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There are a bewildering number of statistical analyses out there, and choosing the right one for a particular set of data can be a daunting task. Here are some web pages that can help:

  1. Statistical Decision Tree, from the developers of the MicrOsiris package. This is an interactive set of web pages to help you select the right kind of analysis to perform on your data. It asks you a simple series of questions about your data (how many variables, etc.), then makes recommendations about the best test to perform.
  2. Choosing a Statistical Test, Chapter 37 of Dr. Harvey Motulsky's book Intuitive Biotatistics.
  3. "Selecting Statistics", by Bill Trochim (Cornell). Another  interactive set of web pages to help you select the right kind of analysis to perform on your data.




"Online Software Package" web sites

As you can see from looking at the web site, there are many "stand-alone" web pages that are each designed to perform only a single test or calculation. In addition, some talented individuals and groups have created coherent website that perform an entire suite of calculations, with a logical organization and consistent user interface. Each of these web sites is really a fairly complete online statistical software package in itself. Here are some of these "comprehensive" statistical analysis web sites:

  • OpenEpi Version 2.2 -- OpenEpi is a free, web-based, open source, operating-system-independent series of programs for use in public health and medicine, providing a number of epidemiologic and statistical tools. Version 2 (4/25/2007) has a new interface that presents results without using pop-up windows, and has better installation methods so that it can be run without an internet connection. Version 2.2 (2007/11/09) lets users run the software in English, French, Spanish, or Italian.
  • SOCR -- Statistics Online Computational Resource. A very comprehensive collection of online calculators and other interactive resources, including: Distributions (interactive graphs and calculators), Experiments (virtual computer-generated analogs of popular games and processes), Analyses (collection of common web-accessible tools for statistical data analysis), Games (interfaces and simulations to real-life processes), Modeler (tools for distribution, polynomial and spectral model-fitting and simulation), Graphs, Plots and Charts (comprehensive web-based tools for exploratory data analysis), Additional Tools (other statistical tools and resources), SOCR Wiki (collaborative Wiki resource), Educational Materials and Hands-on Activities (varieties of SOCR educational materials), SOCR Statistical Consulting and Statistical Computing Libraries.
  • ProtoGenie -- a free extensible web-based environment for research design and data collection for surveys, experiments, clinical trials, time series, cognitive and vision research, and methods courses. Lets you specify groups and define measurement and treatment events and their sequencing. The goal is to let users move smoothly from research design and data collection to interim and final statistical analysis.
  • Statlets -- an "online statistical computing center" providing access to over 50 applets in which you can enter data, compute statistics, create tables and graphs, and print out the results. Provides basic plotting, probability distributions, summary statistics, one-sample analysis, time-series analysis, two-sample comparisons, regression analysis, attribute estimates, ANOVAs, and Statistical Process Control. This public version supports up to 50 rows and 8 columns of data. For larger data sets, a single-user copy or a corporate deployment license can be purchased.
  • The Calcugator -- a calculator, plotting engine, and programming environment. Also available as a free stand-alone downloadable program. Simple to use; rivals programs like MATLAB, with 200 functions/operators to perform real, integer, rational, complex, boolean, statistical, vector, array and matrix computations. Both the input and output of the program are displayed on standard windows which can be further edited, saved, merged, print-previewed and printed. Allows rapid creation of 2D and 3D plots of functions, polar and parametric displays, bar, pie, pareto and xy charts. All plots can be configured using the mouse (zooming, panning, selecting). Titles and labels are supported, and all figures created by the Calcugator can be exported into popular file formats or pasted into an editable window. As a programming environment it has a simple and compact language with identical syntax to Java/C/C++, and allows user-defined functions.
  • SISA (Simple Interactive Statistical Analysis) -- SISA allows you to do statistical analysis directly on the Internet. Click on one of the procedure names below, fill in the form, click the button, and the analysis will take place on the spot. Study the user friendly guides to statistical procedures to see what procedure is appropriate for your problem.
  • The WebMath page performs a large number of numeric calculations and symbolic algebraic manipulations of the type that might arise in high school / college algebra and calculus, including some elementary statistical calculations. In doing so, it provides a detailed step-by-step explanation of how it arrived at the answer.




Calculators, Plotters, Function Integrators, and Interactive Programming Environments...

  • Expression Evaluators -- type in any numeric expression; the computer will evaluate it and display the results...
  • Calculators -- pages that look and act like a pocket calculator...
  • Plotters -- type in any algebraic function; it displays the graph...
    • Function plotter -- Lets you zoom in and out to view any portion of the graph. (Needs Java.)
    • Function plotter -- Produces a small 3D plot of almost any function or relation found in high school and undergraduate college mathematics. Plots functions of the form y = f(x), such as y = x2 or y = 3x + 1, or relations of the form f(x,y) = g(x,y), such as x2 + y2 = 4. (No Java needed.)
    • Linear Programming Grapher-- Enter a linear function of two variables to be minimized, and any number of linear inequality expressions, and the page will instantly solve it and display a graph showing the feasible region and the constraints.
    • Simplex Tool -- Similar to the Linear Programming Grapher, but works with functions of more than two variables, and doesn't graph the results.
  • Integrators -- type in any function; the computer displays the indefinite integral function (if one exists) and/or the value of the definite integral (area under the curve) between two endpoints...
  • Interactive Programming Environments -- These pages implement various mathematical programming languages. You can enter commands or entire programs (type or copy/paste) into the web page, and they will be executed immediately.
    • Rweb -- an interactive web-based interface to the "R" statistical programming language (similar to S or S-plus)
    • SHAZAM -- a programming environment for econometricians, statisticians, and others who use statistical techniques. Its primary strength is estimating and testing many types of regression models. Provides a flexible command language and capabilities for programming procedures. Has an interface to the GNUPLOT package for high quality graphics.
    • Mx  -- a matrix algebra interpreter and numerical optimizer for exploration of matrix algebra. Many built-in fit fuctions for structural equation modeling and other statistical modeling. Has fitting fuctions like those in LISREL, LISCOMP, EQS and CALIS, along with facilities for maximum likelihood estimation of parameters from missing data structures, under normal theory. Users can easily specify complex 'nonstandard' models, define their own fit functions, and perform optimization subject to linear and nonlinear equality or boundary constraints.




Probability Distribution Functions: Tables, Graphs, Random Number Generators...




Descriptive Statistics, Histograms, Charts...




Confidence Intervals, Single-Population Tests, Measurement Errors...




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




Contingency Tables, Cross-tabs, Chi-Square Tests...




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




Analysis of Survival Data...

  • Kaplan-Meier Survival Plot (with 95% Conf.Intervals) and LogRank Test -- Type or copy/paste data, or read it in from a file. Prepares  tables, graphs, and statistical comparison output. Can perform stratified log-rank test.
  • Life Table (Kaplan-Meier) -- Enter the number died and censored at each time period, and the page calculates the cumulative survival probability and 95% confidence intervals. Also graphs the survival curve, and exports the data, so you can create a better graph using another program.
  • Cox Proportional Hazards Survival Regression Analysis -- specify each subject's observation time and status (last seen alive or dead), and any number of independent variables (predictors, confounders, and other covariates). This web page will perform a proportional-hazards regression analysis and return the regression coefficients, their standard errors, hazard (risk) ratio, and their confidence intervals, and the baseline survivor curve, along with goodness-of-fit information. You can also use a faster version by Ronald Brand (Leiden University), or an enhanced version by Kevin Sullivan (Emory University) that has illustrative examples and explanatory material.
  • Comparison of Two Survival Distributions, using data from a data file in your computer (many different file types are supported). A graph is returned to your browser with the two survival curves plotted, along with the estimated relative risk, standard error and p-value.




Bayesian Methods...




Other Statistical Tests and Analyses... 

  • ReliCheck -- an online reliability analysis tool that allows users to check the reliability of the scores on their survey. The free option provides reliability score, statistical strength of survey, general item analysis, and a statistical summary of the survey. Pay-for plans also provide an auto-optimizer, optimization comparison, manual optimizer, and control of survey analysis.
  • Queueing Theory Calculator -- Performs classic calculations for single-server or multi-server queues (queue length, waiting time, etc.).
  • Universal Inventory/Test Scorer will instantly and automatically score ANY objective  test or personality inventory/questionnaire. For any particular questionnaire, you create a text file that describes the scores associated with each possible answer to each question (True/False, A/B/C/D/E, Likert Scale, etc.). It is available as a Java implementation and as JavaScript implementation. These will run online, or can be downloaded to be run locally on your computer (offline from the Internet). 
  • Interactive Cross-Validation -- Performs the "leave-one-out" cross-validation inference for: central tendency, least-squares lines, one-dimensional multinomial tables, two-dimensional contingency tables with structural zeroes, k-sample problems, and block-and-treatment designs. The web page is well-documented, with about a dozen examples worked out and explained.
  • Fittestmodel --an online forum, on which statistical evidence can be presented that is always replicable, testable and extendible at the 'click of a button'. The name Fittestmodel encompasses both the goal and the means of science, namely to find the fittestmodel by fitting, testing and modelling. Users may discuss statistical evidence online or query for results based on search criteria such as dataseries, methods or criteria that measure the 'quality' of results. Publicly available datasets from various sources may be combined into new statistical evidence and statistical techniques will be added on a continuous basis, by user request or otherwise.
  • Bonferroni adjustment of critical p-values when performing multiple comparisons (has an excellent discussion of this topic)
  • Multiple comparisons correction (Bonferroni adjustment)
  • Number Needed to Treat, based on a 2-by-2 table
  • Detect Outliers -- this calculator performs Grubbs' test, also called the ESD method (extreme studentized deviate), to determine whether one of the values in the list you enter is a signficant outlier from the rest.
  • Selection Bias Calculator for Prevalence Estimates
  • Calculate and plot an ROC Curve (for grouped predictor data)
  • Clustering Calculator generates tree structures of data clustering, and much more
  • Misclassification Bias in Prevalence Studies
  • Predictive Value from Sensitivity, Specificity and Prevalence, (when analyzing a clinical test), with a nice explanation
  • Selection Bias in Case-control Studies
  • NetMul: a browser interface to a program that performs:
    • Principal Coordinate Analysis (PCO)
    • co-inertia analysis
    • discriminant analysis and within- or between-class analyses
    • analyses on distance matrices or neighboring graphs.
  • Simultaneous Equations and Matrix Inversion -- up to 10 equations (or 10x10 matrix).
  • Linear Optimization with Tools for Sensitivity Regions -- This page finds the optimal solution, and does a post-optimality analysis of small-size linear programming problems (constrained optimization).




Specialized and Discipline-Specific Tests and Analyses...




Check out the very general and elegant power/sample-size calculator by Russel Lenth (U of Iowa). It handles tests of means (one or two samples), tests of proportions (one or two samples), linear regression, generic chi-square and Poisson tests, and an amazing variety of ANOVAs -- 1-, 2-, and 3-way; randomized complete-block; Latin and Greco-Latin squares; 1-stage, 2-stage, and factorial nested designs; crossover; split-plot; strip-plot; and more! This calculator is implemented in Java, and can be run as a web page, or can be downloaded to your computer to run offline as a stand-alone application.

Here's a collection of online power calculator web pages for specific kinds of tests: