I need to find PHP code that, given a probability (eg 80%), and a number of degrees of freedom (eg 9) returns the t-distribution, as in the chart at the bottom of this page: http://en.wikipedia.org/wiki/T-distribution
. (eg, for p=80%, df=9, the code would therefore return 0.883.)
what I really want to do is slightly more involved, namely for a given probability, and given a group of n values, and a given max range R, return:
1) the mean m of the n values
2) the standard deviation s of the n values (which can be calculated using the formula following "Estimating population standard deviation from sample standard deviation" on this page: http://en.wikipedia.org/wiki/Standard_deviation
3) the number of degrees of freedom, d = n - 1
4) the standard error of the mean, sigma = s/((n)^(1/2))
5) the upper acceptable error bound b = m + Rm
6) the critical t value beyond which error is too high, T= (b - m)/sigma
7) the probability corresponding to this T given d
The seventh thing I want to return is the real problem, since I don't know how to calculate a t value from a probability and I've just been using the table.
I found a couple of bits of code that claim to do t-distributions, but since I don't know how object oriented PHP works, I'm not sure how to extract the part I need, or even how to use them. What I want to do is kind of backwards, because normally you calculate Rm for a known t, whereas I want to calculate t given a value for R.
Links to the t-distribution PHP I found:
(this one is an archive of a bunch of different probability classes, including one for t-distribution)
All I really need is a function that will return a t-value given a probability and number of degrees of freedom.