One-Way ANOVA

Description

anova1way is used to generate multivariate data in order to compute analysis of variance with 1 factor. It provides balanced and unbalanced ANOVA (as long as homogeneity of variances is satisfied. In other case it is provided Welch test).

Usage

anova1way(k = 3,n , mean = 0, sigma = 1,
          coefvar = NULL, method = c("Tukey", "LSD", "Dunnett", "Bonferroni", "Scheffe"),
          conf.level = 0.95, dec = 2)

Arguments

Details

If mean or sigma are not specified it is assumed the default values of 0 and 1.

If coefvar (= sigma/mean) is specified, function omits sigma.

Number of samples is choosen by k (by default k = 3). Therefore, if the others parameters (n, mean, sigma, coefvar) have not same length, function rep will be used. Pay attention if vectors dont have same length.

Moreover, not only gives samples for each level, but also the ANOVA table and post-hoc test (in case of significance). By default conf.level = 0.95 and Tukey method is used. If the homogeneity of variances is not verified (using Bartlett test), the Welch test is performed.

Value

List containing the following components:

• Data: a data frame containing the samples created.

• Anova: anova fitted model.

• Significance: significance of the factor.

• Size.effect: size effect of the factor.

• Test Post-Hoc: test Post-Hoc.

Examples

anova1way(k=4,n=c(40,31,50),mean=c(55,52,48,59),coefvar=c(0.12,0.15,0.13),conf.level = 0.99)

anova1way(k=3,n=15,mean=c(10,15,20),sigma =c(1,1.25,1.1),method ="B")

Two-Way ANOVA

Description

anova2way returns multivariate data in order to compute analysis of variance with 2 factors.

Usage

anova2way(k =2 , j = 2, n,  mean = 0, sigma = 1,
          coefvar = NULL, method = c("Tukey", "LSD", "Dunnett", "Bonferroni", "Scheffe"),
          conf.level = 0.95, dec = 2)

Arguments

Value

A list containing the following components:

• Data: a data frame containing the samples created.

• Size.effect: size effect for each factor and interaction.

• Significance/Test Post-Hoc: significance for each factor and interaction and test Post-Hoc for each factor.

Examples

anova2way(k=3, j=2, n=c(3,4,4,5,5,3), mean = c(1,4,2.5,5,6,3.75), sigma = c(1,1.5))

Clinical Assay

Description

Simulates a clinical Assay with 2 groups (control and treatment) before and after intervention.

Usage

cassay(n, mean = 0, sigma = 1, coefvar = NULL,
        d.cohen = NULL, dec = 2)

Arguments

Value

List containing the following components:

• Data: a data frame containing the samples created (Columns: Group, PreTest & PostTest).

• Model: linear regression model.

Examples

cassay(c(10,12), mean = 115, sigma = 7.5, d.cohen= 1.5)
cassay(24, mean = 100, sigma = 5.1)

Generation of multivariate normal data.

Description

This function generates univariate and multivariate normal data. It allows simulating correlated and independent samples. Moreover, normality tests and numeric informations are provided.

Usage

generator(n , mean = 0, sigma = 1, coefvar = NULL,
    sigmaSup = NULL, dec = 2)

Arguments

Details

If mean or sigma are not specified it's assumed the default values of 0 and 1.

If coefvar (= sigma/mean) is specified, function omits sigma and sigmaSup. It's assumed that independent samples are desired.

Number of samples are choosen by taken the longest parameter (n, mean, sigma, coefvar). Therefore, function rep is used. Pay attention if vectors don't have same length!

If sigma is a vector, samples are independent. In other case (sigma is a matrix), samples are dependent (following information meanst be taken into account: if sigma is a correlation matrix, sigmaSup is required).

Value

List containing the following components for independent (with the same length) and dependent samples:

• Samples: a data frame containing the samples created.

• Test normality test for the data (shapiro.test() for n <= 50 and lillie.test() in other case).

List containing the following components for independent samples with different lengths:

• X_i sample number i.

Examples

generator(4,0,2)

sigma <- matrix(c(1,0.8,0.8,1),nrow = 2, byrow = 2)
d <- generator(4,mean = c(1,2),sigma, sigmaSup = 1)

generator(10,1,coefvar = c(0.3,0.5))

generator(c(10,11,10),c(1,2),coefvar = c(0.3,0.5))

Correlation matrix

Description

Checks if a given matrix is a correlation matrix for non-degenerate distributions.

Usage

is.corrmatrix(matrix)

Arguments

Value

A logical value: True/False.

Examples

m1<-matrix(c(1,2,2,1),nrow = 2,byrow = TRUE)
is.corrmatrix(m1)

m2<-matrix(c(1,0.8,0.8,1),nrow = 2,byrow = TRUE)
is.corrmatrix(m2)

m3<-matrix(c(1,0.7,0.8,1),nrow = 2,byrow = TRUE)
is.corrmatrix(m3)

Covariance matrix

Description

Checks if a given matrix is a covariance matrix for non-degenerate distributions.

Usage

is.covmatrix(matrix)

Arguments

Value

A logical value: True/False.

Examples

m1 <- matrix(c(2,1.5,1.5,1), nrow = 2, byrow = TRUE)
is.covmatrix(m1)

m2 <- matrix(c(1,0.8,0.8,1), nrow = 2, byrow = TRUE)
is.covmatrix(m2)

m3 <- matrix(c(1,0.7,0.8,1), nrow = 2, byrow = TRUE)
is.covmatrix(m3)

Positive definited matrices

Description

Checks if a given matrix is positive definited

Usage

is.posDef(matrix)

Arguments

Value

A logical value: True/False.

Examples

A <- matrix(c(1,2,2,1), nrow = 2, byrow = TRUE)
is.posDef(A)

B <- matrix(c(1,2,3,3,1,2,1,2,1), nrow = 3, byrow = TRUE)
is.posDef(B)

Semi-Positive definited matrices

Description

Checks if a given matrix is semi-positive definited.

Usage

is.semiposDef(matrix)

Arguments

Value

A logical value: True/False.

Examples

A<-matrix(c(2.2,1,1,3), nrow = 2, byrow = TRUE)
is.semiposDef(A)

B<-matrix(c(1,2,3,3,1,2,1,2,1), nrow = 3, byrow = TRUE)
is.semiposDef(B)

Correlation & Covariance matrices.

Description

Given a correlation matrix and vector of standard deviations (or vector of means and vector of variation coefficients) returns a covariance matrix.

Usage

mCorrCov(mcorr, sigma = 1, mu = NULL, coefvar = NULL)

Arguments

Details

coefvar = sigma/mu.

If sigma, mu or coefvar are not specified, it´s assumed that default values for standard error's are 1. Length of standard error's is created using number of rows of correlation matrix. It's necessary to provide sigma or mu and coefvar (both) in order to obtain a desired covariance matrix.

Length of vectors is taken using rep. Pay attention if vectors don't have same length!

Value

mCorrCov gives the covariance matrix for a specified correlation matrix.

Examples

A <- matrix(c(1,2,2,1), nrow = 2, byrow = TRUE)
mCorrCov(A)

B <- matrix(c(1,0.8,0.7,0.8,1,0.55,0.7,0.55,1), nrow = 3, byrow = TRUE)
mCorrCov(B,mu = c(2,3.5,1), coefvar = c(0.3,0.5,0.7))

Paired measures (T-Test & Regression)

Description

Generates two paired measures. It provides T-test and a simple linear regression model for generated data.

Usage

pairedm(n, mean = 0, sigma = 1, coefvar = NULL,
        rho = NULL, alternative = c("two.sided", "less", "greater"),
        delta = 0, conf.level = 0.95, dec = 2,
        random = FALSE)

Arguments

Details

If random = TRUE, rho is omitted and sigma is taken as range for variances of the covariance matrix.

Value

List containing the following components :

• Data: a data frame containing the samples created.

• Model: linear regression model.

• T.Test: a t-test for the samples.

See Also

[clusterGeneration::genpositiveDefMat()]

Examples

pairedm(10, mean = c(10,2), sigma = c(1.2,0.7), rho = 0.5, alternative = "g")
pairedm(15, mean =c(1,2), coefvar = 0.1, random = TRUE)

Repeated Measures (ANOVA & Multiple Regression)

Description

Repeated Measures (ANOVA & Multiple Regression)

Usage

repeatedm(k, n, mean = 0, sigma = 1, coefvar = NULL,
          sigmaSup = NULL, conf.level = 0.95,
          random = FALSE, dec = 2)

Arguments

Details

Number of variables must be greater than 3, in order to ensure an ANOVA of repeated measures or a multiple Linear Regression.

sigma can represent a vector or a covariance/correlation matrix. In case sigma is a vector, independent samples are created. By other hand, if it's a correlation matrix parameter sigmaSup is required. For covariance matrices, the function does not require any other parameter or special treatment.

If random = TRUE, a random covariance matrix is generated by using genpositiveDefMat().

Value

A data frame.

See Also

[clusterGeneration::genpositiveDefMat()]

Examples

randm <- clusterGeneration::genPositiveDefMat(8, covMethod = "unifcorrmat")
mcov <- randm$Sigma
Sigma <- cov2cor(mcov)
is.corrmatrix(Sigma)
repeatedm(k = 8, n = 8, mean = c(20,5, 30, 15),sigma = Sigma, sigmaSup = 2,  dec = 2)

repeatedm(k = 5, n = 5, mean = c(8,10,5,14,22.5), random = TRUE)
repeatedm(k = 3, n = 8, mean = c(10,5,22.5), sigma = c(3.3,1.5,5), dec = 2)

Independent normal data

Description

Generates two normal independent samples. It also provides Cohen's effect and T-Test.

Usage

sample2indp(n , mean = 0, sigma = 1, coefvar = NULL,
            alternative = c("two.sided", "less", "greater"), delta = 0,
            conf.level = 0.95, dec = 2)

Arguments

Details

If mean or sigma are not specified it's assumed the default values of 0 and 1.

n is a vector, so it's possible to generate samples with same or different sizes.

If coefvar is given, sigma is omitted. Vector of means cannot have any 0.

Value

A list containing the following components:

• Data: a data frame containing the samples created.

• T.Test: a t-test of the samples.

• Power: power of the test.

Examples

sample2indp(c(10,12),mean = c(2,3),coefvar = c(0.3,0.5), alternative = "less", delta = -1)

sample2indp(8,sigma = c(1,1.5), dec = 3)

Independent normal data

Description

Generates two normal independent samples with desired power and cohen's effect.

Usage

sample2indp.pow(n1, mean = 0, s1= 1, d.cohen, power,
   alternative = c("two.sided", "less", "greater"), delta = 1,
   conf.level = 0.95, dec = 2)

Arguments

Details

Pooled standard deviation= sp = sqrt((n1 - 1) sigma1^2 +(n2 - 1) sigma2^2) / (n1 + n2 - 2)

d.cohen = |mean1 - mean2| / sqrt(sp)

Value

A list containing the following components:

• Data: a data frame containing the samples created.

• Size: size of each sample.

• T.test: a t-test of the samples.

Examples

sample2indp.pow(n1 = 30, mean = c(2,3), s1= 0.5, d.cohen = 0.8, power = 0.85, delta = 1)
sample2indp.pow(n1 = 50, mean = c(15.5,16), s1=2 , d.cohen = 0.3, power = 0.33, delta = 0.5)

Teaching Statistics Data Simulation

Description

Univariate and multivariate normal data simulation. They also supply a brief summary of the analysis for each experiment/design.

• Independent samples.

• One-way and two-way ANOVA.

• Paired samples (T-Test & Regression).

• Repeated measures (ANOVA & Multiple Regression).

• Clinical Assay.

Author(s)

Esteban Cabello García and Pedro Jesús Femia Marzo.