Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2...
Transcript of Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2...
![Page 1: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/1.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Math 1710 Class 24
Sampling and ExperimentationDr. Back
Oct. 23, 2009
![Page 2: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/2.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Polio Vaccine
NFIP Vaccine Trials
Size Rate (cases/100K)
Grade 2 Vaccine 125K 25Grade 2 No Consent 125K 44Grade 1,3 Control 725K 54
![Page 3: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/3.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Polio Vaccine
NFIP Vaccine Trials
Size Rate (cases/100K)
Grade 2 Vaccine 125K 25Grade 2 No Consent 125K 44Grade 1,3 Control 725K 54
PHS Double Blind Vaccine Trials
Size Rate (cases/100K)
Treatment 200K 28Control 200K 71
No Consent 350K 46
![Page 4: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/4.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Polio Vaccine
NFIP Vaccine Trials
Size Rate (cases/100K)
Grade 2 Vaccine 125K 25Grade 2 No Consent 125K 44Grade 1,3 Control 725K 54
PHS Double Blind Vaccine Trials
Size Rate (cases/100K)
Treatment 200K 28Control 200K 71
No Consent 350K 46NFIP result confusing, but PHS not.
![Page 5: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/5.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Polio Vaccine
NFIP Vaccine Trials
Size Rate (cases/100K)
Grade 2 Vaccine 125K 25Grade 2 No Consent 125K 44Grade 1,3 Control 725K 54
PHS Double Blind Vaccine Trials
Size Rate (cases/100K)
Treatment 200K 28Control 200K 71
No Consent 350K 46NFIP result confusing, but PHS not.Randomized control groups help a lot with unanticipated issues!
![Page 6: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/6.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Portacaval Shunt Studies
51 Studies
Enthusiasm:Design Marked Moderate None
No Controls 24 7 1Controls, not randomized 10 3 2Randomized controls 0 1 3
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Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Gilbert ’75
28 Social and Medical Interventions
++ 21%
+ 21%
0 46%
- 7%
– 4%
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Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Gilbert ’77
36 Surgical and Anaesthetic Innovations
innovation highly preferred 14%
innovation preferred 19%
innovation a success but not much better 11%
innovation a disappointment but not much worse 28%
standard preferred 6%
standard highly preferred 11%
![Page 9: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/9.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Establishing Causation Without Experimentation
(Attempts)
Association strong.
Association consistent.
Higher doses give stronger responses.
Alleged cause precedes effect.
Alleged cause is plausible.
Rule out other plausible explanations.
This is hard to do reliably.
Experimentation is much clearer!
![Page 10: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/10.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Establishing Causation Without Experimentation
(Attempts)
Association strong.
Association consistent.
Higher doses give stronger responses.
Alleged cause precedes effect.
Alleged cause is plausible.
Rule out other plausible explanations.
This is hard to do reliably.
Experimentation is much clearer!
![Page 11: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/11.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Establishing Causation Without Experimentation
(Attempts)
Association strong.
Association consistent.
Higher doses give stronger responses.
Alleged cause precedes effect.
Alleged cause is plausible.
Rule out other plausible explanations.
This is hard to do reliably.
Experimentation is much clearer!
![Page 12: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/12.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Establishing Causation Without Experimentation
(Attempts)
Association strong.
Association consistent.
Higher doses give stronger responses.
Alleged cause precedes effect.
Alleged cause is plausible.
Rule out other plausible explanations.
This is hard to do reliably.
Experimentation is much clearer!
![Page 13: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/13.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Establishing Causation Without Experimentation
(Attempts)
Association strong.
Association consistent.
Higher doses give stronger responses.
Alleged cause precedes effect.
Alleged cause is plausible.
Rule out other plausible explanations.
This is hard to do reliably.
Experimentation is much clearer!
![Page 14: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/14.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Establishing Causation Without Experimentation
(Attempts)
Association strong.
Association consistent.
Higher doses give stronger responses.
Alleged cause precedes effect.
Alleged cause is plausible.
Rule out other plausible explanations.
This is hard to do reliably.
Experimentation is much clearer!
![Page 15: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/15.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Establishing Causation Without Experimentation
(Attempts)
Association strong.
Association consistent.
Higher doses give stronger responses.
Alleged cause precedes effect.
Alleged cause is plausible.
Rule out other plausible explanations.
This is hard to do reliably.
Experimentation is much clearer!
![Page 16: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/16.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Establishing Causation Without Experimentation
(Attempts)
Association strong.
Association consistent.
Higher doses give stronger responses.
Alleged cause precedes effect.
Alleged cause is plausible.
Rule out other plausible explanations.
This is hard to do reliably.
Experimentation is much clearer!
![Page 17: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/17.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Establishing Causation Without Experimentation
(Attempts)
Association strong.
Association consistent.
Higher doses give stronger responses.
Alleged cause precedes effect.
Alleged cause is plausible.
Rule out other plausible explanations.
This is hard to do reliably.
Experimentation is much clearer!
![Page 18: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/18.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Basic Strategies
1) Control extraneous sources of variation.
2) Randomize to deal with uncontrollable sources of variation.
3) Replicate to increase accuracy and gain greater confidencein the scope of your conclusions.
4) Block when possible to increase accuracy/sensitivity andbetter control variability.
![Page 19: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/19.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Basic Strategies
1) Control extraneous sources of variation.
2) Randomize to deal with uncontrollable sources of variation.
3) Replicate to increase accuracy and gain greater confidencein the scope of your conclusions.
4) Block when possible to increase accuracy/sensitivity andbetter control variability.
![Page 20: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/20.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Basic Strategies
1) Control extraneous sources of variation.
2) Randomize to deal with uncontrollable sources of variation.
3) Replicate to increase accuracy and gain greater confidencein the scope of your conclusions.
4) Block when possible to increase accuracy/sensitivity andbetter control variability.
![Page 21: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/21.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Basic Strategies
1) Control extraneous sources of variation.
2) Randomize to deal with uncontrollable sources of variation.
3) Replicate to increase accuracy and gain greater confidencein the scope of your conclusions.
4) Block when possible to increase accuracy/sensitivity andbetter control variability.
![Page 22: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/22.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Sampling Words
Sample vs. Population
Sample Statistic vs. Population Parameter
Sampling Frame
Voluntary Response Sample
Convenience Sample
Biased Sample
Simple Random Sample (SRS)
![Page 23: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/23.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Sampling Words
Census
Strata
Stratified Random Sample
Cluster Sample
Systematic Sampling
Multistage Sample Design
![Page 24: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/24.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Sampling Words
Matching in an observational study
Undercoverage
Non-Response Bias
Response Bias
Leading Questions
Sampling Variability
![Page 25: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/25.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Stratification
Strata – groups of homogeneous individuals.
Stratified Random Sample – same probability of choicewithin each group.
![Page 26: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/26.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Stratification
Strata – groups of homogeneous individuals.
Stratified Random Sample – same probability of choicewithin each group.
Advantages include:
Every stratum well represented.
Can be more accurate for a given sample size.Strata with greater variability should be better represented.
![Page 27: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/27.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Types of Bias
Response bias vs. voluntary response bias vs. non-responsebias?
![Page 28: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/28.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Types of Bias
Response bias vs. voluntary response bias vs. non-responsebias?Response Bias: problems in the questions or how they areasked.
![Page 29: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/29.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Types of Bias
Response bias vs. voluntary response bias vs. non-responsebias?Voluntary Response Bias: problems in surveys where onlyvolunteers participate.
![Page 30: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/30.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Types of Bias
Response bias vs. voluntary response bias vs. non-responsebias?Non-Response Bias: problems associated with which people aremissing in the final results.
![Page 31: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/31.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Types of Bias
Response bias vs. voluntary response bias vs. non-responsebias?Undercoverage: groups somewhat missing from the samplingframe.
![Page 32: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/32.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Experiments
Observational Study vs. Experiment
Prospective vs Retrospective Study
Factor in an experiment
Level
Treatment
![Page 33: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/33.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Experiments
Control Group
Single-Blind vs. Double-Blind Experiment
One Factor vs. Two Factor Experiment
Placebo
Placebo Effect
Hidden Bias
![Page 34: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/34.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Experiments
Block
Completely Randomized Design
Block Design
Matched Pairs Design
Confounding Variables
Statistically Significant Effect
![Page 35: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/35.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Factors and Levels
Factors vs. Levels vs. Treatments?
![Page 36: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/36.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Factors and Levels
Factors vs. Levels vs. Treatments?
Factor in an Experiment: Variable being manipulated.
![Page 37: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/37.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Factors and Levels
Factors vs. Levels vs. Treatments?
Levels: Values of a factor.
![Page 38: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/38.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Factors and Levels
Factors vs. Levels vs. Treatments?
Treatment: What is actively done to the experimental units.
![Page 39: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/39.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Block Related
Block vs. Completely Randomized Design vs. Block Design vs.Matched Pairs Design
![Page 40: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/40.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Block Related
Block vs. Completely Randomized Design vs. Block Design vs.Matched Pairs DesignBlock: homogenous group similar in some important way.
![Page 41: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/41.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Block Related
Block vs. Completely Randomized Design vs. Block Design vs.Matched Pairs DesignBlock Design: random within each block.
![Page 42: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/42.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Block Related
Block vs. Completely Randomized Design vs. Block Design vs.Matched Pairs DesignCompletely Randomized Design: Every subject an equal chanceof every treatment.
![Page 43: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/43.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Block Related
Block vs. Completely Randomized Design vs. Block Design vs.Matched Pairs DesignMatched Pairs Design: block size of 2.
![Page 44: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/44.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Lurking and Confounding
Lurking: Mostly used in observational situations; a variable(not directly studied) which actually accounts for anassociation.
![Page 45: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/45.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Lurking and Confounding
Confounding Variables: Mostly used in experiments; variableswhose effects are difficult or impossible to separate from whatyou are observing.
![Page 46: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/46.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Choose an SRS of size 5 from 30 people
Step 1: Assign ID numbers 01,02,. . .,29,30.all 2-digit!
Step 2: Pick a random place to start in the table.(e.g. row 12, col 3) You might use a wristwatch.
69167 38894 00172 02999 97377 33305
Step 3: Read off pairs of ID digits, selecting those thatcorrespond to real units, rejecting others.
69 16 73 88 94 00 17 20 29 99 97 37 73 33 05
Our SRS is units 16 17 20 29 and 05.
![Page 47: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/47.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Choose an SRS of size 5 from 30 people
Step 1: Assign ID numbers 01,02,. . .,29,30.all 2-digit!
Step 2: Pick a random place to start in the table.(e.g. row 12, col 3) You might use a wristwatch.
69167 38894 00172 02999 97377 33305
Step 3: Read off pairs of ID digits, selecting those thatcorrespond to real units, rejecting others.
69 16 73 88 94 00 17 20 29 99 97 37 73 33 05
Our SRS is units 16 17 20 29 and 05.
![Page 48: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/48.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Choose an SRS of size 5 from 30 people
Step 1: Assign ID numbers 01,02,. . .,29,30.all 2-digit!
Step 2: Pick a random place to start in the table.(e.g. row 12, col 3) You might use a wristwatch.
69167 38894 00172 02999 97377 33305
Step 3: Read off pairs of ID digits, selecting those thatcorrespond to real units, rejecting others.
69 16 73 88 94 00 17 20 29 99 97 37 73 33 05
Our SRS is units 16 17 20 29 and 05.
![Page 49: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/49.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Choose an SRS of size 5 from 30 people
Step 1: Assign ID numbers 01,02,. . .,29,30.all 2-digit!
Step 2: Pick a random place to start in the table.(e.g. row 12, col 3) You might use a wristwatch.
69167 38894 00172 02999 97377 33305
Step 3: Read off pairs of ID digits, selecting those thatcorrespond to real units, rejecting others.
69 16 73 88 94 00 17 20 29 99 97 37 73 33 05
Our SRS is units 16 17 20 29 and 05.
![Page 50: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/50.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Choose an SRS of size 5 from 30 people
Step 1: Assign ID numbers 01,02,. . .,29,30.all 2-digit!
Step 2: Pick a random place to start in the table.(e.g. row 12, col 3) You might use a wristwatch.
69167 38894 00172 02999 97377 33305
Step 3: Read off pairs of ID digits, selecting those thatcorrespond to real units, rejecting others.
69 16 73 88 94 00 17 20 29 99 97 37 73 33 05
Our SRS is units 16 17 20 29 and 05.
![Page 51: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/51.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Choose an SRS of size 5 from 30 people
Step 1: Assign ID numbers 01,02,. . .,29,30.all 2-digit!
Step 2: Pick a random place to start in the table.(e.g. row 12, col 3) You might use a wristwatch.
69167 38894 00172 02999 97377 33305
Step 3: Read off pairs of ID digits, selecting those thatcorrespond to real units, rejecting others.
69 16 73 88 94 00 17 20 29 99 97 37 73 33 05
Our SRS is units 16 17 20 29 and 05.
![Page 52: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/52.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Matched Pairs
Coke/Pepsi Taste Test - matched pairs (50 people)
![Page 53: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/53.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Matched Pairs
Coke/Pepsi Taste Test - matched pairs (50 people)Method 1: Have half the people rate pepsi on a 1-7 scale andthe other half rate coke.1 is bad, 7 is good.
![Page 54: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/54.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Matched Pairs
Coke/Pepsi Taste Test - matched pairs (50 people)Method 1: Have half the people rate pepsi on a 1-7 scale andthe other half rate coke.1 is bad, 7 is good.Problem: One person’s 6 might be another person’s 5.
![Page 55: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/55.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Matched Pairs
Coke/Pepsi Taste Test - matched pairs (50 people)Method 1: Have half the people rate pepsi on a 1-7 scale andthe other half rate coke.1 is bad, 7 is good.Problem: One person’s 6 might be another person’s 5.Would still work if sample size big enough.
![Page 56: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/56.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Matched Pairs
Coke/Pepsi Taste Test - matched pairs (50 people)Method 2: Have each person taste both coke and pepsi.
![Page 57: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/57.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Matched Pairs
Coke/Pepsi Taste Test - matched pairs (50 people)Method 2: Have each person taste both coke and pepsi.Half try pepsi first, half try coke first.
![Page 58: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/58.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Matched Pairs
Coke/Pepsi Taste Test - matched pairs (50 people)Method 2: Have each person taste both coke and pepsi.Half try pepsi first, half try coke first.Look for each person at the difference between their coke andpepsi scores.
![Page 59: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/59.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Matched Pairs
Coke/Pepsi Taste Test - matched pairs (50 people)Method 2: Have each person taste both coke and pepsi.Half try pepsi first, half try coke first.Look for each person at the difference between their coke andpepsi scores.Still some problems, e.g. how thirsty someone is when theystart.That’s why we randomize which soda goes first.
![Page 60: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/60.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Matched Pairs
Coke/Pepsi Taste Test - matched pairs (50 people)Method 2: Have each person taste both coke and pepsi.Half try pepsi first, half try coke first.Look for each person at the difference between their coke andpepsi scores.This is Matched Pairs.
![Page 61: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/61.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Experimental Design Diagrams
Basic Pattern: Units −→ Treatments −→ Results
![Page 62: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/62.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Experimental Design Diagrams
Basic Pattern: Units −→ Treatments −→ ResultsRat experiment - diet to increase weight. (30 rats)
![Page 63: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/63.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Experimental Design Diagrams
Basic Pattern: Units −→ Treatments −→ ResultsRat experiment - diet to increase weight. (30 rats)
![Page 64: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/64.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Experimental Design Diagrams
Basic Pattern: Units −→ Treatments −→ ResultsRat experiment - diet to increase weight. (30 rats)
![Page 65: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/65.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Experimental Design Diagrams
Basic Pattern: Units −→ Treatments −→ ResultsRat experiment - diet to increase weight. (30 rats)
![Page 66: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/66.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Experimental Design Diagrams
Basic Pattern: Units −→ Treatments −→ ResultsRat experiment - diet to increase weight. (30 rats)Reduce Electrical Usage - meter/chart/control. (60 houses)
![Page 67: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/67.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Experimental Design Diagrams
Basic Pattern: Units −→ Treatments −→ ResultsRat experiment - diet to increase weight. (30 rats)Reduce Electrical Usage - meter/chart/control. (60 houses)Treatment of a Serious Disease - Men vs. Women, 3Alternatives
![Page 68: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/68.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Experimental Design Diagrams
Basic Pattern: Units −→ Treatments −→ ResultsRat experiment - diet to increase weight. (30 rats)Reduce Electrical Usage - meter/chart/control. (60 houses)Treatment of a Serious Disease - Men vs. Women, 3AlternativesCoke/Pepsi Taste Test - matched pairs (20 people)
![Page 69: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/69.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
Eyeball Estimate: Take a 5 second look and make a guess:
![Page 70: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/70.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
Eyeball Estimate: Take a 5 second look and make a guess:
![Page 71: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/71.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
Judgement Sample: Each person picks 5 representativerectangles, and computes their average area.
![Page 72: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/72.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
SRS: Each person uses a table of random numbers to choose 5random rectangles, and computes their average area.
![Page 73: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/73.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
Stratified Random Sample: Call a rectangle big if its area isabove 5; small otherwise.
![Page 74: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/74.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
Stratified Random Sample: Call a rectangle big if its area isabove 5; small otherwise.Have 70% of people find averages of big rectangles and 30%study small ones.
![Page 75: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/75.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
Stratified Random Sample: Call a rectangle big if its area isabove 5; small otherwise.Have 70% of people find averages of big rectangles and 30%study small ones.Our overall estimate will be
.48x̄small + .52x̄large
![Page 76: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/76.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
Stratified Random Sample: Call a rectangle big if its area isabove 5; small otherwise.Have 70% of people find averages of big rectangles and 30%study small ones.Our overall estimate will be
.48x̄small + .52x̄large
The numbers .48 and .52 come from the fact that there are 48small and 52 big rectangles.
![Page 77: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/77.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
Stratified Random Sample: Call a rectangle big if its area isabove 5; small otherwise.Have 70% of people find averages of big rectangles and 30%study small ones.The fractions 70% and 30% come from the followingcalculation:Type ni σi niσi
small rectangles 48 1.557 74.74big rectangles 52 3.847 200.04
200.04
200.04 + 74.74= .73 ∼ 70%
74.74
200.04 + 74.74= .27 ∼ 30%
![Page 78: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/78.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
Stratified Random Sample: Call a rectangle big if its area isabove 5; small otherwise.Have 70% of people find averages of big rectangles and 30%study small ones.The fractions 70% and 30% come from the followingcalculation:Type ni σi niσi
small rectangles 48 1.557 74.74big rectangles 52 3.847 200.04
200.04
200.04 + 74.74= .73 ∼ 70%
74.74
200.04 + 74.74= .27 ∼ 30%
![Page 79: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/79.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
Stratified Random Sample: Call a rectangle big if its area isabove 5; small otherwise.Have 70% of people find averages of big rectangles and 30%study small ones.The fractions 70% and 30% come from the followingcalculation:Type ni σi niσi
small rectangles 48 1.557 74.74big rectangles 52 3.847 200.04
200.04
200.04 + 74.74= .73 ∼ 70%
74.74
200.04 + 74.74= .27 ∼ 30%
These proportions give the stratified random sample withsmallest variance for a given sample size.
![Page 80: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/80.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
Histogram of Actual Areas
![Page 81: Math 1710 Class 24pi.math.cornell.edu/~back/m171/slides171/oct23/oct23_v2.pdfMath 1710 Class 24 V2 Experimentation as Gold Standard Causation Without Experiment Experimental Design](https://reader033.fdocuments.us/reader033/viewer/2022060410/5f106c537e708231d449093a/html5/thumbnails/81.jpg)
Math 1710Class 24
V2
Experimentationas GoldStandard
CausationWithoutExperiment
ExperimentalDesign
Vocabulary
Using aRandomNumber Table
Matched Pairs
ExperimentalDesignDiagrams
Area ofSquares
Average Area?
Frequency Breakdown of Actual Areas