Confidence Intervals
Even for quite large values of n, the actual distribution of the mean is significantly nonnormal. Because of this problem several methods to estimate confidence intervals have been proposed.
Let n1 be the number of successes out of n, the total number of trials, and let
be the proportion of successes. Let zα/2 be the 100 ( 1 − α / 2 )th percentile of the standard normal distribution.
- Wald method
A continuity correction of 0.5/n may be added.
- Agresti-Coull method
Here the estimate of p is modified to
- ArcSine method
- Wilson (score) method
The exact (Clopper-Pearson) method is the most conservative. The Wald method although commonly recommended in the text books is the most biased.
Read more about this topic: Binomial Distribution
Famous quotes containing the words confidence and/or intervals:
“In a war everybody always knows all about Switzerland, in peace times it is just Switzerland but in war time it is the only country that everybody has confidence in, everybody.”
—Gertrude Stein (1874–1946)
“Peter the Hermit, Calvin, and Robespierre, sons of the same soil, at intervals of three centuries were, in a political sense, the levers of Archimedes. Each in turn was an embodied idea finding its fulcrum in the interests of man.”
—Honoré De Balzac (1799–1850)