Denis, D. (2010). Persuading with Probability: The Prosecution of O.J. Simpson.
The Jury Expert, 22(4), 29-32.


Recent Book Reviews for Journal of the History of the Behavioral Sciences

Eric Shiraev. A History of Psychology: A Global Perspective (in press)

Graham Richards. Putting Psychology in its Place: Critical Historical Perspectives.

William H. Tucker. The Cattell Controversy: Race, Science, and Ideology.

Research & Data Analysis in the News Every day we see research findings reported in the daily newspapers and on cable television programs. But is it credible? In this section, we critically evaluate research findings that make the popular press, and at minimum, ask questions that require answers before the research report can be taken seriously.  If you've spotted a research finding in the popular press that you feel is misleading or at minimum confusing (or even seemingly ridiculous), please send the link to daniel.denis@umontana.edu. Sensitivity & Specificity - BMJ Rapid Response, July 9, 2010

DATA-ANALYTIC PROCEDURES, SOFTWARE, & THEORY

SOFTWARE & DATA MANAGEMENT Getting to Know R (html) How to read an SPSS (.SAV) file into R (html) Dalgaard (2008) - What is the effect of categorizing a continuous predictor? (Using R to test). Plotting Basic Functions & Curves in R

ANALYSIS OF VARIANCE (ANOVA) Understanding ANOVA I (pdf) Understanding ANOVA II (pdf) Understanding ANOVA III (pdf) The Logic of Linear contrasts in ANOVA (pdf) Factorial ANOVA (pdf) Random Effects ANOVA (pdf) Mixed Model ANOVA (pdf) Simple Effects in SPSS (html)

ANALYSIS OF COVARIANCE Analysis of Covariance Using R (html)

SIMPLE & MULTIPLE REGRESSION Simple Linear Regression Part I (pdf) Simple Linear Regression Part II (pdf) Simple Linear Regression Part III (pdf) Partial and Multiple Regression Part I (pdf) Partial and Multiple Regression Part II (pdf) Partial and Multiple Regression Part III (pdf) Interpreting a Multiple Regression (pdf) Testing Interactions in Multiple Regression I (pdf) Testing Interactions in Multiple Regression II (pdf) Linear Models in R (html) "Classic" Regression - Hays (html) Moderated Regression (html)

REPEATED MEASURES ANOVA 2x2-way Repeated Measures Design in SPSS (with no between factors) (html)

MULTIVARIATE ANALYSIS OF VARIANCE (MANOVA) MANOVA I (pdf) MANOVA II (pdf) MANOVA III (pdf) MANOVA IV (pdf) MANOVA V (pdf) MANOVA VI (pdf) MANOVA VII (pdf)

DISCRIMINANT ANALYSIS  Discrim I (pdf) Discrim II (pdf)

FACTOR ANALYSIS Factor I (pdf) Factor II (pdf)

PRINCIPAL COMPONENTS ANALYSIS (PCA) Principal Components Analysis Using R (html) Principal Components Analysis Using SPSS (html)

BINARY LOGISTIC REGRESSION  Logistic Regression (pdf) Binary Logistic Regression Using R (html) Binary Logistic Regression Using SPSS (html)

BAYESIAN DECISION MODELS Decision I (pdf)  Decision II (pdf)  Decision III (pdf)  Decision IV (pdf)  Denis, D. (2010). Toward a Bayesian Decision-Theoretic Approach to Hypothesis-Testing in Psychology. Journal of Non-Significant Results in Education, 1, 1.

MISC. ITEMS & SELECT STATISTICAL THEORY Partition of Sums of Squares in ANOVA (pdf) The Arithmetic Mean as Balance Point (pdf) Unbiased Sample Variance (pdf) Variance Estimators (biased and unbiased) Sampling Distributions (pdf) Understanding the Derivative Using a Parabola (html) Matrix Algebra for Multivariate Statistics (pdf) Gigerenzer (2002) - Excerpts from Calculated Risks: How to Know When Numbers Deceive You. Simon & Schuster, New York.

STUDY GUIDES Denis, D. (2007). Study Guide for Kirk, R. E. (2008). Statistics: An Introduction. Wadsworth (pdf)

Advice for Graduate Students Completing Theses or Dissertations 1. Hypotheses first, statistical analyses second (unless you have plenty of data to cross-validate your exploratory analyses). The power of the scientist is in his or her ability to predict, not merely observe. 2. When completing your thesis or dissertation, foresee and address statistical issues ASAP. The expression "I'm done my dissertation, all that remains to do are my data analyses," usually means the project is nowhere near complete. Issues (extremely non-trivial ones) come up in data analysis that often require considerable time and thought, and the process should not be hurried. Procrastination on your statistical analyses is usually equivalent to procrastination on your entire thesis or dissertation, and an otherwise well-done project can be turned upside down overnight if a crucial methodological/statistical issue is not detected, addressed and resolved. For instance, hours and hours of analyses and dissertation discussion write-up can turn out to be of little value if you mistakenly assumed a predictor was continuous instead of categorical. Such an error is not minor, not merely a statistical artifact, and can cause an interpretational 360 on your conclusions. Do not underestimate the amount of time and effort and planning that is usually required to analyze your data and make sense of these analyses. When should you start planning your analyses and reading up on the analytical strategy? The day you begin planning the thesis or dissertation proposal. Plan your approach long-term so that when obstacles arise (and they always do), you'll have time built into your schedule to address and learn from them. If you require statistical and methodological advice, seek it out EARLY EARLY EARLY. Procrastinating on statistical issues is 10 times more stressful than addressing them promptly, and can often delay the timely completion of your thesis or dissertation. The best defense is a good offense, so attack your statistical and methodological issues head on. 3. p < .05 is usually always interesting statistically, but not always scientifically. Include effect size estimates in your results and discussion, and interpret them relative to other research in your field. Always contextualize your findings for your readers/audience. Should we be excited by what you found? 4. Verify that the conclusions made in your discussion match up with the conclusions allowed by your statistical analyses. Important as your findings may be, it's all too tempting to claim a solution to world hunger because all of your experimental rats have full bellies. Guard against unwary extrapolation and generalization. 5. Ask yourself as many critical and difficult questions as you can about your own research project, and research answers to them - these are likely to be similar questions posed by your committee at your defense. If you make your project bullet proof and are extremely well-prepared, the defense will likely be a celebratory demonstration of your knowledge, rather than a stressful "under the lights" exam of it. Don't wait until defense day to think about why you did a factor analysis rather than a principal components analysis. Have a well-prepared argument long beforehand. Anticipate as many questions as you can, know your craft, get confident, and you'll have a stronghold going into your defense. You do have a significant measure of control over how your defense proceeds and turns out if you prepare accordingly, and aspire to mastery of your chosen subject or field.

Psychology Colloquia 

Student Corner Looking for a decent price on textbooks? Try Addall.com for the best price. Looking for a job in academia? Try Chronicle of Higher Education, PsycCareers, JobBankUSA, JobBankCANADA. TUTOR PLACEMENT SERVICE - Do you need a tutor for your statistics or research methods class? Contact Dan @ daniel.denis@umontana.edu and we will try to match you up with a knowledgeable, caring, and reliable tutor. The majority of tutors we recommend charge a maximum of $20/hour and work independently. We currently only specialize in matching students for quantitative, statistics, and research methods courses, regardless of subject area (e.g., psychology, sociology, political science, biology, forestry, etc.). Do you require tutoring for another course? Contact us anyway and we'll see what we can do, or advise you on how and where to shop for a good tutor. Want to get a higher degree in psychology but need advice and resources? Visit mastersinpsychology.net Want to find the right psychology degree? Visit www.onlinepsychologydegrees.com Interested in Operations Management? Visit http://www.operationsmanagement.net/

On-line Statistical Calculators & Demos & Useful Links for Psychology, Statistics and Mathematics

Odds & Risk Ratios, Chi-Squared - provides computations for 2x2 table

Statpages - a variety of calculators and computational tools for various tests, including power estimation.

G*Power 3 - a free program for a variety of power analyses (including within-subject designs).

DanielSoper.com - a variety of programs for computing statistical power.

Iowa.edu - java applets for power analyses for various models.

Preacher, K. J., Curran, P. J., & Bauer, D. J. (2006). - Computational tools for probing interaction effects in multiple linear regression, multilevel modeling, and latent curve analysis. Journal of Educational and Behavioral Statistics, 31, 437-448.

Java Applets - a variety of programs that allow you to visualize changes in distributions instantaneously, as well as programs for running statistical tests.

Confidence Interval Simulation - "see" for yourself the meaning of a confidence interval (remember, it's the sample/interval that is random, not the population parameter!)

Prisoner's Dilemma (Game Theory Java)

Normal Distribution Applet - compute proportions under the curve.

Matrix Multiplication Java - multiply matrices of various dimensions.

Eigenvalue/Eigenvector Java

Visual Calculus

Calculus Review

Mathematics with Visualizations

Calculus Page

Paul's On-line Math Notes

Sobel Test Calculator

American Society of Trial Consultants

The Jury Expert

HG.org - World Wide Legal Directories

BMJ

Critical Past

Kids' Zone - Create a Graph

Physics formulas

APA Style

Real Analysis On-line Text

General Links University of Montana Mansfield Library @ University of Montana University of Montana Cyberbear Missoula Federal Credit Union First Interstate Bank PDF to Word Converter Airliners.net TSN The Toronto Star Google Yahoo YouTube DropSend Sage Publications Book Proposal Guidelines Ping-Pong Anyone? Discovery Liftoff April 5, 2010 Kaiser 1 2 3 4 5 Ping-Pong CPU

RECENT COURSEWORK

Psyc. 222 - Psychological Statistics (UGRAD) - Spring 2010 Syllabus Denis, D. (2007). Study Guide for Kirk, R. E. (2008). Statistics: An Introduction. Wadsworth (pdf)

Spring 2010 - Psyc. 521 - Advanced Psychological Statistics II (GRAD) - OFFLINE Syllabus  Seminar Evaluation Criteria  Seminar Schedule Eyesenck (1974) - A Review of Factorial ANOVA   How do I enter SPSS syntax for the Eyesenck Simple Effects? (best viewed in full-screen mode) Pooling the Error Term in Random Effects Analysis of Variance Block Designs & Repeated Measures Covariance Analysis of Covariance (ANCOVA) ANCOVA Using SPSS ASSIGNMENTS Assignment 1 - due Wednesday, Feb. 3, 2010. Assignment 2 - due Monday, Feb. 22, 2010. READINGS Cumming, G. (2007). Inference by Eye: Pictures of Confidence Intervals and Thinking about Levels of Confidence. Teaching Statistics, 29, 89-93. McMinn, M. R., Tabor, A., Trihub, B. L. (2009). Reading in Graduate School: A Survey of Doctoral Students in Clinical Psychology. Training and Education in Professional Psychology, 3, 233-239. Milani, R. M. Parrott, A. C., Turner, J. D., & Fox, H. C. (2004). Gender differences in self-reported anxiety, depression, and somatization among ecstasy/MDMA polydrug users, alcohol/tobacco users, and nondrug users. Addictive Behaviors, 29, 965-971. Schmiege, S., & Russo, N. F. (2005). Depression and unwanted first pregnancy: longitudinal cohort study. British Medical Journal, 331, 1303-1306. Turner, J. & Noh, S. (1988). Physical disability and depression: a longitudinal analysis. Journal of Health and Social Behavior, 29, 23-37. Wang, J. (2004). A longitudinal population-based study of treated and untreated major depression. Medical Care, 42, 543-550. Psyc 520 - Advanced Psychological Statistics - Fall 2009 (GRAD) Chapter 1 - Problems & Solutions pdf Chapter 2 - Problems & Solutions pdf Chapter 3 - Problems & Solutions pdf Chapter 4 - Problems & Solutions pdf Chapter 5 - Problems & Solutions pdf Chapter 6 - Problems & Solutions pdf Chapter 7 - Problems & Solutions pdf Chapter 8 - Problems & Solutions pdf Chapter 10 - Problems & Solutions pdf Chapter 11 - Problems & Solutions pdf Chapter 12 - Problems & Solutions pdf Handouts and other posted documents Sign Test Using SPSS The Arithmetic Mean as the Origin of the Variance (Hays) Quiz 1 Key Test 1 Key Scheffe Tukey Independent Samples T-test as a Contrast ANOVA Simple Effects Final Exam Worksheet Want to Specialize in Quantitative Methods? Here is a Sample Job Opportunity. Many such jobs are limited contract positions, but because they are funded by major granting associations, are often renewable. At minimum, such a position provides you with invaluable experience as you expand your quantitative repertoire and build a record of successful consultantships with public and private enterprise. At $62,000, the money isn't bad either!

^{Quantitative & Scientific Training and Consulting
Are you interested in graduate studies in psychology specializing in quantitative and statistical training? Would you like to learn how to apply your skills through consulting mentorship in a variety of professional domains, both academic and in the private sector? Would you like to gain real hands-on experience in quantitative consulting while studying for a Ph.D? Consider applying to the Department of Psychology's General Experimental Program in Quantitative Psychology.}

Requests? If you have a topic for which you would like to see a tutorial or additional notes, please contact Daniel J. Denis, Ph.D. at the Department of Psychology, University of Montana with your request. Many times brief overview notes are enough to get you started on a particular topic. Depending on your request and our current availability, your desired topic may appear on the site in the near future.

E-mail: daniel.denis@umontana.edu

Essential Mathematics

An Essay on the History of Panel Data Econometrics

Mathematical & Theoretical Statistics

MIT Course

Probability and Mathematical Statistics

Mathematical Proofs

Measure Theory

Expectations

Measure Theory and the Central Limit Theorem

Introduction to Mathematical Statistics

Mathematical Statistics

Statistical Theory

Advanced Calculus

Analysis

DNA (and other statistically-based) Evidence

Communicating DNA Evidence

Trial by Probability: Bayes' Theorem in Court

Bayes' Theorem & Weighing Evidence by Juries

Juror Understanding of DNA Evidence

Fundamentals of Probability and Statistical Evidence in Criminal Proceedings

History of Analysis

Russ, S. (2004). The mathematical works of Bernard Bolzano. Oxford.

Psyx. 521 - Advanced Psychological Statistics II (GRAD) - Spring 2011 Syllabus    Analysis of Variance Using SPSS: One-Way Between-Subjects Design     Random Effects ANOVA (pdf)    Random Effects ANOVA - One-Way Between-Subjects Design in SPSS    SPSS Assignment #1 (pdf)   Random Effects ANOVA - Two-Way Between-Subjects Design in SPSS      Pooling the Error Term in Random Effects Analysis of Variance      Mixed Models (pdf)      Randomized Block Design Analysis of Variance With N = 1 Per Cell Using SPSS      Fixed Effects Factorial Analysis of Variance Using SPSS (with simple effects and post-hoc analyses)      Block Designs & Repeated Measures     One-Way Repeated Measures Analysis of Variance      Two-Way Repeated Measures: Mixed Design      SPSS Assignment #2 (pdf)      Simple Linear Regression Part I (pdf)      Simple Linear Regression Part II (pdf)      Simple Linear Regression Using SPSS      Partial and Multiple Regression Part I (pdf)      Partial and Multiple Regression Part II (pdf)      Partial and Multiple Regression Part III (pdf)      Multiple Regression Using SPSS Part I (pdf)      Multiple Regression Using SPSS Part II (pdf) ------------------------------------------------------------------------------------------------------------------------------------ Seminar Evaluation Criteria Eyesenck (1974) - A Review of Factorial ANOVA   How do I enter SPSS syntax for the Eyesenck Simple Effects? (best viewed in full-screen mode) Covariance Analysis of Covariance (ANCOVA) ANCOVA Using SPSS READINGS Cumming, G. (2007). Inference by Eye: Pictures of Confidence Intervals and Thinking about Levels of Confidence. Teaching Statistics, 29, 89-93. McMinn, M. R., Tabor, A., Trihub, B. L. (2009). Reading in Graduate School: A Survey of Doctoral Students in Clinical Psychology. Training and Education in Professional Psychology, 3, 233-239. Milani, R. M. Parrott, A. C., Turner, J. D., & Fox, H. C. (2004). Gender differences in self-reported anxiety, depression, and somatization among ecstasy/MDMA polydrug users, alcohol/tobacco users, and nondrug users. Addictive Behaviors, 29, 965-971. Schmiege, S., & Russo, N. F. (2005). Depression and unwanted first pregnancy: longitudinal cohort study. British Medical Journal, 331, 1303-1306. Turner, J. & Noh, S. (1988). Physical disability and depression: a longitudinal analysis. Journal of Health and Social Behavior, 29, 23-37. Wang, J. (2004). A longitudinal population-based study of treated and untreated major depression. Medical Care, 42, 543-550.

Decision Analysis for Hypothesis Testing in Psychology Denis, D. (2010). Toward a Bayesian Decision-Theoretic Approach to Hypothesis-Testing in Psychology. Journal of Non-Significant Results in Education, 1, 1. Bayesian decision models are extremely useful to conceptualize and construct decision problems. They have been used in many disciplines (e.g., medicine, business, law), and have been fully developed by decision theorists such as James O. Berger (1993) and Robert L. Winkler (2002). I recently wrote a paper that promotes decision theory for psychology. The following is a table taken from the manuscript, and shows how prior information in the form of probabilities of null and alternative hypotheses can be integrated with data and loss estimates in arriving at an informed decision. The table can be found on p. 18 of the manuscript.

Data & Decision - Challenger, 1986 On January 28, 1986, space shuttle Challenger was launched at a temperature of 31 degrees Farenheit. The coldest temperature of any prior launch was 53 degrees Farenheit. Prior to the launch, data were available to suggest that the rocket booster O-rings had an increased chance of failing in cold temperatures, yet the launch proceeded nonetheless. Was it raw data that informed the decision to launch, or were other factors involved? National Geographic published a documentary on the Challenger accident, of which select outtakes can be viewed in YouTube below [Note: there is no question that television episodes such as those by National Geographic are sensationalized and the facts potentially exaggerated, and I personally have not verified their fact base. However, assuming their report is more or less accurate, sensationalism aside, it serves as a good example of the interplay of how organizations may use (or misuse) data in making decisions, regardless of what actually transpired].   What are the predictors of a "go for launch" decision? What factors explain variance (R-squared like) in the dichotomous variable of the decision "launch yes" vs. "launch no"?  For further details on the Challenger launch decision, including statistical analyses of the probability of failure prior to launch, see the following sources:  Dalal, S. R., Fowlkes, E. B., & Hoadley, B. (1989). Risk Analysis of the Space Shuttle: Pre-Challenger Prediction of Failure. Journal of the American Statistical Association, 84.  Friendly, M. (2000). Visualizing Categorical Data. SAS Publishing, NC. (pp. 208-211) Vaughan, D. (1996). The Challenger Launch Decision: Risky Technology, Culture, and Deviance at Nasa. The University of Chicago Press, Chicago.      Data & Decision- Columbia, 2003 On February 1, 2003, NASA suffered its second loss of a shuttle. This time, space shuttle Columbia, as a result of damage suffered on one of its wings during launch, disintegrated during re-entry into the earth's atmosphere. Post-hoc testing revealed that a piece of foam produced a hole in the wing crippling the shuttle during re-entry. The tragedy is a perfect example of how "common sense," without empirical evidence, can lead even the best of engineers and scientists to false conclusions. Nasa engineers speculated that a piece of foam could not have caused any substantial damage to the shuttle wing. However, in their post-hoc test using real data and while suspending their speculative beliefs, NASA learned that a piece of foam traveling at extremely fast speeds could indeed impart significant damage to the shuttle wing (see second video below). One lesson to take from the Columbia accident is that without proper empirical test, common sense and logic, even by "experts," can grossly deceive. In this case, the data came after the decision to "ok" the shuttle's return to earth (rather than sending a rescue shuttle mission to space to return the astronauts). Pate-Cornell, M. E. & Fischbeck, P. S. (1994). Risk management for the tiles of the space shuttle. Interfaces, 24, 64-86.

Data-Analytic Articles, Books & Guides (some available on-line - if you find any links that do not work, or out of date, please e-mail daniel.denis@umontana.edu and I will either correct the link, upload the paper myself, or delete it permanently).

Bargsted, M. (2010). An empirical assessment of the Bayesian unbiased voter hypothesis. Draft, Department of Political Science, University of Michigan.

Bollen, K. A. (1989). Structural equations with latent variables. Wiley: New York. [considered to be the foundational reference on SEM latent variable models]

Bullock, J. G. (2009). Partisan bias and the Bayesian ideal in the study of public opinion. The Journal of Politics, 71, 1109-1124.  

Byrne, B. M. (2001). Structural equation modeling with AMOS: Basic concepts, applications, and programming. Lawrence Erlbaum Associates: London. 

Clemen, R. T., & Reilly, T. (2001). Making hard decisions. Duxbury: CA. [an excellent book for an introduction to using statistics as an aid for making hard decisions, the applications are in business mostly, though the same technology can be used across virtually all disciplines] 

Cohen, J. (1990). Things I have learned (so far). American Psychologist, 45, 1304-1312.

Cortina, J. M. (1993). What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology, 78, 98-104.

Cumming, G. (2007). Inference by Eye: Pictures of Confidence Intervals and Thinking About Levels of Confidence. Teaching Statistics, 29, 89-93.

Degroot, M. H. & Schervish, M. J. (2002). Probability and Statistics. Addison Wesley: New York. [an excellent "introductory" text on statistics, assumes knowledge of calculus]

Denis, D. (2003). Alternatives to Null Hypothesis Significance Testing. Theory & Science, 4.

Denis, D. (in press). Toward a Bayesian Decision-Theoretic Approach to Hypothesis-Testing in Psychology. 

Field, A. (2009). Discovering statistics using SPSS. Sage Publications: Los Angeles. [a very user-friendly book on how to use SPSS]

Fisher, R. A. (1925). Statistical methods for research workers. Oliver and Boyd: Edinburgh. [original and infamous text on ANOVA, linked from "Classics in the History of Psychology," a site devoted to providing on-line resources to students and researchers who are either learning or teaching the history of psychology (edited by Dr. Christopher D. Green of York University).

Fisher, R.A. (1966). The design of experiments. 8th edition. Hafner:Edinburgh. [foundational text on null hypothesis significance testing and experimental design]

Friendly, M., & Denis, D. (retrieved Oct. 2009). Milestones in the history of thematic cartography, statistical graphics and data visualization. [a collection of annotated graphics over history from pre-1600 to the present, the site originates from York University, Canada, the primary author is Dr. Michael Friendly]

Fox, J. (2009). A mathematical primer for social statistics (Quantitative applications in the social sciences). Sage Publications: Los Angeles. [and excellent overview of the mathematics regularly used in statistics (algebra, calculus), including a presentation of matrix algebra]  

Hays, W. (1994). Statistics. Harcourt College Publishers: New York. [a foundational text for statistics, though it does contain a few typos] 

JSTOR [an historian and researcher's dream come true, a huge archive of on-line papers and articles]

Keith, T. Z. (2006). Multiple regression and beyond. Pearson Education: New York. [a very applied book on regression models including a brief presentation of interactions in regression, as well as confirmatory factor analysis models]  

Maindonald, J. H. (2008). Using R for Data Analysis and Graphics: Introduction, Code and Commentary.

Magidson, J. & Vermunt, J. K. A Nontechnical Introduction to Latent Class Models. Statistical Innovations Inc.

Newsom, J. (retrieved Oct. 2009). Structural Equation Modeling Reference List. [a very thorough collection of articles related to SEM models and related issues]

R-Project for Statistical Computing.

Rozeboom, W. W. (1960). The fallacy of the null-hypothesis significance test. Psychological Bulletin, 57, 416-428. [one of the earlier (of many to come) articles criticizing statistical significance testing]

Searle, S. R. (1982). Matrix algebra useful for statistics. Wiley: New York. [an excellent text on matrix algebra and how they are used in multivariate statistics]

Sijtsma, K. (2009). On the use, the misuse, and the very limited usefulness of Cronbach's alpha. Psychometrika, 74, 107-120 [A critical look at the infamous reliability coefficient]

Sloughter, D. (2009). A primer of real analysis.

Smith, J. E., & Winterfeldt, D. V. (2004). Decision Analysis in "Management Science." Management Science, 50, 561-574.

Upton, G. & Cook, I. (2006). Dictionary of statistics. Oxford University Press: New York. [a good dictionary that serves as a nice accompaniment to any traditional statistics text]

Papers on Latent Curve/Growth Analysis, SEM, Multilevel, Mixed, HLM, Random-Coefficient Models

Bauer, D. J. & Curran, P. J. (2005). Probing interactions in fixed and multilevel regression: Inferential and graphical techniques. Multivariate Behavioral Research, 40, 373-400.

Curran, P. J., Bauer, D. J., Willoughby, M. T. (2004). Testing main effects and interactions in latent curve analysis. Psychological Methods, 9, 220-237.

Curran, P. J., Bauer, D. J., Willoughby, M. T. (2006). Testing and probing interactions in hierarchical linear growth models. In C.S. Bergeman & S.M. Boker (Eds.), The Notre Dame Series on Quantitative Methodology, Volume 1: Methodological Issues in Aging Research, (pp.99-129). Mahwah, NJ: Lawrence Erlbaum Associates.

Hardy, S. A., & Thiels, C. (2009). Using latent growth curve modeling in clinical treatment research: An example comparing guided self-change and cognitive behavioral therapy treatments for bulimia nervosa. International Journal of Clinical and Health Psychology, 9, 51-71.

History Corner & Trivia Click above image for short video on Hubble Deep Field ------------------------------------------------------------------- Do you know the significance of the following diagram (below)? (for a larger version (and the answer), go to the Milestones site and look under 1885) ------------------------------------------------------------------------------------------  Correlation Patterns

web counter