lin.eq: The linear method of equating
In jagonzalb/SNSequate: Standard and Nonstandard Statistical Models and Methods for Test Equating

Description Usage Arguments Details Value Author(s) References See Also Examples

This function implements the linear method of test equating as described in Kolen and Brennan (2004).

1	lin.eq(sx, sy, scale)

`sx`	A vector containing the observed scores of the sample taking test X.
`sy`	A vector containing the observed scores of the sample taking test Y.
`scale`	Either an integer or vector containing the values on the scale to be equated.

The function implements the linear method of equating as described in Kolen and Brennan (2004). Given observed scores sx and sy, the functions calculates

phi(x;mu_x,mu_y,sigma_x,σ_y)=(sigma_x/sigma_y)*(x-mu_x)+mu_y

where mu_y,mu_y,sigma_x,sigma_y are the score means and standard deviations on test X and Y, respectively.

A two column matrix with the values of phi() (second column) for each scale value x (first column)

Jorge Gonzalez B. jgonzale@mat.puc.cl

Gonzalez, J. (2014). SNSequate: Standard and Nonstandard Statistical Models and Methods for Test Equating. Journal of Statistical Software, 59(7), 1-30.

Kolen, M., and Brennan, R. (2004). Test Equating, Scaling and Linking. New York, NY: Springer-Verlag.

mea.eq, eqp.eq, ker.eq

#Artificial data for two two 100 item tests forms and 5 individuals in each group
x1<-c(67,70,77,79,65,74)
y1<-c(77,75,73,89,68,80)

#Score means and sd
mean(x1); mean(y1)
sd(x1); sd(y1)

#An equivalent form y1 score of 72 on form x1
lin.eq(x1,y1,72)

#Equivalent form y1 score for the whole scale range
lin.eq(x1,y1,0:100)

#A plot comparing mean, linear and identity equating
plot(0:100,0:100, type='l', xlim=c(-20,100),ylim=c(0,100),lwd=2.0,lty=1,
ylab="Form Y raw score",xlab="Form X raw score")
abline(a=5,b=1,lwd=2,lty=2)
abline(a=mean(y1)-(sd(y1)/sd(x1))*mean(x1),b=sd(y1)/sd(x1),,lwd=2,lty=3)
arrows(72, 0, 72, 77,length = 0.15,code=2,angle=20)
arrows(72, 77, -20, 77,length = 0.15,code=2,angle=20)
abline(v=0,lty=2)
legend("bottomright",lty=c(1,2,3), c("Identity","Mean","Linear"),lwd=c(2,2,2))