Lambda second distribution or the non-central, non-standard, Lambda distribution.

Source: R/lsecond.R

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.

plsecond(delta, n, d, rho) 
dlsecond(delta, n, d, rho) 
qlsecond(p,     n, d, rho)

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

Value

     The probability or quantile of a Lambda'' distribution.

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.

References

Examples


dlsecond(0.25, 9, 0.26, 0.333) # 1.03753
#> [1] 1.037531
plsecond(0.25, 9, 0.26, 0.333) # 0.494299
#> [1] 0.4942994
qlsecond(0.01, 9, 0.26, 0.333) # -0.6468003
#> [1] -0.6468003