1. Chapter 2 Lesson 2.3a Collecting Data Sensibly 2.3: Simple Comparative Experiments

2. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Randomized, Comparative Experiments An experiment is a study design that allows us to prove a cause-and-effect relationship. An experiment: Manipulates factor levels to create treatments. Randomly assigns subjects to these treatment levels. Compares the responses of the subject groups across treatment levels. In an experiment, the experimenter must identify at least one explanatory variable, aka factor, to manipulate and at least one response variable to measure.

3. Activity: Design an Experiment In groups of 5 or 6, design an hypothetical experiment to answer this question: “Who has the better fries: McDs or In n Out?” Be SPECIFIC in your design (step by step instructions)

4. “Who has the better fries: McDs or In n Out?” Population: SMHS Sample: Stratified Random Sample 1.Stratify by grade level (freshies, sophs, juns, seniors) 2.Collect a random sample of 25 people from each strata by using a random number generator on a roster of each class 3.During SSR, have these students come out to the quad and tell them they are doing a taste test.

5. “Who has the better fries: McDs or In n Out?” 4.Blindfold the every student and give them a fry and record which fry was given first. (flip a coin to determine which fry to first give them: Heads - McDs, Tails - In n Out) 5.Have each student say which fry they preferred (1 st or 2 nd ) (or consider a Matched-Pairs Design) 6.Count and compare how many students preferred the fry from McDs or from In n Out.

6. Chapter 2 Lesson 2.3b Collecting Data Sensibly 2.3: Simple Comparative Experiments

7. Suppose we are interested in determining the effect of room temperature on the performance on a first-semester calculus exam. So we decide to perform an experiment. What variable will we “ measure ” ? the performance on a calculus exam What variable will “ explain ” the results on the calculus exam? the room temperature This is called the response variable. Response variable – a variable that is not controlled by the experimenter and that is measured as part of the experiment This is called the explanatory variable. Explanatory variables – those variables that have values that are controlled by the experimenter (also called factors)

8. We decide to use two temperature settings, 65° and 75°. How many treatments would our experiment have? the 2 treatments are the 2 temperature settings Room temperature experiment continued... Treatments – any particular combination of the explanatory variables

9. Suppose we have 10 sections of first-semester calculus that have agree to participate in our study. On who or what will we impose the treatments? the 10 sections of calculus How would we determine which sections would be in rooms with the temperature set at 65° and which sections in rooms set at 75°? we need to randomly assign them to the treatments Room temperature experiment continued... These are our subjects or experimental units. Random assignment of subjects to treatments ensures that the experiment does not systematically favor one treatment over another.

10. Sections assigned Treatment 1 (65°) Treatment 2 (75°) 3 9 85 7 Room temperature experiment continued... To randomly assign the 10 sections of first- semester calculus to the 2 treatment groups, we would first number the classes 1-10. Place the numbers 1-10 on identical slips of paper and put them in a hat. Mix well. Randomly select 5 numbers from the hat. Those will be the sections that have the room temperature set at 65°. The remaining sections will have the room temperature set at 75°. 97583 124610

11. Sections assigned Treatment 1 (65°)97583 Treatment 2 (75°)124610 Room temperature experiment continued... Notice that there are five sections assigned to each treatment. This is called replication. Replication ensures that we have multiple observations for each treatment. Why is replication an important trait of a well-designed experiment?

12. Remember – the explanatory variable is the room temperature setting, 65° and 75°. The response variable is the grade on the calculus exam. Are there other variables that could affect the response? Room temperature experiment continued... T i m e o f d a y ? Instructor? T e x t b o o k ? A b i l i t y l e v e l o f s t u d e n t s ? These other variables are called extraneous variables. An extraneous variable is a variable that is NOT one of the explanatory variables (factors) but it is thought to affect the response. In an experiment, these extraneous variables need to be “ controlled ”. Direct control is holding the extraneous variables constant so that their effects are not confounded with those of the experimental conditions (treatments ). Can the experimenter control these extraneous variables? If so, how? What about the variables that the experimenter can ’ t directly control? What can be done to avoid confounding results? Remember - two variables are confounding if their effects on the response cannot be distinguished from each other.

13. Suppose that there were five instructors who taught the first-semester calculus. We do not have direct control of this variable; however, we could have each instructor teach 2 sections. Then we could randomly assign which one of the 2 sections would have a temperature setting of 65° and the other would have a temperature setting of 75°. Room temperature experiment continued... This is an example of blocking. Blocking is process by which an extraneous variable’s effects are filtered out. Similar groups, called blocks, are created. All treatments are tried in each block.

14. What about extraneous variables that we cannot control directly or that we cannot block for or that we don ’ t even think about? Random assignment should evenly spread all extraneous variables, that are not controlled directly or that are not blocked, into all treatment groups. We expect these variables to affect all the experimental groups in the same way; therefore, their effects are not confounding. Room temperature experiment continued...

15. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley The Four Principles of Experimental Design 1.Direct Control: We control sources of variation other than the factors we are testing by making conditions as similar as possible for all treatment groups. 2.Randomize: Randomization allows us to equalize the effects of unknown or uncontrollable sources of variation. It does not eliminate the effects of these sources, but it spreads them out across the treatment levels so that we can see past them. 3.Replicate: Repeat the experiment, applying the treatments to a number of subjects.

16. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley The Four Principles of Experimental Design (cont.) 4.Block : Sometimes, attributes of the experimental units that we are not studying and that we can’t control may nevertheless affect the outcomes of an experiment. If we group similar individuals together and then randomize within each of these blocks, we can remove much of the variability due to the difference among the blocks. Note: Blocking is an important compromise between randomization and control, but, unlike the first three principles, is not required in an experimental design.

17. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Experiment Design Diagrams Examples: 4 th edition (pg.58-60) Figure 2.4 Figure 2.5 Figure 2.9 Experimental Units Measure response for A Treatment B Treatment A Measure response for B Random Assignment Compare treatments

18. Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Practice Experimental Design Diagram: pg.64: #39 (from HW)

19. Homework Pg.62: #2.33-2.37, 2.39, 2.45 Reading Notes 2.4