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Stat 1301 Chapter 6 MEASUREMENT ERROR

Stat 1301 Chapter 6 MEASUREMENT ERROR. 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. NOTE: These weights differ from measurement to measurement. possible causes:

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Stat 1301 Chapter 6 MEASUREMENT ERROR

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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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