lsecond: Lambda second distribution or the non-central, non-standard, Lambda distribution.
Description
This distribution was introduced in c22b;textualCohensdpLibrary as the
exact solution to the predictive distribution of the Cohen's dp in repeated-measure
design. A more elegant notation was provided in l22;textualCohensdpLibrary.
It is the dual of the t" distribution, the sampling distribution of dp in repeated-measure
design introduced in c22a;textualCohensdpLibrary.
Usage
plsecond(delta, n, d, rho)
dlsecond(delta, n, d, rho)
qlsecond(p, n, d, rho)
Value
The probability or quantile of a Lambda'' distribution.
Arguments
delta
the parameter of the population whose probability is to assess;
n
the sample size n
d
the observed d_p of the sample;
rho
the population correlation
p
the probability from which a quantile is requested
Details
lsecond are (p,d,q) functions that compute the Lambda-second (L") distribution. This
distribution is an generalization of the lambda-prime distribution
l99CohensdpLibrary.
Note that the parameters are the raw sample size n, the observed Cohen's dp, and the
population rho. All the scaling required are performed within the functions (and so
you do not provide degrees of freedom).This is henceforth not a generic lambda-second
distribution, but a lambda-second custom-tailored for the problem of standardized mean
difference.