frank.fanova  R Documentation 
A oneway functional ANOVA based on the rank envelope applied to F values
frank.fanova( nsim, curve_set, groups, typeone = c("fwer", "fdr"), variances = "equal", test.equality = c("mean", "var", "cov"), cov.lag = 1, savefuns = FALSE, ... )
nsim 
The number of random permutations. 
curve_set 
The original data (an array of functions) provided as a 
groups 
The original groups (a factor vector representing the assignment to groups). 
typeone 
Character string indicating which type I error rate to control,
either the familywise error rate ('fwer') or false discovery rate ('fdr').
Further arguments to the FWER or FDR envelope can be passed in argument 
variances 
Either "equal" or "unequal". If "equal", then the traditional Fvalues are used.
If "unequal", then the corrected Fvalues are used. The current implementation uses

test.equality 
A character with possible values Z_{ij}(r) = T_{ij}(r)  \bar{T}_j(r). If V_{ij}(r) sign(V_{ij}(r)), where V_{ij}(r) = (T_{ij}(r)  \bar{T}_j(r))((T_{ij}(r+s)  \bar{T}_j(r+s))). See Mrkvicka et al. (2020) for more details. 
cov.lag 
The lag of the covariance for testing the equality of covariances,
see 
savefuns 
Logical. If TRUE, then the functions from permutations are saved to the attribute simfuns. 
... 
Additional parameters to be passed to 
The test assumes that there are J groups which contain n1, ..., nJ functions T_{ij}, i=1,...,J, j=1,...,nj. The functions should be given in the argument x, and the groups in the argument groups. The test assumes that there exists non random functions μ(r) and μ_i(r) such that
T_{ij}(r) =μ(r) + μ_i(r) + e_{ij}(r), i=1, ..., J, j=1, ..., nj
where e_{ij}(r) are independent and normally distributed. The test vector is
T = (F(r_1), F(r_2), … , F(r_K)),
where F(r_i) stands for the Fstatistic. The simulations are performed by permuting the test functions. Further details can be found in Mrkvička et al. (2020).
The argument variances="equal"
means that equal variances across groups are assumed.
The correction for unequal variances can be done by using the corrected Fstatistic
(option variances="unequal"
).
Unfortunately this test is not able to detect which groups are different from each other.
Mrkvička, T., Myllymäki, M., Jilek, M. and Hahn, U. (2020) A oneway ANOVA test for functional data with graphical interpretation. Kybernetika 56 (3), 432458. doi: 10.14736/kyb202030432
graph.fanova
data("rimov") groups < factor(c(rep(1, times=12), rep(2, times=12), rep(3, times=12))) res < frank.fanova(nsim = 2499, curve_set = rimov, groups = groups) plot(res) data("imageset3") res2 < frank.fanova(nsim = 19, # Increase nsim for serious analysis! curve_set = imageset3$image_set, groups = imageset3$Group) plot(res2) plot(res2, fixedscales=FALSE)
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