Hi Stefan,
"s.petersson" <[EMAIL PROTECTED]> wrote in message
news:<XBE07.7641$[EMAIL PROTECTED]>...
> Let's say I want to calculate this constant with a security level of
> 93.4563, how do I do that? Basically I want to "unfold" a function like
> this:
>
> f(95)=1.96
>
> Where I can replace "95" with any number ranging from 0-100.
To Eric's reply I'd just add that use of a table is unnecessary.
Especially in a computer program, it is easier to use a numerical
function to calculate the confidence interval.
The tables you've seen are for the cumulative probabilities of the
standard normal curve--otherwise known as the standard normal
cumulative density function (cdf). The standard normal cdf is the
function:
+infinity
p = PHI(z) = INTEGRAL phi(z)
-infinity
where:
z = standard normal deviate
PHI(z) = is the probability (p) of observing a score at or
below z
phi(z) = is the formula for the standard normal curve:
1/sqrt(2*pi) * exp(-z^2/2)
Note that PHI() and phi() -- (these mean the greek letters, upper-case
and lower-case, respectively) are different. PHI() is the cumulant of
phi().
With the function above, one supplies a value for z, and is given a
cumulative probability.
You seek the inverse function for PHI(), sometimes called the "probit
function." With the probit function, one supplies a value for p and
is returned the value of z such that the area under the standard
normal curve from -inf to z equals p. (As Eric noted, you may need to
adjust p to handle issues of 1- vs 2-tailed intervals.)
Both the PHI() and probit() functions are well approximated in simple
applications (such as calculating confidence intervals) by simple
polynomial formulas of a few terms. Some of these take as few as 2 or
3 lines of code. A good reference for such approximations is:
Abramowitz, M., and I. A. Stegan, 1972: Handbook of Mathematical
Functions. Dover.
Hope this helps.
John Uebersax
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