CTTsub {subscore}

This main function estimates true subscores using different methods based on original CTT scores.

Description

This function estimates true subscores using methods introduced in studies of Haberman (2008) <doi:10.3102/1076998607302636> and Wainer et al. (2001) <doi:10.4324/9781410604729>. Hypothesis tests (i.e., Olkin' Z,Williams's t, and Hedges-Olkin's Z) are used to determine whether a subscore or an augmented subscore has added value. Codes for the hypothesis tests are from Sinharay (2019) <doi: 10.3102/1076998618788862>.

Usage

CTTsub(test.data, method = "Haberman")

Arguments

test.data

A list that contains item responses of all subtests and the entire test, which can be obtained using function 'data.prep'.

method

Subscore estimation methods. method="Haberman" (by default) represents the three methods proposed by Haberman (2008) <doi:10.3102/1076998607302636>. method="Wainer" represents Wainer's augmented method.

Value

summary

Summary of estimated subscores (e.g., mean, sd).

PRMSE

(a) PRMSE values of estimated subscores (for Haberman's methods only).(b) Decisions on whether subscores have added value - added.value.s (or added.value.sx) = 1 means subscore.s (or subscore.sx) has added value, and added.value.s (or added.value.sx) = 0 vice versa.

PRMSE.test

All information in PRMSE plus results of hypopthesis testing based on Sinharay (2019) <doi:10.3102/1076998618788862>.

subscore.original

Original subscores and total score.

estimated.subscores

Subscores computed using selected method. Three sets of subscores will be returned if method = "Haberman".

References

Haberman, S. J. (2008). "When can subscores have value?." Journal of Educational and Behavioral Statistics, 33(2), 204-229. doi:10.3102/1076998607302636.

Sinharay, S. (2019). "Added Value of Subscores and Hypothesis Testing." Journal of Educational and Behavioral Statistics, 44(1), 25-44. doi:10.3102/1076998618788862.

Wainer, H., Vevea, J., Camacho, F., Reeve, R., Rosa, K., Nelson, L., Swygert, K., & Thissen, D. (2001). "Augmented scores - "Borrowing strength" to compute scores based on small numbers of items." In Thissen, D. & Wainer, H. (Eds.), Test scoring (pp.343 - 387). Mahwah, NJ: Lawrence Erlbaum Associates, Inc. doi:10.4324/9781410604729.

Examples

# Transferring original scored data to a list format
# that can be used in other functions.
test.data<-data.prep(scored.data,c(3,15,15,20),
                     c("Algebra","Geometry","Measurement", "Math"))
#----------------------------------------------
# Estimating subscores using Haberman's methods       
CTTsub(test.data,method="Haberman") # Estimating subscores using Haberman's methods 

# Obtaining original correlation for the three methods
CTTsub(test.data,method="Haberman")$Correlation  

# Obtaining disattenuated correlation for the three methods
CTTsub(test.data,method="Haberman")$Disattenuated.correlation  

# Obtaining PRMSEs for the three methods
CTTsub(test.data,method="Haberman")$PRMSE  

# Obtaining descriptive statistics summary for estimated subscores  
CTTsub(test.data,method="Haberman")$summary 

# Obtaining raw subscores  
CTTsub(test.data,method="Haberman")$subscore.original  

# Obtaining subscores that are estimated as a function of the observed subscores 
CTTsub(test.data,method="Haberman")$subscore.s 

# Obtaining subscores that are estimated as a function of the observed total score 
CTTsub(test.data,method="Haberman")$subscore.x  

# Obtaining subscores that are estimated as a function of 
# both the observed subscores and the observed total score.
CTTsub(test.data,method="Haberman")$subscore.sx  

#-------------------------------------------      
# Estimating subscores using Wainer's method
CTTsub(test.data,method="Wainer") 
       
# Obtaining descriptive statistics summary for subscores
CTTsub(test.data,method="Wainer")$summary   

# Obtaining original subscores
CTTsub(test.data,method="Wainer")$subscore.original 

# Obtaining subscores that are estimated using Wainer's augmentation method  
CTTsub(test.data,method="Wainer")$subscore.augmented