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)
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