NumeracyMeasurementLevels of MeasurementIn Which Direction?MIT OpenCourseWarehttp://ocw.mit.edu 11.220 Quantitative Reasoning & Statistical Methods for Planners I Spring 2009 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.Numeracy Measurement Levels of Measurement In Which Direction? Quantitative Reasoning and Statistical Methods Ezra Glenn February 5, 2009 Ezra Glenn Quantitative Reasoning and Statistical Methods(That’s $10,600,000,000,000.00)Let’s put this in perspective: a pile of hamburgers from the earthto the sun and back, two and a half times!That’s a lot of hamburgers!Numeracy: National DebtNumeracy Measurement Levels of Measurement In Which Direction? National Dept is currently $10.6 trillion. Ezra Glenn Quantitative Reasoning and Statistical MethodsLet’s put this in perspective: a pile of hamburgers from the earthto the sun and back, two and a half times!That’s a lot of hamburgers!Numeracy: National DebtNumeracy Measurement Levels of Measurement In Which Direction? National Dept is currently $10.6 trillion. (That’s $10,600,000,000,000.00) Ezra Glenn Quantitative Reasoning and Statistical Methodsa pile of hamburgers from the earthto the sun and back, two and a half times!That’s a lot of hamburgers!Numeracy: National DebtNumeracy Measurement Levels of Measurement In Which Direction? National Dept is currently $10.6 trillion. (That’s $10,600,000,000,000.00) Let’s put this in perspective: Ezra Glenn Quantitative Reasoning and Statistical Methodsand back, two and a half times!That’s a lot of hamburgers!Numeracy: National DebtNumeracy Measurement Levels of Measurement In Which Direction? National Dept is currently $10.6 trillion. (That’s $10,600,000,000,000.00) Let’s put this in perspective: a pile of hamburgers from the earth to the sun Ezra Glenn Quantitative Reasoning and Statistical Methods, two and a half times!That’s a lot of hamburgers!Numeracy: National DebtNumeracy Measurement Levels of Measurement In Which Direction? National Dept is currently $10.6 trillion. (That’s $10,600,000,000,000.00) Let’s put this in perspective: a pile of hamburgers from the earth to the sun and back Ezra Glenn Quantitative Reasoning and Statistical MethodsThat’s a lot of hamburgers!Numeracy: National DebtNumeracy Measurement Levels of Measurement In Which Direction? National Dept is currently $10.6 trillion. (That’s $10,600,000,000,000.00) Let’s put this in perspective: a pile of hamburgers from the earth to the sun and back, two and a half times! Ezra Glenn Quantitative Reasoning and Statistical MethodsNumeracy: National DebtNumeracy Measurement Levels of Measurement In Which Direction? National Dept is currently $10.6 trillion. (That’s $10,600,000,000,000.00) Let’s put this in perspective: a pile of hamburgers from the earth to the sun and back, two and a half times! That’s a lot of hamburgers! Ezra Glenn Quantitative Reasoning and Statistical Methods$10,600,000,000,000.00 ÷ 300,000,000 = $35,333The debt is approximately $35,000 for every many, woman, andchild. Ugh.The National Debt: a different storyNumeracy Measurement Levels of Measurement In Which Direction? Population of the country: 300,000,000 Ezra Glenn Quantitative Reasoning and Statistical MethodsThe debt is approximately $35,000 for every many, woman, andchild. Ugh.The National Debt: a different storyNumeracy Measurement Levels of Measurement In Which Direction? Population of the country: 300,000,000 $10,600,000,000,000.00 ÷ 300,000,000 = $35,333 Ezra Glenn Quantitative Reasoning and Statistical MethodsUgh.The National Debt: a different storyNumeracy Measurement Levels of Measurement In Which Direction? Population of the country: 300,000,000 $10,600,000,000,000.00 ÷ 300,000,000 = $35,333 The debt is approximately $35,000 for every many, woman, and child. Ezra Glenn Quantitative Reasoning and Statistical MethodsThe National Debt: a different storyNumeracy Measurement Levels of Measurement In Which Direction? Population of the country: 300,000,000 $10,600,000,000,000.00 ÷ 300,000,000 = $35,333 The debt is approximately $35,000 for every many, woman, and child. Ugh. Ezra Glenn Quantitative Reasoning and Statistical MethodsA Way to Think About Measurement123Numeracy Measurement Levels of Measurement In Which Direction? Definition observation = signal + noise + bias We want measurements that are: reliable and reproducible (reduce noise) unbiased (reduce bias) related to our concepts (increase signal — more on this when we talk validity) Ezra Glenn Quantitative Reasoning and Statistical MethodsBiasIncorrect in a consistent or patterned wayLikely problemssubjectivitycan be precise and non-subjective, but still biasedother problems related to research designMeasurement: a nest of trouble and issues to considerNumeracy Measurement Levels of Measurement In Which Direction? Reliability Would give the same result for the same phenomenon if measured again Threats (things that increase “noise”) lack of precision/accuracy subjectivity (even without bias)—leads to poor precision Ezra Glenn Quantitative Reasoning and Statistical MethodsMeasurement: a nest of trouble and issues to considerNumeracy Measurement Levels of Measurement In Which Direction? Reliability Would give the same result for the same phenomenon if measured again Threats (things that increase “noise”) lack of precision/accuracy subjectivity (even without bias)—leads to poor precision Bias Incorrect in a consistent or patterned way Likely problems subjectivity can be precise and non-subjective, but still biased other problems related to research design Ezra Glenn Quantitative Reasoning and Statistical MethodsValidity12345678123456789Numeracy Measurement Levels of Measurement In Which Direction? Wikipedia lists the following, just related to statistics and research design: Internal validity External validity Ecological validity Population validity Construct validity Intentional validity Representation validity or translation validity Content validity Ezra Glenn Quantitative Reasoning and Statistical Methods Face validity Observation validity Criterion validity Concurrent validity Predictive validity Convergent validity Discriminant validity Social validity Statistical conclusion validityValidity123Numeracy Measurement Levels of Measurement In Which Direction? For now, let’s just worry about these broad ideas: internal validity: