1. Statistics 400 - Lecture 19

2. zLast Day: Randomized Block Design zToday: Experiments

3. Experiments zIn a designed experiment, we deliberately apply a treatment to experimental units zThe response is observed to determine the effect of the treatment zDesigning the experiment deals with how we apply treatments to experimental units

4. Example zSickle cell disease is an inherited disorder of the red blood cells zAn experiment is performed to see if the drug hydroxyurea can reduce the severe pain caused by sickle cell disease zHow might we conduct the experiment?

5. Example (cont.) zWho do we give treatments to? zWhat treatments do we apply? zHow do we assign the treatments to patients?

6. 3 Basic Principles of Experimental Design zRandomization: the assignment of treatments to experimental units should be done randomly ySpreads the effect of unknown lurking variables evenly over all treatment combinations on average yPrevents uncontrolled sources of variation from influencing responses in a systematic manner

7. zReplication: repeating the experiment on several experimental units yReduces chance variation in the results yIncreases power when conducting statistical tests

8. zBlocking: Perform treatments on same (or similar) experimental units yRemoves effect of known variable (e.g. boy in boys’ shoe example or plot in the bio-mass example) yAllows for fairer comparisons yNote: treatments within each block are applied in random order

9. Comparative Experiments zLab experiments in science and engineering often have a single treatment which is applied to all experimental units zTreatment is applied and the the response observed zIn this case, we rely on the controlled environment in the lab to protect the data from the effect of lurking variables

10. zWhen experiments conducted in the field or on living subjects, simple designs often yield invalid data zCannot tell whether data is due to the treatment or a lurking variable

11. zExample: “Gastric Freezing” is a technique to treat ulcers in upper intestines zA patient swallows a balloon and refrigerated liquid is passed through the balloon zUlcer sufferers were selected at random and given the procedure zThis experiment, reported in the Journal of the American Medical Association, showed that gastric freezing reduced ulcer pain zPotential Problem:

12. zIn previous example, gastric freezing was confounded with zTo avoid this difficulty, a control group is used where they receive a sham treatment zWithout the control group, experiment results often biased (i.e., the design of the study is biased if it systematically favors certain outcomes)

13. Blinding zIn evaluating the effect of a treatment, want to filter out the real effect from the effect of patient's own psychology zCan compare what happens in the treatment group with the control group zWill only work if the patients do not know whether they are getting the treatment or placebo

14. zSimilarly, when comparing two or more treatments the subjects should not know which treatment they are receiving zIdea is called blinding the subjects zWhen the experimenter does not know the treatment, called double blinding

15. Example zDoes taking Vitamin C reduce the incidence of colds? zThis is a popular theory - how would you design an experiment to test it using students? zAssume that there are 50 students available

16. zMethod 1: The students take supplements for 6 months and record the number of colds zAfter 6 months, the data was collected, and on average, the group of students had 1.4 colds per subject zWhat is the flaws in this design?

17. zMethod 2: Students are divided into two groups zAll males receive Vitamin C supplements for 6 months while all females receive nothing zEach student records the number of colds incurred in the 6 months zThe males had an average of 1.4 colds per subject; the females had an average of 1.9 colds per subject zWhat is the flaw in this design?

18. zMethod 3: Students are randomly assigned to each of the two groupsrandomly assigned zAccomplished by putting 25 slips of paper marked `Vitamin C', and 25 slips of paper `Control’ into a hat zEach student then selects a slip of paper. Those with the slips marked `Vitamin C' are given Vitamin C supplements for 6 months, while those with the slips marked `Control' are not given anything zAt the end of the 6 months, the Vitamin C group had an average of 1.4 colds per subject; the control group had an average of 1.9 colds per subject zWhat is the flaw in this design?

19. zMethod 4: Researcher makes up 50 identical pill bottles zIn half of the researcher places Vitamin C tables. In the other half, the researcher puts identical looking and tasting sugar pills zThe researcher then asks an associate to randomly assign the jars and to keep track of which jar has which tablet, but the associate is not to tell the researcherrandomly assign z The numbered jars are then placed in a box, and mixed up

20. zEach student then selects a jar and tells the researcher the number on the jar zEach student takes the pill for the next six months. Each student records the number of colds incurred in the 6 month period zEach student reports the number of colds incurred over the period zThe Vitamin C group had an average of 1.4 colds per subject; the control group had an average of 1.9 colds per subject zWhat is the flaw in this design?

21. zMethod 5: The researcher suspects that gender also has an effect on colds zThe students are divided into two groups, male and female. zFor each group, the researcher makes up identical pill bottles - half of the Vitamin C and Sugar Pills bottles are divided equally among the male and female groups zThe experiment in Method 4 is performed on males and females separately zWhat is the flaw in this design?