Matched Pairs Test A special type of t-inference Notes: Page 196

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 or before & after measurements are taken The two measures are dependent on the individual

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

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.

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.

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.) Day Morning After- noon First, you must find the differences for each day. Calculator: Enter Morning data in L1, Enter Afternoon data in L2. Then, L3 = L1 – L2 Since you have two values for each day, they are dependent on the day – making this data matched pairs You may subtract either way – just be careful when writing H a

Day Morning After- noon Differenc es Assumptions: Have an SRS of days for whale-watching  unknown Since the normal probability plot is approximately linear, the distribution of difference is approximately normal. (Stat Plot, Scatter, Xlist: L3, Ylist L1) I subtracted: Morning – afternoon You could subtract the other way! You need to state assumptions using the differences! Notice the granularity in this plot, it still displays a nice linear relationship!

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

Finish the hypothesis test: Since p-value > , I fail to reject H 0. There is insufficient evidence to suggest that more whales are sighted in the afternoon than in the morning. Notice that if you subtracted A-M, then your test statistic t = +.945, but p- value would be the same In your calculator, perform a t-test using the differences (L3). Start with 1-var Stats for your L3 data. Differences How could I increase the power of this test? The best way to increase the power is to increase n

Homework: Page 201 Pages (Test Review) Next Week: Tuesday: Review Thursday: Test Unit 11 and 12