Zimmerman, D.W., & Williams, R.H. (1965). Effect of chance success due to guessing on error of measurement in multiple-choice tests. Psychological Reports, 16, 1193-1196.
Zimmerman, D.W., & Williams, R.H. (1965). Chance success due to guessing and nonindependence of true scores and error scores in multiple-choice tests: Computer trials with prepared distributions. Psychological Reports, 17, 159-165.
Zimmerman, D.W., Williams, R.H., & Rehm, H.H. (1966). Test reliability when error scores consist of independent and nonindependent components. Journal of Experimental Education, 35, 74-78.
Zimmerman, D.W., Williams, R.H., Rehm, H.H., & Elmore, W. (1966). Empirical estimates of intercorrelations among the components of scores on multiple-choice tests. Psychological Reports, 19, 651-664.
Zimmerman, D.W., & Williams, R.H. (1966). Interpretation of the standard error of measurement when true scores and error scores on mental tests are not independent. Psychological Reports, 19, 611-617.
Williams, R.H., & Zimmerman, D.W. (1966). Some conjectures concerning the index of reliability and related quantities when true scores and error scores on mental tests are not independent. Journal of Experimental Education, 35, 76-79.
Zimmerman, D.W., & Williams, R.H. (1966). Generalization of the Spearman-Brown formula for test reliability: The case of nonindependence of true scores and error scores. British Journal of Mathematical and Statistical Psychology, 19, 271-274.
Zimmerman, D.W., Williams, R.H., & Burkheimer, G.J. (1966). Dependence of reliability of multiple-choice tests on number of choices per item: Prediction from the Spearman-Brown formula. Psychological Reports, 19, 1239-1243.
Zimmerman, D.W., & Williams, R.H. (1967). Independence and nonindependence of true scores and error scores in mental tests: Assumptions in the definition of parallel forms. Journal of Experimental Education, 3, 59-64.
Burkheimer, G.J., Zimmerman, D.W., & Williams, R.H. (1967). The maximum reliability of a multiple-choice test as a function of number of items, number of choices, and group heterogeneity. Journal of Experimental Education, 35, 89-94.
Zimmerman, D.W., Williams, R.H., & Burkheimer, G.J. (1968). Dependence of test reliability on heterogeneity of individual and group score distributions. Educational and Psychological Measurement, 28, 41-46.
Williams, R.H., & Zimmerman, D.W. (1968). An extension of the Rulon formula for test reliability: The case of correlated true and error components of scores. Journal of Experimental Education, 36, 94-96.
Zimmerman, D.W., & Burkheimer, G.J. (1968). Coefficient alpha, test reliability, and heterogeneity of score distributions. Journal of Experimental Education, 37, 90-95.
Zimmerman, D.W. (1969). An item sampling model for the reliability of composite tests. Educational and Psychological Measurement, 29, 45-59.
Zimmerman, D.W. (1969). Test reliability and parameters of observed score distributions. Journal of Experimental Education, 37, 92-96.
Zimmerman, D.W. (1969). Estimation of the reliability of composite tests by a computer simulation method. Psychological Reports, 24, 115-122.
Zimmerman, D.W. (1969). A simplified probability model of error of measurement. Psychological Reports, 25, 175-186.
Zimmerman, D.W. (1970). Expected values of correlated measurements and correction for attenuation. Psychological Reports, 26, 907-911.
Zimmerman, D.W. (1971). Probability spaces and the theory of error of measurement. Psychological Reports, 28, 291-301.
Zimmerman, D.W. (1972). Test reliability and the Kuder-Richardson formulas: Derivation from probability theory. Educational and Psychological Measurement, 32, 939-954.
Zimmerman, D.W. (1972). Error and reliability in stochastic processes and psychological measurement. Psychological Reports, 31, 131-140.
Zimmerman, D.W. (1975). Two concepts of "true score" in test theory. Psychological Reports, 36, 795-805.
Zimmerman, D.W. (1975). Probability spaces, Hilbert spaces, and the axioms of test theory. Psychometrika, 40, 395-412.
Zimmerman, D.W. (1976). Test theory with minimal assumptions. Educational and Psychological Measurement, 36, 85-96.
Zimmerman, D.W., & Williams, R.H. (1977). Validity coefficients and correlated errors in test theory. Journal of Experimental Education, 45, 4-9.
Williams, R.H., & Zimmerman, D.W. (1977). The reliability of difference scores when errors are correlated. Educational and Psychological Measurement, 37, 679-689.
Zimmerman, D.W., & Williams, R.H. (1977). The theory of test validity and correlated errors of measurement. Journal of Mathematical Psychology, 16, 135-152
Zimmerman, D.W. (1979). A simple duality principle in test theory. Journal of Mathematical Psychology, 20, 256-262.
Zimmerman, D.W., & Williams, R.H. (1980). Is classical test theory "robust" under violation of the assumption of uncorrelated errors? Canadian Journal of Psychology, 34, 227-237.
Zimmerman, D.W., Williams, R.H., & Brotohusodo, T.L. (1981). The reliability of sums and differences of test scores: Some new results and anomalies. Journal of Experimental Education, 49, 177-186.
Williams, R.H., & Zimmerman, D.W. (1981). Error of measurement and statistical inference: Some anomalies. Journal of Experimental Education, 49, 71-73.
Zimmerman, D.W. (1981) On the perennial argument about grading "on the curve" in college courses. Educational Psychologist, 16, 175-178.
Williams, R.H., & Zimmerman, D.W. (1982). The comparative validity of simple and residualized difference scores. Psychological Reports, 50, 91-94.
Zimmerman, D.W. (1982). Are blind reviews really blind? Canadian Psychology, 23, 46-48.
Williams, R.H., & Zimmerman, D.W. (1982). Reconsideration of the "attenuation" paradox—and some new paradoxes in test validity. Journal of Experimental Education, 3, 164-171.
Zimmerman, D.W., & Williams, R.H. (1982). Gain scores in research can be highly reliable. Journal of Educational Measurement, 19, 149-154.
Zimmerman, D.W., & Williams, R.H. (1982). On the high predictive potential of change and growth measures. Educational and Psychological Measurement, 42, 961-968.
Zimmerman, D.W., & Williams, R.H. (1982) A note on the correlation of gains and initial status. Journal of General Psychology, 107, 203-207.
Zimmerman, D.W., & Williams, R.H. (1982). The element of chance and the comparative reliability of matching tests and multiple-choice tests. Psychological Reports, 50, 975-980.
Zimmerman, D.W., & Williams, R.H. (1982). The relative error magnitude in three measures of change. Psychometrika, 47, 141-147.
Zimmerman, D.W. (1983). The mathematical definition of test validity. Educational and Psychological Measurement, 43, 791-796.
Williams, R.H., & Zimmerman, D.W. (1983). The comparative reliability of simple and residualized difference scores. Journal of Experimental Education, 51, 94-97.
Williams, R.H., & Zimmerman, D.W. (1984). A critique of Knapp's "The (un)reliability of change scores in counseling research." Measurement and Evaluation in Guidance, 16, 179-182.
Zimmerman, D.W., Williams, R.H., & Symons, D.L. (1984). Empirical estimates of the comparative reliability of matching tests and multiple-choice tests. Journal of Experimental Education, 52, 179-182.
Williams, R.H., & Zimmerman, D.W. (1984). On the virtues and vices of the standard error of measurement. Journal of Experimental Education, 52, 231-233.
Frary, R.B., & Zimmerman, D.W. (1984). Effect of bias on validity and reliability. Educational and Psychological Measurement, 45, 191-197.
Williams, R.H., Zimmerman, D.W., Rich, J., & Steed, J.L. (1984). An empirical study of the relative error magnitude in three measures of change. Journal of Experimental Education, 53, 55-57.
Zimmerman, D.W., Andrews, D.A., Robinson, D., & Williams, R.H. (1985). A note on non-parallelism of pretest and posttest measures in assessing change. Journal of Experimental Education, 53, 234-236.
Zimmerman, D.W. (1985). Variability of deviation I.Q.'s based on multiple-choice test scores. Educational and Psychological Measurement, 45, 745-751.
Zimmerman, D.W., & Williams, R.H. (1986). Note on the reliability of experimental measures and the power of significance tests. Psychological Bulletin, 100, 123-124.
Zimmerman, D.W., & Williams, R.H. (1987). A note on short multiple-choice tests. Indian Journal of Psychometry and Education, 18, 29-36.
Williams, R.H., Zimmerman, D.W., & Mazzagatti, R.D. (1988). Large sample empirical estimates of the reliability of simple, residualized, and base-free gain scores. Journal of Experimental Education, 55, 116-118.
Williams, R.H., & Zimmerman, D.W. (1989). Statistical power analysis and reliability of measurement. Journal of General Psychology, 116, 359-369.
Williams, R.H., & Zimmerman, D.W. (1992). A note on the reliability of simple and residualized differences. Journal of Experimental Education, 61, 84-85.
Zimmerman, D.W. (1992). A note on the inadequacy of percentage grading scales for almost all ability distributions. Canadian Psychology, 34:2.
Zimmerman, D.W., Zumbo, B.D., & Lalonde, C. (1993). Coefficient alpha as an estimate of test reliability under violation of two assumptions. Educational and Psychological Measurement, 53, 33-49.
Zimmerman, D.W., Williams, R.H., & Zumbo, B.D. (1993). Reliability of measurement and power of significance tests based on differences. Applied Psychological Measurement, 17, 1-10.
Zimmerman, D.W., Williams, R.H., & Zumbo, B.D. (1993). Reliability, power, functions, and relations: A reply to Humphreys. Applied Psychological Measurement, 17, 15-16.
Zimmerman, D.W. (1994). A note on interpretation of formulas for the reliability of differences. Journal of Educational Measurement, 31, 143-147.
Williams, R.H., Zimmerman, D.W., & Zumbo, B.D. (1995). Impact of measurement error on statistical power: Review of an old paradox. Journal of Experimental Education, 63, 363-370.
Williams, R.H., Zimmerman, D.W., & Cummings, N. (1996). Note on reliability and validity of change scores. Perceptual and Motor Skills, 82, 1-2.
Williams, R.H., & Zimmerman, D.W. (1996). Are simple gain scores obsolete? Applied Psychological Measurement, 20, 59-69.
Williams, R.H., & Zimmerman, D.W. (1996). Commentary on the commentaries of Collins and Humphreys. Applied Psychological Measurement, 20, 295-297.
Zimmerman, D.W. (1997). A geometric interpretation of the validity and reliability of difference scores. British Journal of Mathematical and Statistical Psychology, 50, 73-80.
Zimmerman, D.W., & Williams, R.H. (1997). Properties of the Spearman correction for attenuation for normal and realistic non-normal distributions. Applied Psychological Measurement, 21, 253-270.
Williams, R.H., & Zimmerman, D.W. (1998). A note on May and Hittner's three scenarios for the reliability and validity of gain scores. Perceptual and Motor Skills, 86, 664-666.
Zimmerman, D.W., & Williams, R.H. (1998). Reliability of gain scores under realistic assumptions about properties of pretest and posttest scores. British Journal of Mathematical and Statistical Psychology, 51, 343-351.
Zimmerman, D.W. (1998). How should classical test theory have defined validity? Social Indicators Research (special edition, edited by B.D. Zumbo). Dordrecht, The Netherlands: Kluwer. pp. 233-251.
Zimmerman, D.W. (1998). Comment on "Science, measurement, and validity: Is completion of Samuel Messick's synthesis possible?" by Keith A. Markus. Social Indicators Research (special edition, edited by B.D. Zumbo). Dordrecht, The Netherlands: Kluwer. pp. 69-72.
Williams, R.H., & Zimmerman, D.W. (1999). Nonindependence of parameters of the validity and reliability of gain scores. Perceptual and Motor Skills, 88, 679-681.
Zimmerman, D.W., & Williams, R.H. (2000). Restriction of range and correlation in outlier-prone distributions. Applied Psychological Measurement, 24, 267-280.
Zimmerman, D.W., & Zumbo, B.D. (2001). The geometry of probability, statistics, and test theory. International Journal of Testing, 1(3&4), 283-303.
Williams, R.H., Zimmerman, D.W., Zumbo, B.D., & Ross, D. (2003). Charles Spearman: British behavioral scientist. Human Nature Review, 3: 114-118.
Zimmerman, D.W., & Williams, R.H. (2003). A new look at the influence of guessing on the reliability of multiple-choice tests. Applied Psychological Measurement, 27, 357-371.
Zimmerman, D.W., Williams, R.H., Zumbo, B.D., & Ross, D. (2005). Louis Guttman's contributions to classical test theory. International Journal of Testing. 5(1), 81-95.
Zimmerman, D.W., & Zumbo, B.D. (2005). Can percentiles replace raw scores in statistical analysis of test data? Educational and Psychological Measurement, 65, 616-638.
Zimmerman, D.W. (2007). Correction for attenuation with biased reliability estimates and correlated errors in populations and samples. Educational and Psychological Measurement, 67, 920-939.
Zimmerman, D.W. (2009). The reliability of difference scores in populations and samples. Journal of Educational Measurement, 46, 19-42.
Zimmerman, D.W. (2011). Sampling variability and axioms of classical test theory. Journal of Educational and Behavioral Statistics, 36, 586-615.
"The classical theory of mental tests ... suffers from some imprecision of statement so that, from time to time, controversies arise that appear to raise embarrassing questions concerning its foundations."—Melvin R. Novick
"A fundamental fact concerning unreliability is that, in general, it cannot be estimated from only a single trial. Two or more trials are needed to prove the existence of variation in the score of a person on an item, and to estimate the extent of such variation if there is any. The experimental difficulties in obtaining independent trials have led to many attempts to estimate the reliability of a test from only a single trial by bringing in various hypotheses. Such hypotheses usually do not afford a real solution, since ordinarily they cannot be verified without the aid of at least two independent trials, which is precisely what they are intended to avoid."—Louis Guttman
"... however pleasant it may be to shuffle through the internal statistics of a compound test in search of a formula which gives the closest estimate of a test's reliability under conditions of uncorrelated errors, this is for practical applications like putting on a clean shirt to rassle a hog."—William W. Rozeboom
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