Designing Experiments

1. Designing Experiments

2. Experimental Units • The individuals on which an experiment is done are the experimental units. • When the units are people, they are called subjects. • A specific experimental condition applied to units is called a treatment.

3. Factors and Levels • The explanatory variable is often called a factor. • Most experiments have multiple factors, when a treatment is formed from these factors is often called a level.

4. The ability to grow in shade may help pines found in the dry forest of Arizona to resist drought. How well do these pines grow in shade? Investigators planted pine seedlings in a greenhouse in either full light or light reduced to 5% of normal by shade cloth. At the end of the study they dried the young trees and weighed them. Example 1

5. Example 1 • 1) What are the experimental units? • 2) What are the factors? • 3) What are the treatments? • 4) What is the response variable? The individual trees The amount of light Full light and reduced light Weight of the trees

6. Example 2 • You are investigating the effect of various amounts of sunlight and moisture on some tulips. You will measure the height of the tulips to measure the effectiveness of the various treatments. You can subject the samples to direct sunlight, partial sunlight, or no sunlight. You could also water the plants daily or every other day. Answer the following: a. What are the experimental units? b. What are the factor(s)? c. What are the factor levels? d. What are the possible treatments? e. What is the response variables?

7. Example 2 Answers The tulips Factor 1: Moisture • Experimental Units: • Treatment Matrix: • Factors: • Factor Levels: • Treatments: • Response Variable: Every Day Every other day Direct Sunlight Partial Sunlight Factor 2: Sunlight No Sunlight Sunlight and Moisture See the matrix above 6 total. See the matrix above for the combinations Tulip height

8. Comparative Experiment • Treatment→Observation • Observation 1 →Treatment →Observation 2 Simple Study: Gastric freezing: cooling stomach to relieve ulcer pain Subjects  Gastric Freezing  Observe Pain Relief What could complicate the observed results? Confounding, lurking variable: subjects feel better due to the fact they are receiving any treatment

9. Placebo Effect and Control Groups • A placebo effect is a dummy treatment that has no physical effect. • A control group is a group of subjects that have had no treatment or have been given a placebo. • In double blind experiments neither the subjects nor the people who have contact with them know which treatment a subject receives

10. 3 Statistical Design Principles • The control of the effects of lurking variables is the first principle of statistical design of experiments. • We call the units assigned the control: the control group. Either receive a standard treatment or a placebo – a treatment with no effect. • Randomization is the second major principle of statistical design of experiments. • Assign individuals to treatments randomly(use the random number table) • Replication is the third major principle of statistical design of experiments.

11. Completely Randomized Design • Simplest Experimental Design • Basic Layout for all similar designs: Group 1 (how many) Treatment 1 (description) Description of test subjects Group 2 (how many) Treatment 2 (description) Compare response variable value(describe) Randomly Assigned Group 3 (how many) Treatment 3 (description)

12. Example 3 - Design • A study is being conducted to compare the effectiveness of 3 medications (2 new drugs and the old standard drug) to reduce cholesterol in adults. 60 adult subjects have volunteered to participate. Design a double-blind, completely randomized experiment for testing the effectiveness of these three medications. Describe how to assign subjects to their respective treatment groups using the random number table.

13. Example 3 Answer • Overall Description of Experiment: • In order to ensure a random selection, we will assign subjects to their group using the random number table. Number each subject with 2 digits starting at 01 and ending with 60. Pick a line in the random number table – the first 20 numbers found are assigned to one group which will receive new drug #1, the next 20 numbers to the second group which receive new drug #2, and the rest to the control group which will receive the old, standard drug. • To ensure the experiment is double-blind, neither the subjects nor the medical personnel administering the treatments and blood tests will know which subject receives what treatment.

14. Example 3 Answer cont. • Algorithm Design Group 1 20 adults Treatment 1 New Drug #1 60 adults Group 2 20 adults Treatment 2 New Drug #2 Compare cholesterol levels Randomly Assigned Group 3 20 adults Treatment 3 Control Group – standard drug

15. Statistical Significance • An observed effect too large to attribute plausibly to chance is called statistically significant

16. Block Design • A block is a group of experimental units or subjects that are similar in ways that are expected to affect the response to the treatments • In block design, the random assignment of units to treatments is carried out separately within each block.

17. Block Design Cont. • Suppose medical researchers feel that gender might have impacted the results of the cholesterol experiment described in example 3. Suppose 120 men and 75 woman have volunteered for a new experiment. Describe how to modify example 3 to block the effect of gender.

18. Block Example Answer • Modified Algorithm Design Group 1 40 adults Treatment 1 New Drug #1 Compare male’s cholesterol levels Treatment 2 New Drug #2 120 adults males Group 2 40 adults Randomly Assigned Treatment 3 Control Group – standard drug Group 3 40 adults 195 adults Group 1 25 adults Treatment 1 New Drug #1 Compare female’s cholesterol levels Treatment 2 New Drug #2 75 adults females Group 2 25 adults Randomly Assigned Treatment 3 Control Group – standard drug Group 3 25adults

19. Matched Pairs • Matched Pairs Design: • A type of blocking • Used when: (a) only two treatments are possible (b) subjects can be paired up based on some blocking variable(s) a.k.a. we pair up similar subjects. • Within each pair, we randomly assign the two treatments to the two subjects. • Another version of matched pairs: • Each subject gets both treatments in a random order and then we compare the results.

20. Matched Pairs Example • We wish to evaluate the effectiveness of 2 different fish foods on fish growth. The experiment is to be conducted in a room with 8 fish tanks. See the diagram below for the layout of the room. Design a matched-pairs experiment to control the environmental conditions.

21. Matched Pairs ex. answer • We will pair up the fish tanks by their location in the room. 2 tanks closest to the heater, 2 tanks close to the windows, 2 tanks nearest the door, and 2 tanks in the center of the room. Within each pair, we will randomly assign the type of fish food to each tank. We will measure the fish’s weight in order to assess growth Matching pairs controls: environment variable Randomization controls: unknown influences among the tanks.