Warm Up Imagine you want to conduct a survey of all public high school seniors in San Jose to determine how many colleges they plan to apply to this year. Your sample size will be about 150 students. 1) Describe how you would conduct this survey using a simple random sample. How would you ensure random selection? 2) Describe how you would conduct this survey using a stratified random sample. What would you choose as strata? How would you ensure random selection? 3) Do you think a cluster sample would be a good choice? Why or why not?

Observational Study vs. Experiment Observational Study – We randomly select a sample of individuals from the population and observe some characteristic. Experiment - We randomly assign individuals to different treatment groups and observe their responses. For experiments, we may randomly select a sample of individuals from a population OR we may use a group of volunteers.

Experimental Design The individuals on which the experiment is done are the experimental units. If units are humans, they are called subjects. The experimental conditions applied to the units (aka the thing we ‘do’ to the units) is called a treatment. The goal of an experiment is to establish a causal link between a particular treatment and a response. Only experiments can establish cause and effect, not observational studies.

Factors, Levels and Response Variables Factors: The variables controlled by the experimenter (e.g. the drug given in a medical experiment) Levels: The number of settings for each factor (e.g. doses of 0 mg, 50 mg, and 100 mg in a drug study) A treatment is a particular factor at a particular level. Response variable: The output or result an experimenter thinks will be affected by the treatments. (e.g. size of patients’ cancerous tumor after drug treatment)

Experimental Design - Practice Imagine you want to conduct an experiment to determine if using a cheat sheet and/or a calculator affects the grades of Algebra 1 students on their Unit Test. Identify the following in this experiment: Experimental Units (Subjects) Factors Levels Treatments Response Variable

Principles of Experimental Design Control - Hold the levels of other factors constant to prevent variations from affecting the results. Control prevents lurking variables from affecting the results of our experiment. Replicate - Even with control, natural variability occurs among experimental units. If we assign many individuals to each treatment group, the effects of chance (and individual differences) will average out. Randomize – Randomly assign units to different treatments to account for the effects of variables that were not controlled for. Random assignment makes the effect of these other variables similar in all groups of a study.

Additional Experimental Design Concerns Blind experiment – Either the subject or the experimenter/evaluator does not know which treatment the subject received. Double Blind experiment – Neither the subject nor the experimenter/evaluator know which treatment a subject received. Placebo effect – Positive response of a subject to a “dummy” treatment. If not designed as a separate “treatment” this can be a lurking variable in many experiments.

Randomized Experiment Consider again our experiment on Algebra 1 students using calculators and cheat sheets for the Unit Test. Identify how Control, Replication and Randomization are or should be used in this experiment. Can this experiment be made blind or double blind? Can we use a placebo? Group 1 Treatment 1 15 students No Cheat Sheet/No Calc Group 2 Treatment 2 15 students Yes Cheat Sheet/No Calc Random Compare Unit Assignment Group 3 Treatment 3 Test Scores 15 students No Cheat Sheet/Yes Calc Group 4 Treatment 4 15 students Yes Cheat Sheet/Yes Calc

Statistical Significance We hope to see big differences (differences so large they are not likely just due to chance or individual differences) in the response variable between different treatment groups. If we do have an observed effect so large that it would rarely occur by chance, we call our result Statistically Significant.

Design an Experiment Design an experiment you might use to determine if restricting phone usage at home will improve students’ grades. The potential subjects for your study are the 132 students in all of my AP Stats sections. The experiment will last until the end of the semester. You and your partner will write a one page summary of your experimental design. Create a diagram for your experiment. Describe how you will randomly assign people to different treatments. Identify the following in the summary of your experiment: treatments factors levels control randomization replication response variable

Design an Experiment Some groups will move to new seats, some will stay home. You will consult with the new group sitting across from you. Explain your experimental design to them and get feedback. Listen to their proposal and provide constructive criticism. We will have 2-3 rounds of exchanging ideas and providing critiques.

Design an Experiment Use the constructive criticism you received to revise your experimental plan. Produce a revised plan on a separate sheet of paper. Again make sure you have a diagram for your experiment and define all the terms we listed: treatments factors levels control randomization replication response variable Some groups will be selected to share their revised plans with the class. All groups will turn in their experimental plans.