getEffectSizesABBA {reproducer}

getEffectSizesABBA

Description

Function to calculate both effect sizes (dIG, dRM), i.e., independent groups and repeated measures standardized effect sizes and variances, for AB/BA crossover design studies. Function is used in a paper 'Effect Sizes and their Variance for AB/BA Crossover Design Studies' by Lech Madeyski and Barbara Kitchenham.

Usage

getEffectSizesABBA(simulationData)

Arguments

simulationData

- data set in a form required to calculate effect sizes in AB/BA crossover experimental designs

Value

data frame incl. calculated effect sizes and variances: # dIG - independent groups standardized effect size # var.dIG - variance of independent groups standardized effect size # dRM - repeated measures (within-subjects) standardized effect size # var.dRM - variance of repeated measures (within-subjects) standardized effect size # dIG.Fromt - independent groups standardized effect size calculated from t: dIG.Fromt=t*sqrt(1-r)*sqrt((N1+N2)/(2*N1*N2)) # var.dIG.Fromt - variance of independent groups standardized effect size calculated from t: var.dIG.Fromt=var.t*(1-r)*((N1+N2)/(2*N1*N2)) # dRM.Fromt - dRM calculated from t: dRM.Fromt=t*sqrt((N1+N2)/(2*N1*N2)) # var.dRM.Fromt - var.dRM calculated from t: var.dRM.Fromt = var.t*((N1+N2)/(2*N1*N2)) # var.dRM.Fromt2 - var.dRM calculated from t or rather dRM.Fromt: var.dRM.Fromt2=(df/(df-2))*((N1+N2)/(2*N1*N2)+dRM.Fromt^2)- dRM.Fromt^2/c^2 # var.dRM.Approx - var.dRM calculated on a basis of Johnson and Welch (1940) report an approximate formulate for the variance of a t variable: var.dRM.Approx=((N1+N2)/(2*N1*N2)) + (dRM^2)/(2*(N1+N2-2)) #see paper and Equation 49 # var.dIG.Approx - var.dIG calculated on a basis of Johnson and Welch (1940) report an approximate formulate for the variance of a t variable: var.dIG.Approx=(((N1+N2)*(1-r))/(2*N1*N2)) + (dIG^2)/(2*(N1+N2-2)) #see paper and Equation 50 # unstandardizedES - estimated unstandardized technique effect size # periodES - estimated period effect # var.sig - sum of within-subjects variance and between-subjects variance # var.within - within-subjects variance # var.between - between-subjects variance # t - t-value # var.t - variance of t-variable # gRM - Hedges and Olkin (1985) unbiased estimator of the repeated measures effect size gRM=dRM*c # var.gRM - variance of gRM calculated as follows: var.gRM=(df/(df-2))*(((N1+N2)/(2*N1*N2))*c^2+gRM^2)- gRM^2/c^2 #Equation 56 # var.gRM2 - variance of gRM calculated as follows: var.gRM2=var.dRM*c^2 # gIG - Hedges and Olkin (1985) unbiased estimator of the independent groups effect size gIG=dIG*c # var.gIG - variance of gIG calculated as follows: var.gIG=(df/(df-2))*(((N1+N2)/(2*N1*N2))*c^2+gIG^2)- gIG^2/c^2 #Equation 57 # var.gIG2 - variance of gRM calculated as follows: var.gIG2=var.dIG*c^2 # r - the correlation between the values observed for the same subject

Author(s)

Lech Madeyski and Barbara Kitchenham

Examples

simulationData <- getSimulationData(25, 18.75, 50, 10, 5, 500) # generate simulated data set
es <- getEffectSizesABBA(simulationData) # return effect sizes and variances
# OR
simulationData <- getSimulationData(25, 18.75, 50, 10, 5, 15)
es <- getEffectSizesABBA(simulationData) # return effect sizes and variances