# P-values based on permutation tests for ANOVA and repeated measures ANOVA designs. Provides p-values for omnibus tests based on permutations for factorial and repeated measures ANOVA. This function produces the F statistics, parametric p-values (based, on Gaussian and sphericity assumptions) and p-values based on the permutation methods that handle nuisance variables. ```r aovperm( formula, data = NULL, np = 5000, method = NULL, type = "permutation", ... ) ``` ## Arguments - `formula`: A formula object. The formula for repeated measures ANOVA should be written using the same notation as aov by adding `+Error(id/within)`, where `id` is the factor that identify the subjects and `within` is the within factors. - `data`: A data frame or matrix. - `np`: The number of permutations. Default value is `5000`. - `method`: A character string indicating the method used to handle nuisance variables. Default is `NULL` and will change if to `"freedman_lane"` for the fixed effects model and `"Rd_kheradPajouh_renaud"` for the random effect models. See Details for other methods. - `type`: A character string to specify the type of transformations: "permutation" and "signflip" are available. Is overridden if P is given. See help from Pmat. - `...`: Futher arguments, see details. ## Returns A `lmperm` object containing most of the objects given in an lm object, an ANOVA table with parametric and permutation p-values, the test statistics and the permutation distributions. ## Details The following methods are available for the fixed effects model defined as $y = D\eta + X\beta + \epsilon$. If we want to test $\beta = 0$ and take into account the effects of the nuisance variables $D$, we transform the data : ||||| |:--|:-:|:-:|:-:| |`method` argument|$y*$|$D*$|$X*$| |`"draper_stoneman"`|$y$|$D$|$PX$| |`"freedman_lane"`|$(H_D+PR_D)y$|$D$|$X$| |`"manly"`|$Py$|$D$|$X$| |`"terBraak"`|$(H_{X,D}+PR_{X,D})y$|$D$|$X$| |`"kennedy"`|$PR_D y$||$R_D X$| |`"huh_jhun"`|$PV'R_Dy$||$V'R_D X$| |`"dekker"`|$y$|$D$|$PR_D X$| The following methods are available for the random effects model $y = D\eta + X\beta + E\kappa + Z\gamma+ \epsilon$. If we want to test $\beta = 0$ and take into account the effect of the nuisance variable $D$ we can transform the data by permutation: ||||||| |:--|:-:|:-:|:-:|:-:|:-:| |`method` argument|$y*$|$D*$|$X*$|$E*$|$Z*$| |`"Rd_kheradPajouh_renaud"`|$PR_D y$||$R_D X$|$R_D E$|$R_D Z$| |`"Rde_kheradPajouh_renaud"`|$PR_{D,E}y$||$R_{D,E} X$||$R_{D,E}Z$| Other arguments could be pass in `...` : `P` : a matrix, of class `matrix` or `Pmat`, containing the permutations (for the reproductibility of the results). The first column must be the identity permutation (not checked). `P` overwrites `np` argument. `rnd_rotation` : a random matrix of size $n \times n$ to compute the rotation used for the `"huh_jhun"` method. `coding_sum` : a logical set to `TRUE` defining the coding of the design matrix to `contr.sum` to test the main effects. If it is set to `FALSE` the design matrix is computed with the coding defined in the dataframe. The tests of simple effets are possible with a coding of the factors of the dataframe set to `contr.treatment`. ## Examples ```r ## data data("emergencycost") ## centrering the covariate to the mean emergencycost$LOSc <- scale(emergencycost$LOS, scale = FALSE) ## ANCOVA ## Warning : np argument must be greater (recommendation: np>=5000) mod_cost_0 <- aovperm(cost ~ LOSc*sex*insurance, data = emergencycost, np = 2000) mod_cost_0 ## same analysis but with signflip ## Warning : np argument must be greater (recommendation: np>=5000) mod_cost_0s <- aovperm(cost ~ LOSc*sex*insurance, data = emergencycost, type="signflip", np = 2000) mod_cost_0s ## Testing at 14 days emergencycost$LOS14 <- emergencycost$LOS - 14 mod_cost_14 <- aovperm(cost ~ LOS14*sex*insurance, data = emergencycost, np = 2000) mod_cost_14 ## Effect of sex within the public insured contrasts(emergencycost$insurance) <- contr.treatment contrasts(emergencycost$sex) <- contr.sum emergencycost$insurance <- relevel(emergencycost$insurance, ref = "public") mod_cost_se <- aovperm(cost ~ LOSc*sex*insurance, data = emergencycost, np = 2000, coding_sum = FALSE) mod_cost_se ## Repeated measures ANCOVA ## data data(jpah2016) ## centrering the covariate jpah2016$bmic <- scale(jpah2016$bmi, scale = FALSE) ## Warning : np argument must be greater (recommendation: np>=5000) mod_jpah2016 <- aovperm(iapa ~ bmic*condition*time+ Error(id/(time)), data = jpah2016, method = "Rd_kheradPajouh_renaud") mod_jpah2016 ``` ## See Also `lmperm` `plot.lmperm` Other main function: `clusterlm()`, `lmperm()` ## Author(s) jaromil.frossard@unige.ch

aovperm function