Contents

invstu()

Usage:

invstu(P, df [,upper:T or lower:F]), P and df REAL, elements of P
  between 0 and 1, those of df > 0

Keywords: probabilities, random numbers, comparisons, confidence intervals

invstu(P,df) computes the quantiles (probability points, critical
values) of Student's t- distribution with df degrees of freedom
corresponding to each element of P.  P must be a REAL vector or array
with elements between 0 and 1 and df must be a REAL vector or array with
positive but not necessarily integral elements.

If df is a scalar the result has the same size and shape as P and df is
used to compute all the values.

If P is a scalar, the result has the same size and shape as df and
consists of P-th probability points for the different values of df.

If neither P nor df are scalars, they must be the same size and shape
and corresponding elements of P and df are used to compute elements of
the result.

invstu(P,df,upper:T) and invstu(P,df,lower:F) compute upper tail
quantiles.  The result is mathematically equivalent to invstu(1 - P, df)
but may be more accurate for small P.

invstu() is the inverse of cumstu() in the sense that, within rounding
error, invstu(cumstu(x,df),df) should be the same as x and
cumstu(invstu(P,df),df) should be the same as P.

A critical value for a two-tail t-test on df degrees of freedom with
significance level alpha or for a 1-alpha confidence interval may be
computed as invstu(alpha/2,df, upper:T) or invstu(1-alpha/2,df).

Critical values for a one-tail t-test on df degrees of freedom with
significance level alpha are computed as invstu(alpha,df) (lower tail
test) and invstu(alpha,df,upper:T) or invstu(1-alpha,df) (upper tail
test).

Bonferronized critical values for K simultaneous two-tail t-tests with
significance level alpha or K simultaneous 1 - alpha confidence
intervals are computed as invstu(.5*alpha/K,df, upper:T).

invstu(runi(n),df) will generate a random sample of size n from a
Student's t-distribution .

See also cumstu(), runi().