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## STAT131 Week 2 Lecture 1a Measurement in Statistics

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**STAT131Week 2 Lecture 1aMeasurement in Statistics**Anne Porter**Lecture Outline**• Review • Measurement • Making sense of Data • Measurement scales • Questions asked • Structure of Data**Learning framework**• What are we to do? • How are we to do it? • Why are we doing this? • When do we need to do this?**Problem solving process**• Ethics • Expertise • Research question • Design • Sampling • Measurement • Description and analysis • Decision making V A R I A T I O N**Causality**• Observational studies involves observing and recording data for some variables. The media may report relationships between say heart disease and cholesterol - a statistician requires stronger evidence of causality. • Experimentation. In an experiment some treatment is imposed upon the subject and it influences the observations being made. By manipulating the treatment in a statistically sensible manner we may observe change (variation) in the measurement and attribute causality to the treatment.**Sampling**• Size depends upon variability in population • Different sampling techniques • Simple random sample • Systematic random sample • Cluster sample • Multistage sample • Samples are used estimate some statistical feature of the population**Measurement and sampling**Can be complex**Physical Measurement**Task 1: What was the distance from the Library to the closest eatery in metres? Data: 48, 30, 14, 27, 10, 45, 25, 15, 18 and so on • What do you notice with this data? • What went wrong?**Physical MeasurementWhat went wrong?**• Measurement can be a source of variation • The distance between the bank is constant but there needs to be some instructions or standards regarding how to measure • We needed to know where to start and end Data: 48, 30, 14, 27, 10, 45, 25, 15, 18 and so on • What do you notice with this data? • What went wrong?**Physical Measurement**• Task 2: A simpler task, we know where to begin and end - measure the perimeter of the desk extension in 67.107 Perimeter First Second Third Subject 1 Subject 2 Subject 3 Subject 4 97cm 96 97 96 96 96 95 95 95 94.5 95 95**Physical Measurement**• There is variation in measurement between people • Perhaps there is variation in the perimeters of the desks • There is variation in the three measurements taken by one person • Measurement may be a source of variation often termed measurement error • What do you notice from the data? First Second Third 97cm 96 97 96 96 96 95 95 95 94.5 95 95 Subject 1 Subject 2 Subject 3 Subject 4**Seven units of measurement**• Metre (Distance) • Second (Time) • Kilogram (Weight) • Kelvin (temperature) • Mole (amount of substance) • Ampere (unit of current) • Candela (luminous intensity) • (Tipler, 19 ,p. )**Measuring Uncertainty**• Task 3: The likelihood that the train returning from North Wollongong to Wollongong after the last STAT131 lecture will be late.**Measuring Uncertainty**Probability of the event 1.0 0.5 0 Event certain to happen Event likely to happen Event equally likely to happen or not Event unlikely to happen Event impossible**Measurement by Estimation**• Task 4: Estimate the age of the lecturer Stem (decades) 6 6 5 5 4 4 3 3 2 Leaf (years) 03 5556 0000123 556799 01244 789 0**Measurement by Estimation**What do you notice about the ‘measurements’? • There is variation in the estimates • Estimates are often unreliable • Similarly for recall • But the centre of the distribution • may provide a good estimate! • (What do we mean by centre?) Stem 6 6 5 5 4 4 3 3 2 Leaf 03 5556 0000123 556799 01244 789 0**Psychological Measurement**• Homework: Dolly girl measure of personality. Example question • 1. To pull up your marks in English, you have to work on the school paper. You... • a)Dread the idea! You prefer solo projects to being involved in team efforts. • b)Use it as an excuse to make loads of new friends. • c)Work diligently at it. Maybe you'll end up Editor! • d)immediately write an article on the subject of global destruction.**Psychological Measurement**• Task 5: Treating each row as a sample, how many of you were loner, activist…**Psychological Measurement**• What do you notice about the data ?**Psychological Measurement**• What do you notice about the data ? • Different samples suggest a different proportion • of each personality type but • The estimates of proportion might be • close to what is in the population • May need to convert numbers to % of sample to compare**Psychological Measurement**• What did you do when you couldn’t answer a question?**Psychological Measurement**• What did you do when you couldn’t answer a question? • Missed the question • Marked any response • Stopped completing the questionnaire**Psychological Measurement**• Needs to be reliable and valid • Does the questionnaire measure what it says it measures, ie personality? Is it valid? • Are there other dimensions of personality? Is it valid? • Would the same measure be obtained if it were repeated • for an individual? Is it reliable?**Psychological Measurement**There are many psychological measures • Intelligence, Depression, Anxiety • These need to be thoroughly tested and validated • Are the questions culturally appropriate? • Are the questions appropriate for both sexes? • Are they appropriate for a given age group?**Making sense of data**We need to know: • the context and units of measurement • Which statistical technique depends upon • the measurement scale of the data • the questions asked of the data • the structure of the data**Scales of measurement**• Qualitative • Nominal (categorical) • Ordinal • Quantitative • Interval • Ratio Eg sex (male , female) Eg rare, medium, well done steaks (not equal distance between points) Equal distance between points Eg. Weight has a true zero, 2 units is half of four**Another classification of data**• Discrete • No other possible values in between • Eg Counting people in queues 0,1,2,… nothing in between • Continuous • Scale is infinitely divisible • Eg Time, hours, minutes, seconds…**What questions are asked?**Stem 6 6 5 5 4 4 3 3 2 Leaf 9 001 5678899 00123455 789 01 9**What questions are asked?**• Shape • Centre of data • (mean, median, mode) • Spread of data • Outliers • Patterns • Unusual features Stem 6 6 5 5 4 4 3 3 2 Leaf 9 001 5678899 00123455 789 01 9**Structure of data**• Univariate - • Bivariate • Time dimension • Batches of data • Multivariate Observations on one variable Observations on two variables Two batches, many batches Many variables**Perspectives on Measurement**• It is a source of variation in data • Different ways of classifying measures • Nominal, ordinal,interval,ratio • Qualitative, quantitative • Discrete, continuous • Physical vs psychological measurement • Estimation, recall versus actual measurement • Measurement of Uncertainty**Making Meaning from data**• Video Clip, Decisions through data, Tape1, Unit 2 Stemplots • Measurement of variables • Definition of variables • Context of measurement • Distibutions • Stemplot (centre, spread, outliers, distibution) • Patterns and Deviations • Note Up to Mash**Problem solving process**• Ethics • Expertise • Research question • Design • Sampling • Measurement • Description and analysis • Decision making Focus next lecture