company wants to test its new weight-loss drug. Before giving the drug to a random sample, company researchers take a weight measurement on each person. After a month of using the drug, each person’s weight is measured again.
Yes, you have two measurements that are dependent on each individual.

6. A whale-watching company noticed that many customers wanted to know whether it was better to book an excursion in the morning or the afternoon. To test this question, the company collected the following data on 15 randomly selected days over the past month. (Note: days were not consecutive.)
You may subtract either way – just be careful when writing Ha
Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Morning
After-noon
Since you have two values for each day, they are dependent on the day – making this data matched pairs
First, you must find the differences for each day.

7. -1 -2 I subtracted: Morning – afternoon
Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Morning
After-noon
Differences -1 -2
I subtracted:
Morning – afternoon
You could subtract the other way!
Assumptions:
Have an SRS of days for whale-watching
s unknown
Box plot of the differences appears to be normal
You need to state assumptions using the differences!
Plot the differences as a box plot to check for normality!

8. Differences -1 -2 1 2
Is there sufficient evidence that more whales are sighted in the afternoon?
Be careful writing your Ha!
Think about how you subtracted: M-A
If afternoon is more should the differences be + or -?
Don’t look at numbers!!!!
If you subtract afternoon – morning; then Ha: mD>0
H0: mD = 0
Ha: mD < 0
Where mD is the true mean difference in whale sightings from morning minus afternoon
Notice we used mD for differences
& it equals 0 since the null should be that there is NO difference.

9. finishing the hypothesis test:
Differences -1 -2 1 2
finishing the hypothesis test:
Since p-value > a, I fail to reject H0. There is insufficient evidence to suggest that more whales are sighted in the afternoon than in the morning.
In your calculator, perform a t-test using the differences (L3)
Notice that if you subtracted A-M, then your test statistic
t = , but p-value would be the same
How could I increase the power of this test?