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STAT131 Week 2 Lecture 1a Measurement in Statistics

STAT131 Week 2 Lecture 1a Measurement 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?

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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

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