Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Elementary Statistics and Inference 22S:025 or 7P:025 Lecture 8 1 Elementary Statistics and Inference 22S:025 or 7P:025 Chapter 6 2 7.) Measurement Error A. Introduction The difference between a measurement (score) and the “true” value of the measurement is called “chance” error – X=T–E Score = True Value – Error The less the values of E, the more reliable the measurement. 3 1 7.) Measurement Error (cont.) B. Chance Error Precision of measurements at the National Bureau of Standards. International Prototype Kilogram (kilogram) is the “standard weight” of one kilogram. All other weights are defined and compared to the kilogram under standard conditions – Paris. 1 pound = .4539237 of one kilogram 2.203 pounds = 1 kilogram 4 7.) Measurement Error (cont.) The USA was assigned kilogram #20 (k20). The US National Bureau of Standards (1940) has a NBIO – the weight of 10 grams, which is the weight of about 2 nickels. The NB weighs g NBIO about every y week to determine the reliability of the measurement process. On page 99 of the text – a display of 100 measurements of NBIO, and the measurements represent micrograms below 10 grams. Note the variability of the measurements. – This is due to chance error. 5 7.) Measurement Error (cont.) 6 2 7.) Measurement Error (cont.) The average of the 100 measurements is 405 micrograms below 10 grams and the standard deviation was 6 micrograms (chance error). The NB does these repeated measurements from time to time to check the consistency of the instruments used to weigh NBIO. 7 7.) Measurement Error (cont.) The SD of a series of measurements is the likely size of the “chance error” of the measurements. X = T + E (see p. 101) individual measurement or score = exact value or true value + chance error Such measurement error occurs with nearly all behavioral research because the measurement process is not perfect – e.g., heights, weights, abilities, attitudes, physiological traits. 8 7.) Measurement Error (cont.) C. Outliers If the measurements are normally distributed, you would expect 95% of them to be within 2 standard deviations of the mean. mean Any measurement that is more than 3 standard deviations from the mean is considered highly unusual (outlier). 9 3 7.) Measurement Error (cont.) 10 7.) Measurement Error (cont.) 11 7.) Measurement Error (cont.) D. Bias If some aspect of the measurement process is affected systematically – the measuring process is biased (i.e., not truly representative of the true measurement process). E.g., if heights of men were determined by only measuring the heights of college basketball players, l th the measurements t would ld b be bi biased. d Or, if the measurement of heights of men was done with a “cloth tape” that could stretch or shrink, depending on humidity, the measurements would be biased. X=T+E+B measurement = exact value + chance error + bias 12 4 7.) Measurement Error (cont.) E. Review Exercises – (pages 104-105) #4, 5 F. Special Review Exercises – (pages 105-108) #2, 3, 4, 6 9 6, 9, 11 13 7.) Measurement Error (cont.) 14 7.) Measurement Error (cont.) 15 5 16 17 18 6 7.) Measurement Error (cont.) 19 20 21 7 7.) Measurement Error (cont.) 22 23 7.) Measurement Error (cont.) 24 8 25 9