lin.eq {SNSequate} | R Documentation |
The linear method of equating
Description
This function implements the linear method of test equating as described in Kolen and Brennan (2004).
Usage
lin.eq(sx, sy, scale)
Arguments
sx |
A vector containing the observed scores of the sample taking test |
sy |
A vector containing the observed scores of the sample taking test |
scale |
Either an integer or vector containing the values on the scale to be equated. |
Details
The function implements the linear method of equating as described in Kolen and Brennan (2004). Given observed scores
sx
and sy
, the functions calculates
\varphi(x;\mu_x,\mu_y,\sigma_x,\sigma_y)=\frac{\sigma_x}{\sigma_y}(x-\mu_x)+\mu_y
where \mu_x,\mu_y,\sigma_x,\sigma_y
are the score means and standard deviations on test X
and Y
,
respectively.
Value
A two column matrix with the values of \varphi()
(second column) for each scale value x
(first column)
Author(s)
Jorge Gonzalez jorge.gonzalez@mat.uc.cl
References
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.
See Also
Examples
#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))