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Understanding Measurement Errors in Weight Estimation: NB-10 Case Study

Learn about chance errors in repeated weight measurements, estimating true weight, typical chance error size, biased measurements, and the importance of variability in different settings. Discover how experts address measurement discrepancies.

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Understanding Measurement Errors in Weight Estimation: NB-10 Case Study

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  1. Stat 1301Chapter 6MEASUREMENT ERROR

  2. National Bureau of Standards • NB 10 • supposed to be 10 grams • weighed weekly under the “same conditions” • same scales • temperature and humidity • very carefully done by experts

  3. NOTE:These weights differ from measurement to measurement • possible causes: • “play” in balance mechanism • slight variation in position on balance pan • dust particles on weights • ...

  4. CHANCE ERRORS Errors or discrepancies that are not readily explainable BASIC POINT: Repeated measurements of this type are going to vary at least slightly no matter how much care is taken

  5. NOTE ALSO: These weights seem to be consistently less than 10 grams What is the true weight of NB10? • We don’t know! • We can estimate itby taking an average over repeated weighings -- AVG = 9.999595 (100 weighings) -- probably “close” to true weight

  6. What is the likely size of the chance error? • i.e. typically how far off are we from the true weight? • SD of the measurements is usually a good estimate of this • this measures typical amount by which measurements differ from the AVG(recall: AVG is “close” to true weight) -- SD = .000006 (I.e. 6 micrograms)

  7. A Model Observed Value = true value + chance error

  8. Biased Measurement • measurements are systematically off the mark in the same direction • Example: • cloth tape measure that has “stretched” • scale that is improperly adjusted at the factory

  9. More Precise Model observed value = bias + true value + chance error

  10. IMPORTANT: • variability occurs in many settings other than repeated measurements of a fixed object • Examples: • % red beads out of the 50 beads drawn from a box with 20% red beads • scores on Exam I in this class • weight gain of a sample of 50 babies during the first month VARIABILITY IS EVERYWHERE!

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