Populations and SamplesInferencesExampleHypothesesExampleStatistical SignificanceExampleAssignmentThe Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentThe Language of Statistical Decision MakingLecture 2Section 1.3Robb T. KoetherHampden-Sydney CollegeFri, Aug 29, 2008The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentOutline1Populations and Samples2InferencesExample3HypothesesExample4Statistical SignificanceExample5AssignmentThe Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentStudy: Low-Carb DietsArticleStudy: Low-carb diet gets best resultsWhat is the relevant information here?What is known to be true and what is conjecture?Are there any weaknesses to this study?The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentPopulations and SamplesDefinition (Population)The population is the set of all individuals of interest to thestudy.Definition (Sample)A sample is a set of individuals in the population from whichdata were obtained. Their characteristics were observed ormeasured.The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentInferencesDefinition (Statistical inference)A statistical inference is a conclusion that is drawn about thepopulation, based on what was observed in the sample.The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentSamples and InferencesPopulationThe Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentSamples and InferencesPopulationSampleSelecta sampleThe Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentSamples and InferencesPopulationSampleSelecta sampleDataMake theobservationsThe Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentSamples and InferencesPopulationSampleSelecta sampleDataInferenceMake theobservationsDraw aninferenceThe Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentSamples and InferencesPopulationSampleSelecta sampleDataInferenceRefers tothe populationMake theobservationsDraw aninferenceThe Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentExampleExample (Samples and Inferences)Is the earth getting warmer?How can we tell?The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentExampleExample (Samples and Inferences)All points on theearth's surface(Population)The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentExampleExample (Samples and Inferences)A few points(Sample)Selecta sampleAll points on theearth's surface(Population)The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentExampleExample (Samples and Inferences)A few points(Sample)Selecta sampleTemperaturereadings(Data)Measure thetemperatureAll points on theearth's surface(Population)The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentExampleExample (Samples and Inferences)A few points(Sample)Selecta sampleTemperaturereadings(Data)The earth isgetting warmer(Inference)Measure thetemperatureDraw aninferenceAll points on theearth's surface(Population)The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentExampleExample (Samples and Inferences)A few points(Sample)Selecta sampleTemperaturereadings(Data)The earth isgetting warmer(Inference)Refers tothe entire earthMeasure thetemperatureDraw aninferenceAll points on theearth's surface(Population)The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentHypothesesDefinition (Hypothesis)A hypothesis is often a statement that is proposed to explaina phenomenon that is known to be true.In statistics the phenomenon is that which wasobserved in the sample.The hypothesis is a statement about the population thatexplains the phenomenon.The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentHypothesesSuppose we observe that when we roll a die, thenumber 6 comes up unusually often.One hypothesis could be that the die is not properlybalanced, thereby making the number 6 more likely.What is another plausible hypothesis?The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentNull HypothesisDefinition (Null Hypothesis)The null hypothesis is the conventional belief about thepopulation, or the status quo, or the neutral position.It requires no special justification.That is, it receives the benefit of the doubt.The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentAlternative HypothesisDefinition (Alternative (Research) Hypothesis)The alternative hypothesis is an alternative to the nullhypothesis.It requires evidence for its justification.That is, it bears the burden of proof.The Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand SamplesInferencesExampleHypothesesExampleStatisticalSignificanceExampleAssignmentPopulationSampleSelecta sampleDataAlternativehypothesisMake theobservationsNullhypothesisThe Languageof StatisticalDecisionMakingRobb T.KoetherPopulationsand
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