# Item Equating with same Group – SAT, ACT example

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# Item equating is the practice of making the results from two # different assessments equivalent. This can be done by either # 1. having the same group take both assessments # 2. having equivalent groups take the different assessments # 3. having non-equivalent groups which use common items take the different # assessments. # In this post I will cover topic 1. # For this code I will use the catR package to generate my assessments # and responses. library("catR") # Let's attempt the first proceedure: # First let's generate our item parameters for assessment 1. # Let's create an item bank with 100 items for the assessments nitems <- 100 bank1 <- createItemBank(model="2PL", items=nitems)$itemPar bank2 <- createItemBank(model="2PL", items=nitems)$itemPar # Now let's generate a 1000 person population sample to take our assessment npeep <- 1000 theta <- rnorm(npeep) # Calculate the score on both assessments resp1 <- resp2 <- matrix(0, nrow=npeep, ncol=nitems) for (i in 1:npeep) { resp1[i,Pi(theta[i],bank1)$Pi32] <- 32 ACT[ACT<4] <- 4 ACT <- round(ACT) # ACT rounds to whole numbers # The standard deviation is 100 and average score around 500 for the ACT SAT <- (score2-mean(score2))/sd(score2)*100 + 500 SAT[SAT>800] <- 800 SAT[SAT<200] <- 200 SAT <- round(SAT/10)*10 # SAT rounds to nearest 10 summary(cbind(SAT,ACT)) # Now let's see if we can transform our SAT scores to be on our ACT scale (A <- sd(ACT)/sd(SAT)) (B <- mean(ACT)-A*mean(SAT)) SATscaled <- A*SAT + B summary(cbind(SAT,ACT,SATscaled)) # The results from taking parrellel tests should fall on a linear form plot(ACT,SATscaled, main="SAT results placed on ACT scale")

# This is the easiest method of equating two tests. # However, it is not usually the most practical since it is costly to get the same # group of individuals to take two different tests. In addition, there # may be issues with fatigue which could be alleviated somewhat if for half of the # group the first assessment was given first and for a different half # the second assessment assessment was given first.

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