5.2.1 Designing Experiments

1. 5.2.1 Designing Experiments AP Statistics

2. Experimental Units, Subjects, Treatment The individuals on which the experiment is done are the experimental units. When the units are human beings, they are called subjects. A specific experimental condition applied to the units is called a treatment.

3. Laboratory experiments in science and engineering often have a simple design with only a single treatment which is applied to all of the experimental units. The design of such an experiment can be outlined as: Units  Treatment  Observe response

4. Response, Explanatory, & Lurking Variables Response variable (pg. 172) – measures an outcome of a study Explanatory variable (pg. 172) – helps explain or influences changes in a response variable; (the explanatory variables in an experiment are usually called “factors”) Lurking variable (pg. 239) - a variable that is not among the explanatory or response variables in a study; may influence the interpretation of the relationship between the variables. ** open textbook to pg. 239, read example 3.18

5. Control vs. Control Group We rely on a controlled environment to protect our experiment from lurking variables Control is the overall effort to minimize variability in the way the experimental units are obtained and treated. *Comparison of several treatments in the same environment is the simplest form of control. The group of individuals who receives no treatment is the control group

6. 5.33 pg. 357 Describe the experimental units, the factors, the treatments, and response variables. • The ability to grow in shade may help pines found in the dry forests of Arizona to resist drought. How well do these pines grow in the shade? Investigators planted pine seedlings in a greenhouse in either full light, light reduced to 25%, or light reduced to 5% of normal by shade cloth. At the end of the study, they dried the young trees and weighed them. • The experimental units are the individual trees. The factor is the amount of light. Treatments are full light, light reduced to 25% and light reduced to 5%. • Response variable is the weight of the trees. When we map this out it will look like: • Full light • Planted pine seeds 25% light Compare weight of trees • 5% light

7. 5.2.1 (Day 1) Homework H.W. pg. 357 # 5.34, 5.35 and Read pg. 358-364 “Selecting random samples by calculator” pg. 363-364

8. Randomization * Randomization produces groups of experimental units that should be similar in all respects before the treatments are applied. (Ex. 5.17 pg. 360) * Comparative Design ensures that influences other than the treatment operate equally on both groups. (Figure 5.4 pg. 360)

9. Principles of Experimental Design • Control the effects of lurking variables on the response, most simply by comparing two or more treatments • 2) Replicate each treatment on many units to reduce chance variation in the results • 3) Randomize—use impersonal chance to assign experimental units to treatments

10. An observed effect so large that it would rarely occur by chance is called STATISTICALLY SIGNIFICANT. When all experimental units are allocated at random among all treatments, the experiment is said to have a Completely Randomized Design (Ex. 5.19 pg. 362)

11. A food company assesses the nutritional quality of a new instant breakfast product by feeding it to newly weaned male white rats. The response variable is a rat’s weight gain over a 28 day period. A control group of rats eats a standard diet, but otherwise receives the same treatment as the experimental group. We must first randomly assign the rats to the two different groups (the control group and the experimental group). To do this, we choose an SRS of 15 rats from the population of 30 rats. Use Table B starting at line 130 Label the rats 01-30 and randomly select 15 rats to be in our control group. (the remaining 15 are in our experimental group) 6905164817 87174 09517 84534 06489 8720197245 05007 16632 81194 14873 04197 85576 45195 96565 6873255259 84292 08796 43165 93739 31685 97150 45740 41807 6556133302 07051 93623 18132 09547 27816 78416 18329 21337 35213 37741 04312 68508 We have selected rats 5, 16, 17, 20, 19, 04, 25, 29, 18, 07, 13, 02, 23, 27, and 21 for our control group. (Call it Group 2)

12. We will place the remaining 15 rats into our experimental group. Here is the mapping for our experiment and sampling: Here, all of our experimental units have been allocated at random among the treatments. Therefore, our experiment is completely randomized.

13. pg. 364 # 5.39, 5.41, 5.44 5.2.1 (Day 2) Homework