Because error variance alternatively can be considered to be the sum of systematic variance associated with unknown variables and randomness, a tripartite assumption is proposed that total variance in the dependent variable can be partitioned into three variance components. These are variance in the dependent variable that is explained by the independent variable, variance in the dependent variable that is unexplained but systematic (associated with variance in unknown variables), and random variance. Based on the tripartite assumption, classical measurement theory, and simple mathematics, it is shown that these components can be estimated using observable data. Mathematical and computer simulations illustrate some of the important issues and implications.
BorsboomD. (2005). Measuring the mind: Conceptual issues in contemporary psychometrics. Cambridge, England: Cambridge University Press.
2.
FinchS.CummingG.ThomasonN. (2001). Reporting of statistical practices in the Journal of Applied Psychology: Little evidence of reform. Educational and Psychological Measurement, 61, 181-210. doi:10.1177/00131640121971167
3.
GulliksenH. (1987). Theory of mental tests. Hillsdale, NJ: Lawrence Erlbaum.
4.
HarrisR. J. (1994). ANOVA: An analysis of variance primer. Itasca, IL, F. E. Peacock.
5.
HaysW. L. (1994). Statistics (5th ed.). Fort Worth, TX: Harcourt Brace.
6.
HuntT. (1936). The value of measurement in psychology. New York, NY: Prentice Hall.
7.
KaplanR. M.SaccuzzoD. P. (2010). Psychological testing: Principles, applications, and issues (8th ed.). Belmont, CA: Wadsworth/Cengage Learning.
8.
LordF. M.NovickM. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.
9.
MichellJ. (1999). Measurement in psychology. Cambridge, England: Cambridge University Press.
10.
RosenthalR.RosnowR. L. (1991). Essentials of behavioral research: Methods and data analysis (2nd ed.). New York, NY: McGraw-Hill.
11.
RosenthalR.RosnowR. L.RubinD. B. (2000). Contrasts and effect sizes in behavioral research: A correlational approach. New York, NY: Cambridge University Press.
12.
RosenthalR.RubinD. B. (1982). A simple general purpose display of magnitude and experimental effect. Journal of Educational Psychology, 74, 166-169. doi:10.1037/0022-0663.74.2.166
13.
RussoF. (2009). Causality and causal modeling in the social sciences (Methods Series 5). New York, NY: Springer.
ThompsonB. (1999). If statistical significance tests are broken/misused, what practices should supplement or replace them?Theory and Psychology, 9, 165-181. doi:10.1177/095935439992006
16.
ThurstoneL. L. (1959). The measurement of values. Chicago, IL: University of Chicago Press.
17.
TrafimowD. (2014). Estimating true standard deviations. Frontiers in Quantitative Psychology and Measurement, 5, 235. doi:10.3389/fpsyg.2014.00235
18.
TrafimowD.MarksM. (2015). Editorial. Basic and Applied Social Psychology, 37, 1-2. doi:10.1080/01973533.2015.1012991
19.
TrafimowD.RiceS. (2008). Potential performance theory (PPT): A general theory of task performance applied to morality. Psychological Review, 115, 447-462. doi:10.1037/0033-295X.115.2.447
20.
TrafimowD.RiceS. (2009). Potential performance theory (PPT): Describing a methodology for analyzing task performance. Behavior Research Methods, 41, 359-371. doi:10.3758/BRM.41.2.359
21.
Vacha-HaaseT.NilssonJ. E.ReetzD. R.LanceT. S.ThompsonB. (2000). Reporting practices and APA editorial policies regarding statistical significance and effect size. Theory and Psychology, 10, 413-425. doi:10.1177/0959354300103006
22.
WilkinsonL., & The APA Task Force on Statistical Inference. (1999). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 54, 594-604. doi:10.1037/0003-066X.54.8.594
