[9] For large populations, the 95 percent confidence interval can be estimated as ±1.96 × sqrt [p(1-p)/n]. To obtain a 99 percent confidence interval, multiply by 2.58 instead of 1.96. Yes, the interval is larger when you’ re more confident (which should make sense; if you want to be more sure that the range you quote includes the true value, you need a larger range). For smaller populations, the formula is to first compute the standard error: sqrt [{(Observed proportion) × [1 – (Observed proportion)}/sample size] The width of the 95 percent confidence interval then is ±2 × standard error. For example, if you sampled fifty overpasses in a large city, you might have found that 20 percent of them needed repair. You calculate the standard error as: sqrt [(.2 × .8)/50] = sqrt (.16/50) = .057. So the width of your 95 percent confidence interval is ±2 ×.057 = ±.11 or ±11%. Thus the 95 percent confidence interval is that 20 percent of the overpasses in this town need repair, plus or minus 11 percent. In a news report, the reporter might say that the survey showed 20 percent of overpasses need repair, with a margin of error of 11 percent. To increase the precision of your estimate, you need to sample more. If you go to 200 overpasses (assuming you obtain the same 20 percent figure), your margin of error reduces to about 6 percent.
[10] Lusinchi, D. (2012). “President”Landon and the 1936 Literary Digest poll: were automobile and telephone owners to blame? Social Science History, 36 (1), 23–54.
[11] Clement, S. (2013, June 4 ). Gallup explains what went wrong in 2012. https://www.washingtonpost.com/news/the-fix/wp/2013/06/04/gallup-explains-what-went-wrong-in-2012/? postshare= 3241456695567153& tid= ss_ mail.http://www.gallup.com/poll/162887/gallup-2012-presidential-election-polling-review.aspx.
[12] Taken from http://www.ropercenter.uconn.edu/support/polling-fundamentals-total-survey-error/.
[13] Elaborated from an example in Huff, op.cit., p. 16.
[14] This definition taken verbatim from http://www.cancer.gov/publications/dictionaries/cancer-terms?cdrid= 45696. Accessed March20, 2016.
[15] http://www.csmonitor.com/Science/2012/0223/CERN-researchers-find-flaw-in-faster-than-light-measurement.
[16] 一般来说，在选民投票选举所支持的候选人之后，美国总统大选的选票上候选人名字旁边的孔印会被打穿，产生一个方形的纸块，这个纸块就叫作孔芯。当选票上有打孔的痕迹，但是孔芯未被打穿时，这种选票就被称为“酒窝”选票；当孔芯被打穿，但并未离开选票时，这种选票就被称为“悬挂”选票。——译者注
[17] This is from De Veaux, R. D. & Hand, D. J. (2005). How to lie with bad data. Statistical Science, 20 (3), 231–238,p. 232.They cite Kruskal, W. (1981). Statistics in society: Problems unsolved and unformulated. Journal of the American Statistical Association, 76 , 505–515 and Coale, A. J. and Stephan, F. F. (1962). The case of the Indians and the teen-age widows. Journal of the American Statistical Association, 57 , 338–347.
[18] Kryk, J .Patriots strike back with compelling explanations to refute deflate-gate chargers.Ottowa Sun, May15, 2015.http://www.ottawa.sun.com/2015/05/14/patriots-strike-back-with-compelling-explanations-to -refute-deflate-gate-chargers.
[19] This example from Spirer, H., Spirer, L, & Jaffe, A. J. (1998). Misused Statistics, Second edition, revised and expanded. New York, NY: Marcel Dekker, p. 16.
[20] This example based on one in Huff, op. cit., p. 80.
[21] From Best (2005). op. cit.
