Modeling in Undergraduate Statistics Michael M Granaas Psychology University of South Dakota
Modeling In its simplest form a statistical model is just a simplified mathematical representation of reality. The mean and median, instead of being descriptive statistics, are simple mathematical models that describe a distribution of data (i.e., parameter estimates). The regression line is a model that describes the relation between two variables.
Null Hypothesis Statistical Testing (NHST) The focus of NHST is the “straw person” nil hypothesis. A generic “no effect” hypothesis. NHST is still the dominant form of statistical testing taught to undergraduate psychology majors. A haphazard survey of available undergraduate texts finds only one that uses a modeling approach (Lockhart, 1998), which is out of print. As taught, NHST is a collection of loosely related procedures.
Modeling: The Quiet Revolution While much of the field has been arguing about the place of NHST in psychological research (c.f. Nickerson, 2000), methodologists have been increasingly becoming modelers (Rodgers, 2010) In addition to books devoted explicitly to models and modeling (e.g. Structural Equation Modeling, Multi-level Modeling) introductory graduate texts are incorporating a modeling approach to multiple regression (Cohen et al, 2003) and ANOVA (Keppel and Wickens, 2004).
Unlike NHST a statistical model is based on the predictions of a theoretical model. Instead of testing a “straw person” nil hypothesis the model based hypothesis uses predictions based on a theoretical model or prior knowledge. This is consistent with…
Cohen’s 1994 Critique of NHST included this overlooked disclaimer: “There is a form of Ho testing that has been used in astronomy and physics for centuries, what Meehl (1967) called the "strong" form, as advocated by Karl Popper (1959). Popper proposed that a scientific theory be tested by attempts to falsify it. In null hypothesis testing terms, one takes a central prediction of the theory, say, a point value of some crucial variable, sets it up as the Ho, and challenges the theory by attempting to reject it. This is certainly a valid procedure, potentially even more useful when used in confidence interval form. What I and my ilk decry is the "weak" form in which theories are confirmed" by rejecting null hypotheses.” (p99)
Fisher (1955) argued that the null hypothesis “…(i) it [the null hypothesis] must be in accordance with the facts of nature as so far known… (iv) it must not be contradicted, in any way judged relevant, by the data at hand.” (Fisher, 1955, p 75, emphasis in the original)
Why Modeling For Undergrads? There are many reasons to teach undergraduate statistics. Among them: Educating undergraduates about the practices in their field of study. Preparation for graduate study. In addition: With proper notation and explanation modeling is a single, unified topic rather than a disjointed collection of procedures.
Modeling is too Different/Hard? It is different, but it is only hard because of proactive interference. Modeling is just an alternative (better) framing for statistical hypothesis testing. (c.f., Granaas, 1998, 2002; Lockhart, 1998) Because of the unified approach students are learning variations on a single theme rather than multiple procedures.
References Cohen, J. (1994). The earth is round (p < .05), American Psychologist, 49(12), 997-1003. Cohen, J., Cohen, P., West, S.G., & Aiken, L. (2003). Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences. Lawrence Erlbaum Assoc. Mahwah, NJ. Fisher, R.A. (1955). Statistical methods and scientific induction. Journal of the Royal Statistical Society. Series B (Methodological), 17, (1), 69-78. Granaas, M.M. (1998). Model fitting: A better approach. American Psychologist, 53(7), 800 – 801. Granaas, M.M. (2002). Hypothesis Testing in Psychology: Throwing the Baby out with the Bathwater? Invited paper Presented to the Sixth International Conference on Teaching of Statistics, July 2002, Cape Town, South Africa. http://www.stat.auckland.ac.nz/~iase/publications/1/3m1_gran.pdf Keppel, G. & Wickens, T.D. (2004). Design and Analysis: A Researcher’s Handbook. Pearson, Upper Saddle River, NJ. Lockhart, R.S. (1998). Introduction to Statistics and Data Analysis. W.H. Freeman and Co., New York. Nickerson, R. S. (2000). Null hypothesis statistical testing: A review of an old and continuing controversy, Psychological Methods, 5, 241-301. Rodgers, J.L. (2010) The epistemology of mathematical and statistical modeling: A quiet methodological revolution. American Psychologist, 65(1), 1 – 12.