Description Usage Arguments Details Value Examples
Computes an order k Glaz–Johnson approximation to a multivariate standard normal probability with a given correlation matrix. Gives a familywise error rate level bound in multiple testing for a given local (per-hypothesis) significance level.
1 |
k |
Order of the approximation. |
alphaloc |
Local significance level (se above). |
corr |
Either a list of correlations
in which the
first component is a vector of first-order correlations, the second is a vector
of second-order correlations,
up to a vector of |
miwasteps |
The |
genz |
If |
The function is quite slow. For second-order approximation, it is better to use gamma2
.
P(|T_1| < c, …, |T_m| <
c) is approximated for (T_1, …, T_m) multivariate standard normal
with covariances (at least up to order k-1
) given by corr
, where c is
qnorm(1 - alphaloc/2)
. If (T_1,… T_m) is a test statistic vector
for m hypotheses, a local significance level of alphaloc
, i.e. rejection of
a null hypothesis if the p-value is less than alphaloc
, will control
familywise error rate at the 1 - gamma_k(alphaloc, corr)
level.
1 2 3 4 5 6 7 8 | # Normal model with three environmental covariates:
result <- scorestatcorr(y_normal ~ sex + activity + agecategory, xg[,1:200], 2)
al <- uniroot(function(a) gamma2(a, result$corrs[[1]]) - .95, c(1e-5, 5e-4), tol = 1e-14)$root
al3 <- uniroot(function(a) gamma_k(3, a, result$corrs) - .95, c(1e-5, 5e-4), tol = 1e-14)$root
0.05/2000 # Bonferroni
1 - 0.95^(1/2000) # Sidak
al # order 2 FWER approximation
al3 # order 3 FWER approximation
|
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