1 Chapter 11 Understanding Randomness

2 Why Random? What is it about chance outcomes being random that makes random selection seem fair? Two things:  Nobody can guess the outcome before it happens  When we want things to be fair, usually some underlying set of outcomes will be equally likely (although in many games some combinations of outcomes are more likely than others).

3 It’s Not Easy Being Random

4 A Simulation A simulation consists of a collection of things that happen at random. The most basic event is called a component of the simulation. Each component has a set of possible outcomes, one of which will occur at random. The sequence of events we want to investigate is called a trial.  Trials usually involve several components.  After the trial, we record what happened—our response variable.

5 Simulation Steps 1.Identify the component to be repeated. 2.Explain how you will model the outcome. 3.Explain how you will simulate the trial. 4.State clearly what the response variable is. 5.Run several trials. 6.Analyze the response variable. 7.State your conclusion (in the context of the problem, as always).

6 What Can Go Wrong? Don’t overstate your case.  Always be sure to indicate that future results will not match your simulated results exactly. Model the outcome chances accurately. Run enough trials.

7 What have we learned? We will harness the power of randomness. A simulation model can help us investigate a question for which:  many outcomes are possible,  we can’t (or don’t want to) collect data, and  a mathematical answer is hard to calculate. We base our simulations on random values. Like all models, simulations can provide us with useful insights about the real world.

Sample Surveys Chapter 12

Designing Samples Population:  The entire group of individuals that we want information about Sample:  A part of the population that we actually examine in order to gather information Voluntary response sample:  People who choose themselves by responding to a general appeal (usually biased since people with strong opinions are most likely to respond) Convenience sample:  Chooses the individuals that are easiest to reach (also biased)

Bias:  Systematically favors certain outcomes Simple Random Sample (SRS):  Consists of n individuals from the population chosen in such a way that every set of n individuals has an equal chance of being chosen  Table of random digits (choosing an SRS) Probability sample:  Gives each member of the population a known chance to be selected Stratified random sample:  First divide the population into groups of similar individuals, called strata. Then choose a separate SRS in each stratum and combine these SRSs to form the full sample. Multistage samples:  Chooses the sample in stages (i.e. states, counties, cities, blocks, homes)

Cautions Undercoverage:  Some groups in the population are left out of the process of choosing the sample Nonresponse:  When an individual chosen for the sample can’t be contacted or refuses to cooperate Response bias:  May be caused by the respondent or the interviewer (lies, attitude towards questions, memory) Wording effects:  Confusing or leading questions can introduce strong bias

Chapter 13 Experiments and Observational Studies

Observation vs Experiment Observational Study:  Observes individuals and measures variables of interest (imposes no treatment) Experiment:  Manipulates factor levels to create treatments, randomly assigns subjects to these treatment levels, and compares the responses of the subject groups across treatment levels

Designing Experiments Random Assignment:  To be valid, an experiment must assign experimental units to treatment groups at random Experimental Units:  The individuals on which the experiment is done Subjects:  Human experimental units Response:  A variable whose values are compared across different treatments. Treatment:  A specific experimental condition applied to the units Factor:  The explanatory variable in an experiment (distinction between variables is important)

Principles of Experimental Design Control of the effects of lurking variables on the response Randomization, the use of impersonal chance to assign experimental units to treatments Replication of the experiment on many units to reduce chance variation in the results Block to reduce effects of identifiable attributes of the subjects that can be controlled.

Other Definitions Statistical Significance:  An observed effect so large that it would rarely occur by chance Placebo effect:  The response to a dummy treatment Control Group:  The group of patients who received a sham treatment Double Blind:  Neither the subjects nor the experimenter knew which treatment each subject received Lack of realism:  Setting or treatment does not realistically duplicate conditions of interest

Designs Matched Pairs Design:  Compares just two treatments by choosing pairs of subjects that are as closely matched as possible Block Design:  The random assignment of units to treatments is carried out separately within each block Confounding:  When the levels of one factor are associated with the levels of another factor so their effects cannot be separated

An Example: Randomized comparative experiment Random Assignment Group 1Treatment 1 Treatment 2 (Control) Compare Results Group 2