SNSequate (version 1.3-4)

lin.eq: 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)

Value

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

Arguments

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.

Author

Jorge Gonzalez

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.

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

mea.eq, eqp.eq, ker.eq

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))