Abstract
If a layman were given the task of describing the average height of the population of white male college students at a certain university, he would no doubt take a sample from the population, measure the heights, and average the results. A quicker estimate would be the average of the smallest and largest heights in the sample. Another estimate would be the sample median (a number smaller than half the measurements and larger than the other half of them). Which of those estimates is “best” and why? If he were to take a different sample, the estimates would be different and he would need to express that sampling uncertainty in some way. This chapter defines the desirable properties of point estimates (which consist of 1 number). The uncertainty of the estimate resulting from sampling will be expressed in the form of interval estimates (which will consist of 2 numbers) of the quantity being estimated (in this case the height of men).
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References
A good elementary text that is easy reading is Dixon, W. J., and Massey, F. J. 1983. Introduction to Statistical Analysis. 4th ed.
Following this I recommend Brownlee K. A. 1965. Statistical Theory and Methodology in Science and Engineering, 2nd ed. New York: Wiley, or
Bowker A. H., and Lieberman, G. J. 1972. Engineering Statistics. 2nd ed. Englewood Cliffs, N.J.: Prentice-Hall.
A good step-by-step text in simple linear regression and hypothesis testing is Natrella M. G. 1963. Experimental Statistics, NBS Handbook 91, Govt. Printing Office, Washington, D.C.
A book with valuable information on less-standard techniques is Hahn, G. J., and Shapiro, S. S. 1967. Statistical Models in Engineering, New York: Wiley and Sons.
The 2 classics in mathematical statistics are Mood, A. M.,Graybill, F. A., and Boes, D. C. 1974. Introduction to the Theory of Statistics. 3rd ed. New York: Graw-Hill
Hogg, R. V., and Craig, A. T. 1978. Introduction to Mathematical Statistics, 4th ed. New York: MacMillan.
In the area of Bayesian estimation, a thorough treatment and link to classical statistics is given in Box, G. E. P., and Tiao, G. 1973. Bayesian Inference in Statistical Analysis, Reading, Mass.: Addison-Wesley.
The very important topic of nonparametric statistics is well covered in Conover, W. J. 1980. Practical Nonparametric Statistics. 2nd ed. New York: Wiley and Sons.
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© 1986 Chapman and Hall
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Tietjen, G.L. (1986). Estimation and Hypothesis Testing. In: A Topical Dictionary of Statistics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1967-2_4
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DOI: https://doi.org/10.1007/978-1-4613-1967-2_4
Publisher Name: Springer, Boston, MA
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