| Title: | Simulate Pedagogical Statistical Data |
|---|---|
| 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. |
| Authors: | Cabello Esteban [aut, cre], Femia Pedro [aut] |
| Maintainer: | Cabello Esteban <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.0 |
| Built: | 2024-10-10 02:59:53 UTC |
| Source: | https://github.com/cran/stats4teaching |
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).
anova1way(k = 3,n , mean = 0, sigma = 1, coefvar = NULL, method = c("Tukey", "LSD", "Dunnett", "Bonferroni", "Scheffe"), conf.level = 0.95, dec = 2)anova1way(k = 3,n , mean = 0, sigma = 1, coefvar = NULL, method = c("Tukey", "LSD", "Dunnett", "Bonferroni", "Scheffe"), conf.level = 0.95, dec = 2)
k |
number of levels. By default k = 3. |
n |
size of samples. |
mean |
vector of means. |
sigma |
vector of standard deviations. |
coefvar |
an optional vector of coefficients of variation. |
method |
post-hoc method applied. There are five possible choices: " |
conf.level |
confidence level of the interval. |
dec |
number of decimals for observations. |
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.
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.
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")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")
anova2way returns multivariate data in order to compute analysis of variance with 2 factors.
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)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)
k |
number of levels Factor I. By default k=2. |
j |
number of levels Factor II. By default j=2. |
n |
number of elements in each group (k,j). |
mean |
vector of means. |
sigma |
vector of standard deviations. |
coefvar |
an optional vector of coefficients of variation. |
method |
post-hoc method applied. There are five possible choices: “ |
conf.level |
confidence level of the interval. |
dec |
number of decimals for observations. |
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.
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))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))
Simulates a clinical Assay with 2 groups (control and treatment) before and after intervention.
cassay(n, mean = 0, sigma = 1, coefvar = NULL, d.cohen = NULL, dec = 2)cassay(n, mean = 0, sigma = 1, coefvar = NULL, d.cohen = NULL, dec = 2)
n |
size of samples. |
mean |
sample mean. Same for both groups before intervention (Pre-test). |
sigma |
sample standard error. |
coefvar |
sample coefficient of variation. |
d.cohen |
size effect (d-Cohen). If not given, randomly generated. |
dec |
number of decimals for observations. |
List containing the following components:
Data: a data frame containing the samples created (Columns: Group, PreTest & PostTest).
Model: linear regression model.
cassay(c(10,12), mean = 115, sigma = 7.5, d.cohen= 1.5) cassay(24, mean = 100, sigma = 5.1)cassay(c(10,12), mean = 115, sigma = 7.5, d.cohen= 1.5) cassay(24, mean = 100, sigma = 5.1)
This function generates univariate and multivariate normal data. It allows simulating correlated and independent samples. Moreover, normality tests and numeric informations are provided.
generator(n , mean = 0, sigma = 1, coefvar = NULL, sigmaSup = NULL, dec = 2)generator(n , mean = 0, sigma = 1, coefvar = NULL, sigmaSup = NULL, dec = 2)
n |
vector size of samples. |
mean |
vector of means. |
sigma |
vector of standard deviations or covariance/correlation matrix. |
coefvar |
an optional vector of coefficients of variation. |
sigmaSup |
an optional vector of standard deviations if sigma is a correlation matrix. |
dec |
number of decimals for observations. |
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).
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.
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))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))
Checks if a given matrix is a correlation matrix for non-degenerate distributions.
is.corrmatrix(matrix)is.corrmatrix(matrix)
matrix |
a (non-empty) numeric matrix of data values. |
A logical value: True/False.
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)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)
Checks if a given matrix is a covariance matrix for non-degenerate distributions.
is.covmatrix(matrix)is.covmatrix(matrix)
matrix |
a (non-empty) numeric matrix of data values. |
A logical value: True/False.
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)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)
Checks if a given matrix is positive definited
is.posDef(matrix)is.posDef(matrix)
matrix |
a (non-empty) numeric matrix of data values. |
A logical value: True/False.
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)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)
Checks if a given matrix is semi-positive definited.
is.semiposDef(matrix)is.semiposDef(matrix)
matrix |
a (non-empty) numeric matrix of data values. |
A logical value: True/False.
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)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)
Given a correlation matrix and vector of standard deviations (or vector of means and vector of variation coefficients) returns a covariance matrix.
mCorrCov(mcorr, sigma = 1, mu = NULL, coefvar = NULL)mCorrCov(mcorr, sigma = 1, mu = NULL, coefvar = NULL)
mcorr |
a (non-empty) numeric correlation matrix. |
sigma |
an optional vector of standard deviations. |
mu |
an optional vector of means. |
coefvar |
an optional vector of coefficients of variation. |
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!
mCorrCov gives the covariance matrix for a specified correlation matrix.
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))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))
Generates two paired measures. It provides T-test and a simple linear regression model for generated data.
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)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)
n |
size of each sample. |
mean |
vector of means. |
sigma |
vector of standard deviations. |
coefvar |
an optional vector of coefficients of variation. |
rho |
Pearson correlation coefficient (optional). If |
alternative |
a character string specifying the alternative hypothesis for T-Test. Must be one of “two.sided“ (default), “greater“ or “less“. Can be specified just the initial letter. |
delta |
true value of the difference in means. |
conf.level |
confidence level for interval in T-Test. |
dec |
number of decimals for observations. |
random |
a logical a logical indicating whether you want a random covariance/variance matrix. |
If random = TRUE, rho is omitted and sigma is taken as range for variances of the covariance matrix.
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.
[clusterGeneration::genpositiveDefMat()]
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)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)
repeatedm(k, n, mean = 0, sigma = 1, coefvar = NULL, sigmaSup = NULL, conf.level = 0.95, random = FALSE, dec = 2)repeatedm(k, n, mean = 0, sigma = 1, coefvar = NULL, sigmaSup = NULL, conf.level = 0.95, random = FALSE, dec = 2)
k |
number of variables. |
n |
number of observations. |
mean |
vector of means. |
sigma |
vector of standard deviations/covariance-correlation matrix. |
coefvar |
vector (optional) of coefficients of variation. |
sigmaSup |
vector (optional) of standard deviations if sigma is a correlation matrix. |
conf.level |
confidence level for interval in T-Test. |
random |
a logical indicating whether you want a random covariance/variance matrix. |
dec |
number of decimals for observations. |
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().
A data frame.
[clusterGeneration::genpositiveDefMat()]
randm <- clusterGeneration::genPositiveDefMat(8, covMethod = "unifcorrmat") mcov <- randm$Sigma Sigma <- cov2cor(mcov) is.corrmatrix(Sigma) repeatedm(k = 8, n = 8, mean = c(20,5, 30, 15),sigma = Sigma, sigmaSup = 2, dec = 2) repeatedm(k = 5, n = 5, mean = c(8,10,5,14,22.5), random = TRUE) repeatedm(k = 3, n = 8, mean = c(10,5,22.5), sigma = c(3.3,1.5,5), dec = 2)randm <- clusterGeneration::genPositiveDefMat(8, covMethod = "unifcorrmat") mcov <- randm$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)
Generates two normal independent samples. It also provides Cohen's effect and T-Test.
sample2indp(n , mean = 0, sigma = 1, coefvar = NULL, alternative = c("two.sided", "less", "greater"), delta = 0, conf.level = 0.95, dec = 2)sample2indp(n , mean = 0, sigma = 1, coefvar = NULL, alternative = c("two.sided", "less", "greater"), delta = 0, conf.level = 0.95, dec = 2)
n |
vector of size of samples. |
mean |
vector of means. |
sigma |
vector of standard deviations. |
coefvar |
an optional vector of coefficients of variation. |
alternative |
a character string specifying the alternative hypothesis for T-Test. meanst be one of “two.sided“ (default), “greater“ or “less“. Can be specified just the initial letter. |
delta |
true value of the difference in means. |
conf.level |
confidence level of the interval. It determines level of significance for comparing variances. |
dec |
number of decimals for observations. |
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.
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.
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)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)
Generates two normal independent samples with desired power and cohen's effect.
sample2indp.pow(n1, mean = 0, s1= 1, d.cohen, power, alternative = c("two.sided", "less", "greater"), delta = 1, conf.level = 0.95, dec = 2)sample2indp.pow(n1, mean = 0, s1= 1, d.cohen, power, alternative = c("two.sided", "less", "greater"), delta = 1, conf.level = 0.95, dec = 2)
n1 |
first sample size. |
mean |
vector of sample means. |
s1 |
standard deviation for first sample. |
d.cohen |
Cohen's effect. |
power |
power of the test. |
alternative |
a character string specifying the alternative hypothesis for T-Test. Must be one of “two.sided“ (default), “greater“ or “less“. Can be specified just the initial letter. |
delta |
true value of the difference in means. |
conf.level |
confidence level of the interval. |
dec |
number of decimals for observations. |
Pooled standard deviation= sp = sqrt((n1 - 1) sigma1^2 +(n2 - 1) sigma2^2) / (n1 + n2 - 2)
d.cohen = |mean1 - mean2| / sqrt(sp)
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.
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)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)
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.
Esteban Cabello García and Pedro Jesús Femia Marzo.