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1.0 The second 1.1 The third 50 60 Number-Correct 5000 replications 60 Number-Correct Score absolute mean deviation Angoff Applied Psychological Measurement average root mean Average Standard Error chain of equatings circular equating paradigm common-item nonequivalent groups criterion for evaluating Deviation for population different equating methods effectiveness of circular equated back equated to form Equating Method Populatoin equipercentile equating function error of equating evaluating equating Hanson identity equating identity function Kolen & Brennan linear equating method Linear Presmoothing Set mean and linear mean equating method Mean Linear Presmoothing Mean Square Error Mean Tucker Linear Method Populatoin Set nonequivalent groups design normally distributed plotted in Figure population 0.0 population distribution population score distributions random error random groups design represents a situation Root Mean Square sample mean sample statistics second year population Set Three simulation study standard deviation summary statistics synthetic group third year population true equating functions Tucker Mean Tucker type of equating