This site contains article references, online tutorials/calculators, and other sources that people have sent to me or that I've looked up to help students and colleagues. Rather than letting these resources sit in my e-mail folders and web favorites list, I thought it would be good to share.  Some basic knowledge of statistics is assumed. My aim, therefore, is to help people branch out from their current statistical repertoire and/or trouble-shoot common roadblocks with various techniques. If you'd like to suggest other links and sources, please e-mail me via my faculty webpage.

LAST UPDATED: July 12, 2018

General Tools, Multiple Techniques

Stat Pages (compilation of hundreds of online statistical calculators, from John C. Pezzullo)
Compendium of Statistical Formulas (StatTrek)
Stat-Help links
Statistical Associates (David Garson, covers numerous statistical techniques)
Statistics Solutions (Directory of Statistical Analyses)
Hossein Arsham's statistics pages (here and here)
Karl Wuensch's statistical resources
Andy Field's Statistics Hell
Loren McMaster's annotated bibliography on numerous statistical techniques
Daniel Arkkelin's multi-chapter SPSS tutorials (with screenshots of how things should appear)
Common Mistakes in Using Statistics (Martha Smith)
Hancock, G. R., & Mueller, R. O. (Eds.). (2010). The reviewer's guide to quantitative methods in the social sciences. New York: Routledge.
Spirer, H. F., Spirer, L., & Jaffe, A. J. (1998). Misused statistics. New York: Dekker.
Good, P. I, & Hardin, J. W. (2006). Common errors in statistics (and how to avoid them). Hoboken, NJ: Wiley.

Selecting statistical techniques based on number and types of variables Interactive Decision Tree
Article "Choosing Statistical Tests"
UCLA -- Tabular form, with advice specific to different software programs

Links to additional tables
Data Management
Data Screening/Cleaning Checklist

Skewness and kurtosis (note that skewness and kurtosis should each be divided by its respective standard error to see if the traditional cut-off for two-tailed .05 significance on the normal curve, +/- 1.96, is attained [for simplicity, a ratio of 2 is often cited]. Some authors recommend larger [absolute-value] cut-offs). Also, the traditional definition of kurtosis in terms of "peakedness" is wrong.
Guidelines for transforming variables to improve distributional qualities

Index (composite variable) creation (SPSS; discusses situation of participants missing responses to some of the variables comprising the index)

Missing Data
-----Acock, A.  (2005). Working with missing values. Journal of Marriage and Family, 67, 1012-1028.
-----Dong, Y., & Peng, C-Y. J. (2013). Principled missing data methods for researchers. Springer Open/Springer Plus, 2, 222.
-----Graham, J. W. (2009).  Missing data analysis: Making it work in the real world. Annual Revuew of Psychology, 60, 549–576.
-----Little, T. D., Jorgensen, T. D., Lang, K. M., & Moore, E. W. G. (2013). On the joys of missing data. Journal of Pediatric Psychology, 39, 151–162

-----Longitudinal attrition: 
Coertjens L, Donche V, De Maeyer S, Vanthournout G, Van Petegem P (2017) To what degree does the missing data technique influence the estimated growth in learning strategies over time? A tutorial example of sensitivity analysis for longitudinal data. PLoS ONE 12(9): e0182615.
Nicholson, J. S., Deboeck, P. R., Howard, W. (2017). Attrition in developmental psychology: A review of modern missing data reporting and practices. International Journal of Behavioral
-Development, 41, 143-153. 
Young, R., & Johnson, D. R. (2015). Handling missing values in longitudinal panel data with multiple imputation. Journal of Marriage and Family, 77, 277–294.

Regression diagnostics (see also Outliers under Trouble-Shooting, below)

Reverse scoring of variables -- On measures with a strongly disagree-strongly agree (Likert) format, where one or more items have an oppositely toned wording to the majority of items (e.g., "I dislike Restaurant A," where the other items are "I like Restaurant A," "I plan to keep going back to Restaurant A," "The food is great at Restaurant A," etc.), the scoring of the oppositely toned item(s) should be reversed before the items are combined into an overall scale. This first document explains how to use the compute command in SPSS, so that for example, on a 1-7 scale, taking 8 minus the original value converts a 1 into a 7, a 2 into a 6, etc. This second document explains using the recode command.  I always recommend giving the new variable a new name (e.g., "item4r" where "r" stands for "reverse"), so that the original variable "item4" remains unperturbed in case you need to go back to it for any reason.

Overview Intros
to Particular Techniques

ANOVA: one-way
ANOVA: factorial designs (here and here)
ANOVA: two-way, between-subjects factorial design (SPSS tutorial)
ANOVA: mixed, between and within, model (here and here)

Canonical Correlation (here and here)

Cluster Analysis
Mathematical Learning Support Centre/Rosie Cornish (here)

......Rapkin, B. D., & Luke, D. A. (1993). Cluster analysis in community research... American J. of Community Psychol., 21, 247-277.

Correlation analogues (e.g., biserial, point-biserial, phi)
Correlation, partial (as opposed to "regular" zero-order)

Dyadic analysis (David Kenny; foundational issue of whether dyads are distinguishable/exchangeable)

Effect Sizes (broad overview; Cohen's d  [primarily]; ANOVA-based [e.g., Eta-squared, Omega-squared], calculator; see also Meta-Analysis);

-------Ferguson, C. J. (2009). An effect size primer: A guide for clinicians and researchers. Professional Psychology: Research and Practice,

-----40, 532-538.
Factor Analysis -- Exploratory (annotated SPSS output);
Russell, D. W. (2002). In search of underlying dimensions... Personality and Social Psychology Bulletin, 28, 1629-1646.
-----(provides excellent overviews of exploratory and confirmatory factor analysis)
Hierarchical Linear Modeling (HLM; here)

Latent Class Analysis (here)
Latent Growth Curves (here and here)
Logistic Regression (here)
Log-Linear Models (like a multi-way chi-square analysis)
Longitudinal Analysis (Patrick Curran's reading list)

Mediation/Moderation (Kristopher Preacher's resources; Andrew Hayes's resources and article "Beyond Baron and Kenny")
Meta-Analysis (here and here; see also Effect Sizes)
Mplus [SEM and related applications] (
Multidimensional Scaling (here)

Poission Regression (here and here; for count data of rare events and where mean = variance)
Reliability (various types in SPSS)

Regression: 10 Types of Regression (based on data distributions and other considerations)
Sobel Test for Mediation (here)
Survival analysis (R-square);
-----Luke, D. A. (1993). Charting the process of change: A primer on survival analysis. American J. of Community Psychol., 21, 203-246.
Turnover tables (change over time on categorical variables)


Penn State Methodology Center (free software page, includes many applications)
Meta-analysis (only some of the listed programs are free)
NORM -- Multiple imputation for missing data
PSPP (thanks to Jan Werner)
RegressIt, "a free Excel add-in for linear regression and multivariate data analysis" (Bob Nau)
SOFA (Statistics Open For All)

"R": The R Project; R Links (Psychology Focus); Intro to R from the Personality Project; J. Baron's R Help Page R Commander*; R Studio*; Quick R* ; R for SAS and SPSS Users; Videos instructing on R: Decision Science News (beginning video, web overview); Google/Flowing Data (here
R-Based Structural Equaltion Modeling Programs: Lavaan; Onyx*; WebSEM*
....................[*Offers or discusses GUI (Graphical User Interface) packages]

General: Cortina, J. M. (2002). Big things have small beginnings: An assortment of “minor” methodological misunderstandings. Journal of Management, 28, 339–362 (abstract; thanks to Austin Houghtaling). Reviews scenarios such as outliers; standardized regression Betas greater than 1; negative variances (Heywood Cases) and correlated errors in SEM; and more!

Chi-square: Which cell(s) are the major contributors to an overall significant chi-square? (standardized residuals)

Comparing correlations: There are different types of correlation comparisons. Do you want to compare correlations of the same variables (A & B) in two independent samples? Or, within the same sample, is the correlation of A & B different from that between A & C (dependent correlations)? This document explains the different types of comparisons and links to an online calculator (where it says "Go to procedure"). For more specialized issues, such as comparing partial correlations, see:

  • Preacher, K. J. (2006). Testing complex correlational hypotheses using structural equation modeling. Structural Equation Modeling, 13, 520-543.

Effect sizes with repeated measures: Dunlap, W. P., Cortina, J. M., Vaslow, J. B., & Burke, M. J. (1996). Meta-analysis of experiments with matched groups or repeated measures designs. Psychological Methods, 1, 170-177.

Guidelines for using one-tailed tests: Ruxton, G. D., & Neuhauser, M. (2010). When should we use one-tailed hypothesis testing? Methods in Ecology and Evolution, 1, 114-117.  (abstract)

Infrequent/count data: Atkins, D. C., & Gallop, R. J. (2007). Re-thinking how family researchers model infrequent outcomes: A tutorial on count regression and zero-inflated models. Journal of Family Psychology, 21, 726-735 (abstract; thanks to Art Kendall)

Infrequent/count data: Elhai, J. D., Calhoun, P. S., & Ford, J. D. (2008). Statistical procedures for analyzing mental health services data. Psychiatry Research, 160, 129-136. (abstract; thanks to Ron Spiro). Quoting from abstract: "...A flowchart is provided to assist the investigator in selecting the most appropriate method.

Interactions in multiple regression and related techniques: Resources from Preacher, Curran, and Bauer

Moderation and Mediation: Resources from Kristopher Preacher

Multicollinarity (here, here, here, and here)
Outliers (suggestions from Peter Westfall)

Presenting Data: "Just Plain Data Analysis"

Spuriousness and Suppressor Effects/Suppressor Variables (here, here, and here; suppression refers, for example, to when a relationship between variables switches from positive to negative, with the introduction of control variables)

Syntax (SPSS)

Terminology Compendium of terms (each place it says "Category" opens to a set of more specific links)

Odds vs. probability (pertinent to logistic regression)
Tips and Tools for Constructing Tables and Figures Tables for multiple regression (Alan Acock)

Plotting regression interactions (Jeremy Dawson)

Lane, D. M. & Sandor, A. (2009) Designing better graphs by including distributional information and integrating words, numbers, and images. Psychological Methods, 14, 239-257.
Power Analysis
for Advanced
Power for multiple techniques (here)

LIFESPAN: Longitudinal Study Planner (A. M. Brandmaier)

Chris Aberson's power-analysis resources ("downloadable resources include SPSS syntax for completing power analysis for a ton of designs. These do come from my text on power analysis but the files can be used without purchase of the book")

Hertzog, C., Lindenberger, U., Ghisletta, P., & von Oertzen, T. (2006). On the power of multivariate latent growth curve models to detect correlated change.
Psychological Methods, 11, 244-252.

Preacher, K. J., & Coffman, D. L. (2006, May). Computing power and minimum sample size for RMSEA [Computer software].
Online journals offering free tutorial articles:  Practical Assessment, Research, and Evaluation  and Frontiers in Quantitative Psychology and Measurement (more advanced)

Carolyn Anderson's
syllabus/lecture notes for Applied Categorical Data Analysis and Multilevel Analysis/HLM" (lots of examples!)
James Grice's Personality Research Lab resource page (discussion of advanced topics in methods and statistics)
Kevin Grimm's computer scripts for advanced longitudinal analyses
Winfred Arthur's vita (on conducting meta-analysis with different software programs; see book [2001] and articles from 1990s)
Statistics Resources for Businesses and Educators (Thanks to Stacy Kozak)
Dr. Reifman's
Introductory Graduate Statistics
Dr. Reifman's Multivariate Statistics
Dr. Reifman's Structural Equation Modeling
Lines of Argument
for Why Small Effect Sizes Can
Still Be Meaningful

1. Importance (i.e., life and death) of the outcome variable.
-----Rosenthal, R. (1990). How are we doing in soft psychology? American Psychologist, 45, 775-777.
2. Difficulty of impacting the outcome variable.
-----Prentice, D.A., & Miller, D.T. (1992). When small effects are impressive. Psychological Bulletin, 112, 160-164.
3. Cumulativity (i.e., small effects repeated frequently over time producing big effects).
-----Abelson, R.P. (1985). A variance explanation paradox: When a little is a lot. Psychological Bulletin, 97, 129-133.
4. When a behavior has multiple determinants, the impact of any one predictor is limited.
-----Ahadi, S., & Diener, E. (1989). Multiple determinants and effect size. Journal of Personality and Social Psychology, 56, 398-406.
-----Strube, M. J. (1991). Multiple determinants and effect size: A more general method of discourse. Journal of Pers. and Social Psych., 61, 1024-1027.

Secondary Data Analysis U. of Michigan (ICPSR) archive of datasets

Andersen, J., Prause, J., & Silver, R. C. (2011). A step-by-step guide to using secondary data for psychological research. Social and Personality Psychology Compass, 5, 56-75 (abstract).

Trzesniewsk, K. , Donnellan, M. B., & Lucas, R. E. (Eds.) (2010). Secondary data analysis: An introduction for psychologists. Washington, DC: American Psychological Association (publisher page).
Dr. Reifman's Other Website Compilations Summer statistics/methodology workshops around the world
Questionnaire instruments (personality traits, social behavior) in the public domain

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