1. Warm-up
Page 260 #91-98 (Please remember that these are not just “busy work”. These are good review for your test.) I will open up the Socrative room after the tardy bell
Late flash cards, reading guides & video notes go on the cart
Get ready for homework questions.
R.E.D.

3. Blocking page 246 Experiments Definition
Completely randomized designs are the simplest statistical designs for experiments. But just as with sampling, there are times when the simplest method doesn’t yield the most precise results.
Experiments
Definition
A block is a group of experimental units that are known before the experiment to be similar in some way that is expected to affect the response to the treatments.
In a randomized block design, the random assignment of experimental units to treatments is carried out separately within each block.
Form blocks based on the most important unavoidable sources of variability (lurking variables) among the experimental units.
Randomization will average out the effects of the remaining lurking variables and allow an unbiased comparison of the treatments.
Control what you can, block on what you can’t control, and randomize to create comparable groups.

4. Matched-Pairs Design page 249
A common type of randomized block design for comparing two treatments is a matched pairs design. The idea is to create blocks by matching pairs of similar experimental units.
Experiments
Definition
A matched-pairs design is a randomized blocked experiment in which each block consists of a matching pair of similar experimental units.
Chance is used to determine which unit in each pair gets each treatment.
Sometimes, a “pair” in a matched-pairs design consists of a single unit that receives both treatments. Since the order of the treatments can influence the response, chance is used to determine which treatment is applied first for each unit.

5. Example: Standing and Sitting Pulse Rate page 250
Consider the Fathom dotplots from a completely randomized design and a matched-pairs design. What do the dotplots suggest about standing vs. sitting pulse rates?
Experiments

6. Pg 256
72)
“Double-blind” means that the treatment assigned to a subject was unknown to both the subject and those responsible for assessing the effectiveness of that treatment.
Experiments
“Randomized” means that patients were randomly assigned to receive either the testosterone supplement or a placebo.
“Placebo-controlled” means that some of the subjects were given placebos. Because some subjects may show improvement or benefits just as a result of participating in the experiment, the placebos allow those doing the study to observe this effect.

7. Pg 257
74)
a) The researchers want to make sure that the two groups are as similar as possible before the treatments are administered.
Experiments
b) The difference in weight loss seen was most likely due to the treatments rather than to chance variability.
c) Even though the low-carb dieters lost 2 kg more over the year than the low-fat group, this difference was small enough that it could be due just to chance variation in the random assignment and not to the treatments themselves.

9. Difference (active – inactive): 4.146
Pg 257
76)
a) The distribution of differences for patients in the active group is multimodal whereas the distribution of patients in the inactive group is unimodal and skewed to the right.
Experiments
The patients in the active group had a higher mean difference than did those in the inactive group and had a distribution with much more variability.
Active group: 5.241
Inactive group: 1.095
Difference (active – inactive): 4.146

10. Pg 258
78)
a) The blocks are the sexes. The cancer reacts differently to treatments in men and women, so we want to test all three types of treatments in both men and women.
Experiments
b) Blocking will control for the variability in subjects’ responses due to their gender. This will allow researchers to look separately at the response for patients of each gender, as well as to better assess the relative effectiveness of each therapy.
c) We would not have to worry about variability in the response due to gender. Unfortunately, we would be able to make conclusions only about how the therapies work in men.

11. 1. Williams-22, Deng-24, Hernandez-25, Moses-25
Pg 258
80)
a) Blocking will allow researchers to control for variability in weight loss due to initial weight.
Experiments
b) The blocks should be based on how overweight the subjects are so that the subjects within a block are as similar as possible.
If we block on last name, there will be potentially many differences between the people in a block.
The five blocks are
1. Williams-22, Deng-24, Hernandez-25, Moses-25
2. Santiago-27, Kendall-28, Mann-28, Smith-29
3. Brunk-30, Obrach-30, Rodriguez-30, Loren-32
4. Jackson-33, Stall-33, Brown-34, Cruz-34
5. Birnbaum-35, Tran-35, Nevesky-39, Wilansky-42

12. 1. Williams-22, Deng-24, Hernandez-25, Moses-25
Pg 258
80)
The five blocks are
1. Williams-22, Deng-24, Hernandez-25, Moses-25
2. Santiago-27, Kendall-28, Mann-28, Smith-29
3. Brunk-30, Obrach-30, Rodriguez-30, Loren-32
4. Jackson-33, Stall-33, Brown-34, Cruz-34
5. Birnbaum-35, Tran-35, Nevesky-39, Wilansky-42
c) Number the subjects from 1-4 within each block, then assign the members of each block to a weight-loss treatment.
For example, starting on line 133 (ignoring repeats and digits 0 and 5, 6, 7, 8, 9), we assign 4-Moses to treatment A, 1-Williams to treatment B and 3-Hernandez to treatment C (so that 2-Deng gets treatment D.

13. Pg 258
Every instructor has his or her own teaching style. If we assign two instructors to teach using standard technology and two to use multimedia technology, and we find a difference between the two sets of sections, we will not know if the difference is due to the technology or to the instructor.
82a)
Experiments
b) Use the instructors as blocks since each instructor teaches two sections. In one randomly chosen section, they would use standard technology and in the other they would use multimedia.

14. a) matched pairs design 84)
Pg 258
a) matched pairs design
84)
Experiments
b) to control for the variability in blood vessel functions among the subjects
c) we want to make sure that any effect we see is due to the chocolate and not to the time at which we measured it.

15. Pg 259
86)
a) randomly assign three of the six circles to be treated with additional CO2 and the other three circles to be left untreated.
Experiments
Table D was used to select 3 areas for treatment, starting at line 104. (ignoring repeats & 7, 8, 9, & 0)
At the end of the study, compare tree growth in the treated and untreated areas. 1 2 3
untreated
treated
treated 4 5 6
untreated
treated
untreated

16. Compare tree growth for the treated and untreated area in each pair.
Pg 259
b) Circles are matched to form pairs with similar soil fertility. Randomly assign one member of each pair to be treated and the other to remain untreated. (again using line 104)
86)
Experiments
Compare tree growth for the treated and untreated area in each pair. 1 2 3
treated
untreated
treated 4 5 6
untreated
untreated
treated

17. Pg 259
a) Confounding: if there is a difference in average wake-up time, Justin won’t know if it is due to the alarm or due to the difference between weekend nights and weeknights.
88)
Experiments
b) Use a randomized block design with the weekend days serving as one block and the weekdays serving as the other. Justin would randomly assign one weekend day to set his alarm and one for having no alarm; he would do likewise for the weekdays.

18. Read pg
Do pg 253 #71-97 odd
Reading Guide Section 4.3 #1-4
Chapter 4 Vocabulary Flash Cards
Test Date is Tuesday, February 16.
Vocabulary Mastery Test TOMORROW

19. Pg 259
90)
Take the 30 students and divide randomly into two equal groups. In the first group, have music playing while a story is read.
Experiments
In the other group, read a story without music in the background. Test the students for recall.
Now reverse the treatments and test the students for recall. Analyze the difference in recall for the individual students.

20. Section 4.2 Experiments Summary In this section, we learned that…
We can produce data intended to answer specific questions by observational studies or experiments.
In an experiment, we impose one or more treatments on a group of experimental units (sometimes called subjects if they are human).
The design of an experiment describes the choice of treatments and the manner in which the subjects are assigned to the treatments.
The basic principles of experimental design are control for lurking variables, random assignment of treatments, and replication (using enough experimental units).
Many behavioral and medical experiments are double-blind.

21. Section 4.2 Experiments Summary, con’t
In this section, we learned that…
Some experiments give a placebo (fake treatment) to a control group that helps confounding due to the placebo-effect.
In addition to comparison, a second form of control is to form blocks of individuals that are similar in some way that is important to the response. Randomization is carried out within each block.
Matched pairs are a common form of blocking for comparing just two treatments. In some matched pairs designs, each subject receives both treatments in a random order.

22. Looking Ahead… In the next Section…
We’ll learn how to use studies wisely.
We’ll learn about
The Scope of Inference
The Challenges of Establishing Causation
Data Ethics
In the next Section…