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Producing DataChapter 5Designing SamplesSection 5.1Convenience SamplingSampling that chooses the individuals that is easiest to reachA sample chosen by chance and that chance, or probability must be knownProbability SampleSimple Random Sample (SRS)Random Sample avoid biasnessAll individuals were chosen in an equal way and have an equal chance of being chosenUsed to help assign a simple random sampleLabel each piece of population with a numerical labelUse table to select labelsTable of Random DigitsStratified Random SampleStrata- groups of similar individualsDivide data into strata then chooses SRS for each Strata and then combineie music genresSelects smaller groups within populations stages and then chooses SRSMulti Stage Sampling DesignDesigning ExperimentsChapter 5.2Designing ExperimentsExperimental UnitsUnit having experiment done to themSubjectsWhen unit is human beingTreatmentExperimental 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 factorsGive good evidence for causationStudy only those factors we are interested in while controlling the othersExplanatory vs Response VariablesExplanatory Independent FactorsResponse DependentPlacebo Dummy VariableMany experiments have multiple factors Levels

Designing ExperimentsExperimentsDesignUnits Treatment Observed ResponseControl GroupControl affects of outside effectsBiasFavoritism for one group/outcomeControlFirst basic principle of statistical design of experiments

Designing ExperimentsOutline of a Random ExperimentSplit into two groups of studentsGive half students blue test and other half green testCheck scores on testHow 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 ExperimentsPrinciples of Experimental DesignControlRandomizeReplicateStatistical SignificanceAn observed effect so large that it would rarely occur by chanceGood Evidence

Designing ExperimentsPrinciples of Experimental DesignControlRandomizeReplicateStatistical SignificanceAn observed effect so large that it would rarely occur by chanceGood Evidence

Designing ExperimentsCautions in ExperimentsNeed to be sure to treat all units identically in every way except tested variableUse of Double Blind TechniqueNeither the units nor the personnel know treatments

Designing ExperimentsDesigns of ExperimentsRandomizedMatched PairsBlock

Simulating ExperimentsSection 5.3Designing ExperimentsChanceWhat 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 difficultDevelop 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 ExperimentsSimulationThe imitation of chance behavior, based on a model that accurately reflects the experiment under considerationSimulation StepsState the problem Define the experimentState the AssumptionsAssign digits to repeat outcomesSimulate many repetitionsState your conclusionIndependence (In terms of probability)One result does not affect the next Designing ExperimentsSimulation StepsState the problem Define the experimentWill I pass three or more of my classes this semester?State the AssumptionsEach class is independent of anotherPassing each class has the same probability (Yea right )Assign digits to repeat outcomes (TORD)Even Digits Pass, Odd Digits FailOne Digit represents one classStart at Line 128Simulate many repetitionsFind 10 repetitions and their outcomesState your conclusionEstimate Probability 2/10= 20%

Designing ExperimentsAssigning Digits in simulationsSex of a ChildPicking a pair of shoesPicking a male student from the classFind Probability then assign numbersSales of ice cream when a store has 35% chocolate, 25% vanilla, 10% peanut butter, and 30% coffee

Simulations with CalculatorRandIntMath Prob Rand( start, end ,# of numbers)