Statistics Tutorials and Resources

Methods of Psychological Research

On Being a Scientists: Responsible Conduct in Research

Research Design Explained

Meta-Analysis Statistical Procedure

Inferential Statistics

Introduction to Descriptive Statistics

Psychological Research on the Net

Symbols in Statistics

Hyperstat Online Textbook:

1. Introduction to Statistics
2. Describing Univariate Data
3. Describing Bivariate Data
4. Introduction to Probability
5. Normal Distribution
6. Sampling Distributions
7. Point Estimation
8. Confidence Intervals
9. The Logic of Hypothesis Testing
10. Testing Hypotheses with Standard Errors
11. Power
12. Introduction to Between-Subjects ANOVA
13. Factorial Between-Subjects ANOVA
14. Within-Subjects/Repeated Measures ANOVA
15. Prediction
16. Chi Square
17. Distribution-Free Tests
18. Measuring Effect Size

Choosing the Right Tests

• StatiBot
• Selecting Statistics
• Intuitive Biostatistics: Choosing a Statistical Test.

Calculators, Plotters, Function Integrators, and Interactive Programming Environments

• The WebMath page
• Scientific Calculator (numeric expression evaluator)
• Expression Evaluator
• Visible Memory Kalculato
• Evaluates various sums, cross-products, and other "building block" expressions that arise in statistical formulas
• MathServe Calculus Toolki
• A simple 5-function calculator, with memory
• Calculator and function plotter
• Plot parametric curves
• Three-dimensional spinning plotter
• Indefinite Integrals -- using the Mathematica engine
• Rweb
• SHAZAM econometricians software
• Run arbitrary Xlisp-Stat expressions
• Mx  -- a matrix algebra interpreter and numerical optimizer for exploration of matrix algebra.

Probability Distribution Functions: Tables, Graphs, Random Number Generators

• Distribution/density calculators, plotters and random number generators
• Calculate and plot probability distributions, cumulative PDF, survivor, hazard, tail areas
• Calculate tail areas and left-integrals
• Tables for 16 continuous and discreet distribution functions

Compute probabilities for the four most common probability distributions

• Normal, t, Chi-Square, and Binomial (density and cumulative) probabilities
• Normal, t, F, Chi-Square, Binomial, and Uniform probabilities and inverses
• Normal, t, Chi-Square, Binomial; Random Digits, Number Needed to Treat
• Central and tail areas for Normal, Student, F, Chi-Square, Binomial, and Poisson distributions
• Statistical probability distribution functions: Normal, Student t, Chi-Square, Fisher F
• Reverse computations

Compute probabilities for a specific distributions

• Normal distribution areas, with nice graphical interpretations
• A very attractive page for Normal distribution (and inverse), with detailed explanations
• Normal area (1-tailed)
• Chi-Square probabilities, and reverse, with a detailed explanation
• Chi Square probabilities and reverse
• Chi-Square Distribution
• Chi-Square Distribution
• Student t Distribution
• Studentized Range
• Probabilities for the Fisher F distribution
• Binomial probability calculator
• Binomial Approximation of the Normal Distribution
• Cumulative frequency for the Binomial distribution
• Probabilities for Gamma, complete Beta, and Incomplete Beta distributions
• Multinomial DistributionNormal Curve
• Critical Values for: Student t, Fisher F, Studentized Range Statistic and Dunnett's Test, Chi-Square, Binomial Test, Wilcoxon Ranked-Sums Test, Wilcoxon Signed Ranks Test, and Correlation Coefficient
• Converting r to Z
• Statistical Power of: Z Test, t-Test for One Sample or Two Related Samples, t-Test for Two Independent Samples, Analysis of Variance, and Correlation Coefficient
• Required Sample Size for various tests

Random Number Generators

• Distribution/density calculators, plotters and random number generators
• Normal, Student t, Chi-Square, Binomial, Random Digits
• Random integers
• Random fractional numbers
• Random Permutations
• Another random permutation generator
• Research Randomizer
• Block Randomizer

• Basic descriptive statistics
• Histogram from a set of numbers
• Histogram
• Point Pattern Analysis
• Draw a scattergram from {x,y} data
• Draw a 3-dimensional scattergram from {x,y,z} data
• Generate a VRML file to view 3-dimensional (x,y,z) data.
• Compute and plot a Kernel Density Estimate
• Compute Poisson change-point
• Boxplot
• Parallel Boxplot
• Q-Q Plot
• Plot up to 10 x,y data points

Confidence Intervals, Single-Population Tests, Measurement Errors

• Confidence Intervals...
  • for the difference between two means, given N, mean, SD for each group
  • Exact C.I.'s for Binomial (observed proportion) and Poisson (observed count)
  • 95% C.I. around an observed proportion
  • Bayesian "credible" intervals around an observed proportion.
  • 95% or 99% C.I. for proportions for any specified sample size and population size
  • 95% C.I. around an observed sample mean
• Single-Population Tests...
  • Test a sample proportion against a postulated population proportion
  • Mean, SD, confidence interval, etc. for a set of values
  • Student t-test of a single mean (vs specified value) from N, mean, SD
  • Another Student t-test of a single mean (vs specified value) from N, mean, SD
  • Similar test of single mean vs 0 (equivalent to a paired Student t) from N, mean, SD
  • Test observed vs. expected rates of occurrence of events
  • Similar to above, but used to study the distribution of accidents and events at the individual level
  • Exact confidence intervals around a rate-ratio
  • Test observed vs expected proportions
  • Binomial Test
• Chi-Square "Goodness of Fit" test for observed vs expected counts
  • Chi Square test
  • Chi-Square test
  • Chi-Square test
  • Chi-Square test (for up to 8 categories)
• Measurement Errors and Error Propagation...
  • Calculate how the standard error of one or two variables propagates through any function of those variables

Sample Comparisons: t-Tests, ANOVAs, Non-parametric Comparisons

• Student t-test (for comparing two samples)...
  • a very general Student t-test web page
  • t-test, paired or unpaired
  • t-test, paired or unpaired
  • t-test, paired or unpaired  
  • t-test, paired
  • t-test, unpaired (tests for equality of variances, and performs both the equal-variance and unequal-variance t-test)
  • t-test, Unpaired  
  • A general 2-sample comparison calculator, for paired, unpaired, equal-variance
  • Unpaired t-test from summary data (N, mean, SD)  
  • Another Unpaired t-test from summary data
  • Very general t-test program for comparing measured quantities, observed counts, and proportions between two unpaired samples 
  • Test differences between two observed proportions
• ANOVA (Analysis of Variance)
  • Factorial ANOVA for uncorrelated samples
    • One-way factorial ANOVA, with graphical output
    • One-way factorial ANOVA for 3 Independent Samples  
    • One-way factorial ANOVA for 4 Independent Samples  
    • One-way factorial ANOVA from summary data (N, mean, and SD or SEM)  
    • Another 1-way factorial ANOVA from summary data
    • Two-way factorial ANOVA for 2 rows by 2 columns  
    • Two-way factorial ANOVA for 2 rows by 3 columns  
    • Two-way factorial ANOVA for 2 rows by 2 columns, from summary data (N, mean, SD)  
    • Very general n-way factorial ANOVA
  • Repeated-Measures ANOVA for correlated samples.
    • One-way repeated-measures ANOVA for 3 correlated samples  
    • One-way repeated-measures ANOVA for 4 correlated samples  
  • Post-Tests
  • Tukey LSD (Least Significant Difference)
  • Scheffe Least Significant Difference
• Non-parametric tests (use these when the data is not normally distributed)...
  • Sign test for matched pairs
  • Median test for unmatched pairs
  • Wilcoxon Signed-Ranks test for matched pairs
  • Another Wilcoxon Signed-Ranks test for matched pairs
  • Wilcoxon Sum-of-Ranks (Mann-Whitney) test for comparing two unmatched samples
  • Kruskal-Wallis test (non-parametric ANOVA) for 2 or more groups of unpaired data
  • Least Significant Difference between mean ranks
  • Two-group ordinal comparisons to assess how probable it is that the two groups come from a single ordering, using Wald-Wolfowitz, Randomness Test, Mann-Whitney, and Kolmogorov-Smirnov  
  • Two-group paired comparisons, using T-test, Wilcoxon, Signs test, and McNemar test  
  • McNemar's test for the paired comparison of proportions (or for matched pairs of labels)
• Comparison of proportions between two groups...
  • Comparison of Binomial proportions
  • Significance Test of Proportions
• Sequential Analysis
  • by Paired Preferences
  • by Paired Differences

  Sample Size and Confidence Interval Calculator

Contingency Tables, Cross-tabs, Chi-Square Tests

• Chi-Square tests...
  • for 2-by-2 table  
  • 2-by-2 table analysis
  • 2-by-2 table analysis
  • for 2-by-2 table, with odds ratio, relative risk, etc. with confidence intervals
  • for 2-by-N table
  • for table up to about 30 cells
  • for up to 10-by-10 tables. 
  • for any-size table
  • another for any-size table
  • another for any-size table
  • Exhaustive analysis of 2-by-2 tables
• Three-dimensional Tables (2x2x2)...
  • Three-dimensional 2x2x2 table
  • Log-Linear Analysis for a 2x2x2 Table of Cross-Categorized Frequency Data   
• Fisher Exact tests for contingency tables...
  • Fisher exact (2x2)
  • Fisher exact (2x2)  
  • Fisher exact (2x2)  
  • Fisher Exact, with good Help discussion  
  • Fisher Exact (2x5)  
• Exact unconditional homogeneity/independence tests for 2-by-2 tables
  Contingency table for sequenced categories (Ordinal by Ordinal, 5-by-5 table or less)  
• Contingency table for sequenced categories, 5-by-2 table, with exact probability calculations  
• Spearman's correlation from cross-tabbed data with sequenced row and column categories
• McNemar's test for paired contingency tables
• Comparison of ratings or rankings by different raters...
  • Friedman test for comparing rankings (Ordinal by Nominal)
  • Cohen's Kappa 
  • Cohen's Kappa
  • Cohen's Kappa
  • Kappa for nominal data as concordance between multiple raters
  • Intraclass correlation for concordance between multiple raters
• Chi-Square test for equality of distributions
• Chi-Square "Goodness of Fit" test for observed vs expected counts
  • Chi Square test
  • Chi-Square test
  • Chi-Square test
  • Chi-Square test (for up to 8 categories)  
  • Chi-Square test for up to 10 categories.  

Regression, Correlation, Least Squares Curve-fitting, Non-parametric Correlation

• Straight Lines and Correlation Coefficients...
  • Least squares regression line and Pearson correlation coefficient.  
  • Variations on straight-line fitting, when X and Y have error
  • Least squares regression. (nice interface)
  • Linear correlation and regression (nicely designed)  
  • Draw a scatterplot, and compute various statistics
  • Correlation and regression calculator
  • The Data Applet
  • Least squares straight line
  • Least squares straight line, also creates a high-quality Postscript graph of your data and the fitted line
  • Least squares straight line, allows several common types of y-value weighting (constant, proportional, or Poisson errors); also allows you to recall recently-entered data (for a limited time)
  • Calculate partial correlation coefficients
  • WebStat (an integrated   applet) can perform simple regression analysis
• Correlation Tests.
  • Spearman's rank correlation (non-parametric)...
    • Spearman
    • Spearman  
    • Spearman   (newer version here)
    • Spearman's correlation from cross-tabbed data with sequenced row and column categories
  • Correlation test
  • Significance level corresponding to a correlation coefficient
  • Minimum significant correlation coefficient for a given sample size
  • Comparison of two correlation coefficients
  • Comparison of two or more correlation coefficients
  • Comparison of two sets of (X,Y) data to see if they are consistent with the same straight line
  • Biserial and point-biserial correlation analysis
  • Biserial correlation coefficient from summary data
  • Point-biserial correlation analysis
  • Manipulation of a correlation matrix

  Beyond Simple 2-parameter Curve-fitting...

  • Very general non-linear least squares curve-fitter
  • Linear, parabolic, or cubic fit, with graphics   (newer version here)
  • Multivariate linear or univariate polynomial regression, with graphical output.
  • Univariate and multiple regression, with very extensive graphical output (histograms, scatterplots, scatterplot matrices) and residual analysis (QQ, histogram, residuals vs dependent or predictors). 
  • Multiple regression, if you already have the correlation coefficient matrix between all independent and dependent variables...
    • for 2 independent variables  
    • for 3 independent variables  
    • for 4 independent variables  
  • Fit any of five families of curves (linear, polynomial, exponential, descending exponential, Gaussian) and draw a graph  
  • Curve fitting, smoothing, parameter estimating, data correlating and forecasting utility  
  • Logistic Regression 
  • Regression and GLM Calculator
  • Cox Proportional Hazards Survival Regression Analysis  
  • A faster version of Cox Proportional Hazards Analysis  
  • Regression by Prevalence
  • Test Bias Assessment Program

Analysis of Survival Data

• Cox Proportional Hazards Survival Regression Analysis  
• A faster version of Cox Proportional Hazards Analysis  
• Comparison of Two Survival Distributions

Bayesian Methods

• Bayes' theorem calculations
• Bayesian calculations for diagnostic tests
• Sequential Experimental Design for testing the probability ratios  
• 2-by-2 table analysis (Chi-Square, sensitivity, odds ratio, relative risk, etc. with confidence intervals  
• for 2-by-2 table, with odds ratio, relative risk, etc. with confidence intervals 
• Wald's Sequential Probability Ratios

Other Statistical Tests and Analyses

• Bonferroni adjustment of critical p-values when performing multiple comparisons (has an excellent discussion of this topic)
• Detect Outliers
• Selection Bias Calculator for Prevalence Estimates  
• Clustering Calculator generates tree structures of data clustering, and much more  
• Misclassification Bias in Prevalence Studies  
• Selection Bias in Case-control Studies  
• A Web-Based SAS Code Developer for Experimental Designs

Specialized and Discipline-Specific Tests and Analyses

Martindale's Reference Desk -  Calculators On-Line - Statistics 

• Biostatistical Calculators...
  • Number Needed to Treat
  • Number Needed to Treat
  • Clinical Significance Calculator
  • Thorough analysis of 2-by-2 table relevant to Predictions and Diagnostic Tests
  • Calculation of posttest probability from Likelihood Ratio and pretest probability
  • Conversion of Sensitivity and Specificity to Likelihood Ratios
  • Calculator to predict the probability of a successful outcome to lumbar disc surgery
  • LODS - Logistic Organ Dysfunction System calculator  
  • APACHE-II Score for acute physiology and chronic health evaluation  
  • Calculators for Clinical Formulas -- A-a Gradient, Anion Gap, Body Surface Area, Body Mass Index, Estimated Creatinine Clearance, Fractional Excretion of Sodium, Heart Disease Risk, Ingested Substance Blood Level, Pregnancy Due Date , Serum Osmolality , and Weights and Measures (converts lbs. to kgs. and F to C)
• Disparate Impact Analysis
• Item Analysis -- for multiple choice questionnaires
• Theoretical Expectancy Calculator
• Investment Derivative Calculations

Power, Sample Size and Experimental Design Calculations

• Comparing a mean to a specified value   (also available at another website)
• Power or sample size for one-group comparison, when you can assume that the values come from a normal distribution.
• Comparing a proportion to a specified value
• Comparing a proportion to a specified value   (also available at another website)
• Sample size needed for a given confidence and a given maximum allowable deviation, for means, proportions, and totals
• Comparing on observed number of occurrences to a specified rate of occurrence
• Sample size and 95% confidence interval for a variable, knowing the population standard deviation
• Sample size required for specified precision of a proportion
• Another sample-size for specified precision of a proportion
• Another sample-size / confidence interval calculator for proportions in finite samples
• Power vs sample size for survey questionnaire results, with graphical output
  • Same-size samples   (also available at another website)
  • Equal- or unequal-size samples
  • Same-size samples; equal or unequal variances  
  • Power or sample size for equal-variance two-group tests, when the values come from a normal distribution
  • Power or sample size for unequal-variance two-group tests, when the values come from a normal distribution
• Difference between two proportions...
  • Equal sample sizes (easy to use; with a good explanation)
  • Equal- or unequal-size samples  
  • Equal- or unequal-size samples
  • T independent samples   (also available at another website)
• Difference between two rates of occurrence of events
• Survival outcome analysis
• Sample size needed for comparison of 2 or more groups
• Sample size computation for multiple comparisons 
  • One-way ANOVA
  • Two-sample pooled t test
  • One-way ANOVA
  • Randomized complete-block design (one factor)
  • Latin square design
  • -way ANOV>
  • Nested-factorial design
  • Crossover design

  Professional Organizations

  
  The American Association for the Advancement of Science

  Home page for AAAS. Information on membership, sections, science policy, and their flagship journal, Science.

  American Mathematical Society

  American Mathematical Society's home page. Gives info on membership, activities, and other useful things like employment opportunities and a preprint server.

  American Society for Quality (formerly American Society for Quality Control)

  Offers information for those interested in quality issues. Site includes links for membership, calendar, a quality glossary, and information on Standards and Certification.

  American Statistical Association

  A very active professional organization for statisticians, ASA now has a home page. They have info on membership, upcoming events, publications, meetings, etc.

  The Bernoulli Society for Mathematical Statistics and Probability

  The Bernoulli Society is a section of the International Statistical Institute focusing on probability and mathematical statistics. Links to membership info and meetings.

  Classification Society of North America

  The Classification Society of North America (CSNA) is a nonprofit interdisciplinary organization whose purposes are to promote the scientific study of classification and clustering (including systematic methods of creating classifications from data), and to disseminate scientific and educational information related to its fields of interests.

  Institute of Mathematical Statistics

  This is the IMS homepage. Contains info on membership, publications, meetings, etc. Also contains a list of statistics links.

  Royal Statistical Society

  RSS home page. Includes links to RSS news, conferences, membership info, committees, etc. Also includes a link to the RSS Centre for Statistical Education.

  Society for Industrial and Applied Mathematics

  SIAM home page. Includes the standard links to membership info, conferences, publications, and career information (nice because it allows online browsing of job listings from their newsletter, SIAM News). Also some links to other math sites. The home page is graphics intensive, so be prepared to wait if using a slow Internet connection. (This is true only for the main home page--other pages at this site seem to be mostly text and transfer pretty quickly.)

  Statistical Society of Canada

  SSC home page. Includes links to membership lists, by-laws, meetings, and their journal, Canadian Journal of Statistics

  SOFTWARE

  PC-Size: Consultant (sample size calculations)

  Logistic regression for Epi Info

  Logistic regression for SYSTAT (includes ASCII to SYSTAT conversion program)

  Miscellaneous statistical procedures for SYSTAT (normality, unimodality, two-phase regression, Johnson-Neyman ANCOVA, Alternating Conditional Expectations, incomplete paired data, dependent correlations, ...)

  Exact randomization tests for SYSTAT (includes ASCII to SYSTAT conversion program)

  The Statistician's Swiss Army Knife (probability distributions (normal, t, chi-square, F, binomial, Poisson, studentized range); exact confidence intervals for binomial p's; Fisher's exact test for 2 by 2 tables; exact confidence intervals for an odds ratio from a 2 by 2 table; Mantel-Haenszel test and approximate 95% confidence interval for the common odds ratio; Bartholomew's test for increasing proportions; Bartholomew's test for increasing normal means; one and two sample t-tests from summary statistics; correlation coefficients: test that a population value is 0, confidence interval for a single coefficient, test of equality of two independent coefficients, test of equality of two coefficients from the same correlation matrix)

  A version of James Steiger's MULTICORR program that operates directly on SYSTAT system files. MULTICORR tests hypotheses about the elements of a correlation matrix. A complete description can be found at Steiger's website http://www.interchg.ubc.ca/steiger/multi.htm. Professor Steiger has made his source code publicly available, allowing me to attach a SYSTAT-like front end and let the program operate directly on SYSTAT data files. This version and Steiger's should give identical results.

  PCT--the routine SYSTAT forgot--for calculating distribution percentiles. PCT is a stand-alone program that operates directly on SYSTAT system files. It includes all 5 definitions of percentiles found in SAS's PROC UNIVARIATE. The download is a self-extracting ARC file that contains the DOS-like executable and a documentation file. I wrote this program in 1993 after a long delay and with some reluctance because I expected SYSTAT to make it obsolete with each update to the software. Yet, it's still useful today!

  MISC. LINKS

  Bible Keeper - Online Bible Study Tools  BibleKeeper.com is a free online database of the Bible in several languages and also Bible study tools.

  Continuing Education: A directory of continuing education on-campus and online degree programs organized by area of study and geographical location.

  Translation services by freelance translators - network of professional translators offering technical and commercial translation services in English, French, Spanish, Dutch, Italian, German.

  Information Services -- Research the Way You Want It. Information Brokers provide research, database searching, online research, data retrieval, information gathering. Information providers supplying answers & solutions.

  Advice Monkey: Medical malpractice information and medical malpractice lawyers.

  Directory of Online Distance Learning programs and schools offering accredited bachelors, masters and doctoral degrees in business, computer science, engineering and nursing.

  The College Loan TheCollegeLoan.org was created to guide students, parents, and graduates with the difficulties of the college loan.

  Online directory of bachelors, masters and doctoral degree schools offering programs in animation, design, business, technology, health care nursing, criminal justice and education.

  State-by-state directory of computer schools and colleges providing courses in computer science, computer programming, computer networking, computer graphics, engineering and technology.

  Directory of computer certification schools offering technical certifications: MCSE, MCSA, A+, MCP, Cisco, Microsoft, Novell and Oracle.

  MathJobs.com Banking, Insurance, Finance, Statistics, Biology, Medicine, Academic, Teaching, General Management, IT, Technology.

  Education Online Search - Great information resource for US and Canadian colleges and
  universities

  Photography Schools - Free information on US and Canadian Photography Schools

  Culinary Schools - Free information on US and Canadian Culinary Schools

  Distance Learning -- World Wide Learn is the directory of online courses, accredited online degrees, distance learning, online training, and online education.

  Interior Design Schools - Free information on US and Canadian Interior Design Schools

  Higher education degree programs offered online via the Internet by online higher education institutions.

  MCSE certification programs for aspiring IT professionals.

  Career Education for aspiring career professionals.

  Vocational Schools offering vocational training and career degree programs.

  Distance Learning for working professionals needing a distance learning education.

  University of Phoenix website offering University of Phoenix adult education information.

  Fashion Design Schools - Free information on US and Canadian Fashion Design Schools

  www.smartdegrees.com -- Online and Campus College Degree Programs

  www.meriteducation.com provides a large selection of accredited and reputable career training schools, colleges and institutions offering online training programs, accredited degree programs, continuing education courses, and wide variety of e-learning and distance learning resources.

  www.career-training-education.com -- Browse an extensive directory of career training and career education schools offering adult education, vocational, job-specific and academic degree programs in an assortment of career fields.

  www.computercolleges.info -- Our website provides a complete directory of computer colleges offering professional and degree programs in computer animation, computer graphics, computer programming, computer science, computer engineering, computer networking and computer games. We also offer a large selection of online computer colleges to choose from.

  www.online-degree-programs.info - Online degree programs, schools, class and courses presented by subject and level.

  EMR Software for Electronic Medical Records: Misys Electronic Medical Records (EMR) and Healthcare Systems is the leading provider of electronic medical records (EMR) and healthcare software and information systems to physician organizations worldwide.

  Healthcare Software: Misys Healthcare Systems offers Misys EMR, a customizable, modular product including Orders Management, Transcription Assistant, Chart Entry/Summary, Charge Passing, Messaging, Security and Portable Pen Units for documentation at the point-of-care.

  Online Education degrees designed for career professionals seeking online education. Online Degrees designed to be completed 100% online. Computer schools offering computer training for aspiring computer professionals.

  Higher education degree programs offered online via the Internet by online higher education institutions.

  MCSE certification programs for aspiring IT professionals.

  Career Education for aspiring career professionals.

  Vocational Schools offering vocational training and career degree programs.

  Distance Learning for working professionals needing a distance learning education.

  University of Phoenix website offering University of Phoenix adult education information.

  Georgia DUI Attorney: Michael Hawkins. Experienced DUI attorneys in Atlanta, Georgia.

  Georgia Criminal Lawyer: Atlanta, Georgia criminal lawyer and former Federal Prosecutor, Howard J. Weintraub.

  Fellowship of the Metroplex - Arlington, Texas. The church meeting the needs of real people in a real world. Bible-based, contemporary, casual.

  Florida DUI Attorney: Andrew Parks. Miami, Florida experienced DUI lawyers.

  Data Recovery - DataLeach hard disk drive recovery service recovers lost data from damaged drives and storage devices.

  Florida DUI Lawyer: Michael Braxton. Miami, Florida experienced DUI lawyers.

  Florida Speeding Ticket DUI Lawyer: South Florida attorney specializing in defending against speeding ticket violations.

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