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0.002 Beta Binomial 0.002 Post Smooth 25 Raw Score 3000 Squared Bias 4-para Beta Bino ACT English test ACT Reading subscore ACT Science Reasoning American College Testing average mean squared Average Squared Bias Beta Binomial 0.004 beta binomial model beta distribution binomial distribution common item Educational Testing Service equating function based equating methods equipercentile equating function estimated equating functions fitted distribution form is designated four-parameter beta binomial given in Equation groups equating design Hanson Licensure test Linear Beta Bino linear equating log-linear model mean squared error methods of smoothed MSE s.e.(MSE observed data observed distributions old form pairs of population population equating function Post Smooth 0.25 Post Smooth 0.50 presmoothing and postsmoothing random groups equating raw score distributions Raw Score Sample s.d. Skewness Kurtosis Sample Size 1000 Sample Size 250 sample statistics Science Reasoning test smoothed equipercentile equating smoothing cubic spline smoothing parameter standard error true score distribution Unsmoothed Linear Beta