Asymptotic Standard Error of Equipercentile Equating

1995 ◽  
Vol 20 (3) ◽  
pp. 259-286 ◽  
Author(s):  
Michelle Liou ◽  
Philip E. Cheng
Keyword(s):  
Empirical Study ◽  
Standard Error ◽  
Test Scores ◽  
Frequency Estimation ◽  
Estimation Method ◽  
Standard Errors ◽  
Asymptotic Standard Error ◽  
Equipercentile Equating

We propose simplified formulas for computing the standard errors of equiper-centile equating for continuous and discrete test scores. The suggested formulas are conceptually simple and easily extended to more complicated equating designs such as chained equipercentile equating, smoothed equipercentile equating, and equating using the frequency estimation method. Results from an empirical study indicate that the derived formulas work reasonably well for samples with moderate sizes (e.g., 1,000 examinees).

The Standard Error of Equipercentile Equating

1982 ◽  
Vol 7 (3) ◽  
pp. 165-174 ◽  
Author(s):  
Frederic M. Lord
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Standard Error ◽  
Real Data ◽  
Numerical Results ◽  
Standard Errors ◽  
Equipercentile Equating ◽  
Data Standard ◽  
Methods Numerical

The standard error of an equipercentile equating is derived for four situations. Some numerical results are checked by Monte Carlo methods. Numerical standard errors are computed for two sets of real data. Standard errors of linear and equipercentile equating are compared.

scholarly journals Conditional Precision of Measurement for Test Scores: Are Conditional Standard Errors Sufficient?

2018 ◽  
Vol 79 (1) ◽  
pp. 5-18
Author(s):  
W. Alan Nicewander
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Standard Error ◽  
Test Scores ◽  
Latent Variable ◽  
Standard Errors ◽  
Information Function ◽  
Score Distribution ◽  
True Variance ◽  
Variance Formula

This inquiry is focused on three indicators of the precision of measurement—conditional on fixed values of θ, the latent variable of item response theory (IRT). The indicators that are compared are (1) The traditional, conditional standard errors, [Formula: see text] = CSEM; (2) the IRT-based conditional standard errors, [Formula: see text] (where [Formula: see text] is the IRT score information function); and (3) a new conditional reliability coefficient, [Formula: see text]. These indicators of conditional precision are shown to be functionally related to one another. The IRT-based, conditional CSEM, [Formula: see text], and the conditional reliability, [Formula: see text], involve an estimate of the conditional true variance, [Formula: see text], which is shown to be approximately equal to the numerator of the score information function. It is argued—and illustrated with an example—that the traditional, conditional standard error, CSEM, is not sufficient for determining conditional score precision when used as the lone indicator of precision; hence, the portions of a score distribution, where scores are most-and-least precise, can be misidentified.

Revisiting the Standard Errors of Measurement, Estimate, and Prediction and Their Application to Test Scores

1996 ◽  
Vol 82 (3_suppl) ◽  
pp. 1139-1144 ◽  
Author(s):  
Richard A. Charter
Keyword(s):  
Confidence Intervals ◽  
Standard Error ◽  
Test Scores ◽  
Test Score ◽  
Standard Errors ◽  
Score Interpretation ◽  
Standard Error Of Measurement ◽  
Error Of Measurement ◽  
Standard Errors Of Measurement

In 1979 Dudek presented a simplification of Lord and Novick's 1968 work on standard errors and their application to test scores. However, the standard error of measurement has continued to be misinterpreted. The interpretations of the standard errors of measurement, estimate, and prediction are presented. The use of confidence intervals and their importance to test score interpretation are discussed.

Multi-Center Calibration of the Second Reference Material for Thromboplastin, Rabbit, Plain, Coded CRM 149R

1991 ◽  
Vol 65 (03) ◽  
pp. 263-267 ◽  
Author(s):  
A M H P van den Besselaar ◽  
R M Bertina
Keyword(s):  
Reference Material ◽  
Standard Error ◽  
Standard Errors ◽  
Sensitivity Index ◽  
Long Term Stability ◽  
Significant Bias ◽  
The Mean ◽  
The Relationship ◽  
International Sensitivity Index

SummaryIn a collaborative trial of eleven laboratories which was performed mainly within the framework of the European Community Bureau of Reference (BCR), a second reference material for thromboplastin, rabbit, plain, was calibrated against its predecessor RBT/79. This second reference material (coded CRM 149R) has a mean International Sensitivity Index (ISI) of 1.343 with a standard error of the mean of 0.035. The standard error of the ISI was determined by combination of the standard errors of the ISI of RBT/79 and the slope of the calibration line in this trial.The BCR reference material for thromboplastin, human, plain (coded BCT/099) was also included in this trial for assessment of the long-term stability of the relationship with RBT/79. The results indicated that this relationship has not changed over a period of 8 years. The interlaboratory variation of the slope of the relationship between CRM 149R and RBT/79 was significantly lower than the variation of the slope of the relationship between BCT/099 and RBT/79. In addition to the manual technique, a semi-automatic coagulometer according to Schnitger & Gross was used to determine prothrombin times with CRM 149R. The mean ISI of CRM 149R was not affected by replacement of the manual technique by this particular coagulometer.Two lyophilized plasmas were included in this trial. The mean slope of relationship between RBT/79 and CRM 149R based on the two lyophilized plasmas was the same as the corresponding slope based on fresh plasmas. Tlowever, the mean slope of relationship between RBT/79 and BCT/099 based on the two lyophilized plasmas was 4.9% higher than the mean slope based on fresh plasmas. Thus, the use of these lyophilized plasmas induced a small but significant bias in the slope of relationship between these thromboplastins of different species.

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