Producing DataChapter 5

Designing SamplesSection 5.1

Convenience SamplingSampling that chooses the individuals that is

easiest to reach

• A sample chosen by chance and that chance, or probability must be known

Probability Sample

Simple Random Sample (SRS)Random Sample – avoid biasnessAll individuals were chosen in an equal way

and have an equal chance of being chosen

• Used to help assign a simple random sample• Label each piece of population with a

numerical label• Use table to select labels

Table of Random Digits

Stratified Random SampleStrata- groups of similar individualsDivide data into strata then chooses SRS for each

Strata and then combineie music genres

• Selects smaller groups within populations stages and then chooses SRS

Multi Stage Sampling Design

Designing ExperimentsChapter 5.2

Designing ExperimentsExperimental Units

Unit having experiment done to themSubjects

When unit is human beingTreatment

Experimental condition

Designing ExperimentsWhat is the purpose of an experiment?

To look at the response of one variable to the change in another or interaction of several factors

Give good evidence for causationStudy only those factors we are interested in while

controlling the othersExplanatory vs Response Variables

Explanatory Independent FactorsResponse DependentPlacebo “Dummy Variable”

Many experiments have multiple factors Levels

Designing ExperimentsExperiments

Design Units Treatment Observed Response

Control GroupControl affects of outside effects

BiasFavoritism for one group/outcome

ControlFirst basic principle of statistical design of

experiments

Designing ExperimentsOutline of a Random Experiment

Split into two groups of studentsGive half students blue test and other half

green testCheck scores on test

How does change affect this study?Effects of chance will average out with large

enough sample of populationYou must use enough experimental units to

reduce chance variation

Designing Experiments Principles of Experimental Design

Control Randomize Replicate

Statistical Significance An observed effect so large that it would rarely

occur by chance “Good Evidence”

Designing Experiments Principles of Experimental Design

Control Randomize Replicate

Statistical Significance An observed effect so large that it would rarely

occur by chance “Good Evidence”

Designing ExperimentsCautions in Experiments

Need to be sure to treat all units identically in every way except tested variable

Use of “Double Blind” Technique Neither the units nor the personnel know

treatments

Designing ExperimentsDesigns of Experiments

RandomizedMatched PairsBlock

Simulating ExperimentsSection 5.3

Designing ExperimentsChance

What is the chance of a flight actually being overbooked?

What is the chance of a cop catching you speeding?

What is the chance of you marrying your high school sweetheart?

How can we answer these questions?

Designing ExperimentsDo an actual experiment many times and calculate

the relative frequencyCan be costly, slow, and logistically difficult

Develop a probability model and use it to calculate a theoretical answerMust know probability which may be unknown because

of too many variablesDevelop a model that reflects the truth about the

experiment and then simulate repetitions for the experiment.Quicker than actually repeating the experimentAllows us to analyze mathematically

Designing ExperimentsSimulation

The imitation of chance behavior, based on a model that accurately reflects the experiment under consideration

Simulation StepsState the problem Define the experimentState the AssumptionsAssign digits to repeat outcomesSimulate many repetitionsState your conclusion

Independence (In terms of probability)One result does not affect the next

Designing ExperimentsSimulation Steps

State the problem Define the experiment Will I pass three or more of my classes this semester?

State the Assumptions Each class is independent of another Passing each class has the same probability (Yea right )

Assign digits to repeat outcomes (TORD) Even Digits Pass, Odd Digits Fail One Digit represents one class Start at Line 128

Simulate many repetitions Find 10 repetitions and their outcomes

State your conclusion Estimate Probability 2/10= 20%

Designing ExperimentsAssigning Digits in simulations

Sex of a ChildPicking a pair of shoesPicking a male student from the class

Find Probability then assign numbersSales of ice cream when a store has 35%

chocolate, 25% vanilla, 10% peanut butter, and 30% coffee

Simulations with CalculatorRandInt

Math Prob Rand( start, end ,# of numbers)