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STAT131 Week 2 Lecture 1a Measurement in Statistics

STAT131 Week 2 Lecture 1a Measurement in Statistics

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STAT131 Week 2 Lecture 1a Measurement in Statistics

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  1. STAT131Week 2 Lecture 1aMeasurement in Statistics Anne Porter

  2. Lecture Outline • Review • Measurement • Making sense of Data • Measurement scales • Questions asked • Structure of Data

  3. 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?

  4. Problem solving process • Ethics • Expertise • Research question • Design • Sampling • Measurement • Description and analysis • Decision making V A R I A T I O N

  5. 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.

  6. 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

  7. Measurement and sampling Can be complex

  8. 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?

  9. 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?

  10. 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

  11. 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

  12. 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. )

  13. Measuring Uncertainty • Task 3: The likelihood that the train returning from North Wollongong to Wollongong after the last STAT131 lecture will be late.

  14. 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

  15. 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

  16. 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

  17. 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.

  18. Psychological Measurement • Task 5: Treating each row as a sample, how many of you were loner, activist…

  19. Psychological Measurement • What do you notice about the data ?

  20. 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

  21. Psychological Measurement • What did you do when you couldn’t answer a question?

  22. Psychological Measurement • What did you do when you couldn’t answer a question? • Missed the question • Marked any response • Stopped completing the questionnaire

  23. 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?

  24. 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?

  25. 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

  26. 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

  27. 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…

  28. What questions are asked? Stem 6 6 5 5 4 4 3 3 2 Leaf 9 001 5678899 00123455 789 01 9

  29. 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

  30. 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

  31. 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

  32. 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

  33. Problem solving process • Ethics • Expertise • Research question • Design • Sampling • Measurement • Description and analysis • Decision making Focus next lecture