/math-5b06fac1fa58bffaee7f4e26a59d4053.png "double prob = srangecdf(q, v, group)")
computes the probability associated with the lower tail of the distribution of the Studentized range statistic. computes the probability associated with the lower tail of the distribution of the Studentized range statistic.
The externally Studentized range, /math-7694f4a66316e53c8cdd9d9954bd611d.png "q")
, for a sample, /math-932d5a4b9fda90df2a13e707cb46f01f.png "x_1,x_2,\cdots,x_r")
is defined as:
/math-5e763a17241410e3acfaf745ab613e29.png "q=\frac{\max (x_i)-\min (x_i)}{\hat{\sigma _e}}")
where /math-42eb468f7a5ac38a12c67695a1744990.png "\hat{\sigma _e}")
is an independent estimate of the standard error of the /math-1ba8aaab47179b3d3e24b0ccea9f4e30.png "x_i")
's.
For a Studentized range statistic the probability integral,/math-a0bb9c43a8223592352988b8a0c424e5.png "P(q)")
, for /math-4fdefba26320686bb2bd0579a0df421c.png "\nu")
degrees of freedom and /math-4b43b0aee35624cd95b910189b3dc231.png "r")
groups, can be written as:
![P(q)=C\int_0^{+\infty }x^{\nu -1}e^{-\nu x^2/2}\{r\int_{-\infty }^{+\infty }\Phi (y)[\Phi (y)-\Phi (y-qx)]^{r-1}dy\}dx](../images/Srangecdf_(function)/math-b42c9cf4efca69c15eb14bdd778345d0.png "P(q)=C\int_0^{+\infty }x^{\nu -1}e^{-\nu x^2/2}\{r\int_{-\infty }^{+\infty }\Phi (y)[\Phi (y)-\Phi (y-qx)]^{r-1}dy\}dx")
where /math-fa044f537738ba241c9928793f9e03ee.png "C=\frac{\nu ^{\nu /2}}{\Gamma (\nu /2)2^{\nu /2-1}}")
, /math-9eed5f2de0408bd62f90ebdb121dfb45.png "\Phi (y)=\int_{-\infty }^y\frac 1{\sqrt{2\pi }}e^{-t^2/2}dt")
(input, double)/math-e8d7bc1a67db44e249ed90a160afd0b5.png "q.")
/math-6bc6aea3fea25575d5f0c138e2cb9c79.png "q>0")
/math-9e3669d19b675bd57058fd4664205d2a.png "v")
(input, double)/math-4a4907bfeb1b57734b5a5bef3daee01d.png "\nu .")
/math-83cf6266aad32ed623255773e92ed6dc.png "\nu \geq 1.0")
/math-db0f6f37ebeb6ea09489124345af2a45.png "group")
(input,int)/math-e1eb9eb43fe77cc3c7359b40e94949a7.png "r.group\geq 2")
/math-7c4140b57de874ca5efa23bd515eecf8.png "prob")
(output, double)