By the normal approximation to a binomial this is the squared of one standard normal variate, and hence is distributed as chi-squared with 1 degree of freedom.
22.
Just as de Moivre and Laplace sought for and found the normal approximation to the binomial, Pearson sought for and found a multivariate normal approximation to the multinomial distribution.
23.
Just as de Moivre and Laplace sought for and found the normal approximation to the binomial, Pearson sought for and found a multivariate normal approximation to the multinomial distribution.
24.
The appropriate statistical test for an approximate method involves approximating dN & minus; dS with a normal approximation, and determining whether 0 falls within the central region of the approximation.
25.
:Using a normal approximation should get a pretty good answer for n = 800 ( I haven't checked to see if you calculated it right, but the method is good ).
26.
When using a " Z "-test for maximum likelihood estimates, it is important to be aware that the normal approximation may be poor if the sample size is not sufficiently large.
27.
For the 95 % interval, the Wilson interval is nearly identical to the normal approximation interval using \ tilde p = \ tfrac { n _ S + 2 } { n + 4 } instead of \ hat { p }.
28.
Since the test in the middle of the inequality is a Wald test, the normal approximation interval is sometimes called the Wald interval, but Pierre-Simon Laplace first described it in his 1812 book " Th�orie analytique des probabilit�s " ( page 283 ).
29.
In cases where the expected value, E, is found to be small ( indicating a small underlying population probability, and / or a small number of observations ), the normal approximation of the multinomial distribution can fail, and in such cases it is found to be more appropriate to use the G-test, a likelihood ratio-based test statistic.
30.
The main article it links to, Binomial proportion confidence interval, gives various ways of getting a confidence interval; in the section Normal approximation interval, for one class of confidence interval calculations, it says " A frequently cited rule of thumb is that the normal approximation works well as long as np > 5 and n ( 1 " p ) > 5 ".
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