**Web Pages that Perform Statistical
Calculations**

Calculators, plotters, function integrators, and interactive programming environments

Probability distribution functions: tables, graphs, random number generators

Descriptive statistics, histograms, chartsSample comparisons: t-tests, ANOVAs, non-parametric comparisons

Contingency tables, cross-tabs, Chi-Square testsRegression, correlation, least squares curve-fitting, non-parametric correlation

**Other Statistical Resources...**

- Online statistics textbooks, reference manuals, and journals
- Interactive statistical demonstrations and tutorials
- Links to other statistics-related pages
- About this Project

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:

- "Selecting Statistics", by Bill Trochim (Cornell). 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.
*Choosing a Statistical Test*, Chapter 37 of Dr. Harvey Motulsky's book*Intuitive Biotatistics*.- The very extensive test-selection routine used in Dr. Robert Knodt's MODSTAT statistical package.

- 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.
- Expression Evaluators -- type in any numeric expression; the
computer will evaluate it and display the results...
- Scientific Calculator (numeric expression evaluator) (JavaScript)
- Expression Evaluator, similar to above, but doesn't require Java or JavaScript capability
- Visible Memory Kalculator -- provides a growing visible memory of all values inputed or computed for use at any time later (just click on it). Can also read text (ascii) files. (Java)
- Evaluates various sums, cross-products, and other "building block" expressions that arise in statistical formulas
- The Vanderbilt MathServe Calculus Toolkit has separate calculating/graphing pages for: Factoring Polynomials, Partial Fractions, Polynomial Equations, Graphs of Functions, Graphs of Equations, Limits, Derivatives, Antiderivatives (Indefinite Integrals), Definite Integrals, Inverse Functions, Newton's Method, Polynomial Interpolation, Sums, Parametric Equations, and Polar Functions
- Inverse Symbolic Calculator -- tells you where a number came from -- you type in 1.55838744, and this program tells you that it's really the square root of 17/7.

- Calculators -- pages that look and act like a pocket calculator...
- Plotters -- type in any algebraic function; it displays the
graph...
- Here's one that requires (Java)
- Calculator and function plotter (Java)
- Here's anone that requires (Java)
- Here's one that plots parametric curves (x and y are both functions of another variable, t), and doesn't require either Java or JavaScript
- Three-dimensional
"spinning" plotter -- enter {x,y,z} data; this page will generate a 3-d
"virtual world" (VRML), with the data as little spheres. You should have Live3D
in Netscape 3.0, or you can save the file and display it with
*vrweb*or*whurlwind*.

- 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...
- Indefinite Integrals -- using the
*Mathematica*engine

- Indefinite Integrals -- using the
- 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.
- Run arbitrary Xlisp-Stat expressions (as long as they do not produce graphical output); with on-line Xlisp manual and reference guide
- 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 Integrals -- these pages take the place of a
handbook of statistical functions. They're arranged with the most
comprehensive,multi-function pages first...
**These pages contain calculations for a very wide assortment of probability distribution functions**, including Normal, Bivariate Normal, Student t, Chi-Square, Fisher F, Bivariate Normal, Noncentral Student t, Non-central Chi-Square, Non-central Fisher F, Poisson, Log-normal, Exponential, Beta, Gamma, Logistic, Binomial, Negative Binomial, Multinomial, Cauchy, Gumbel, Laplace, Pareto, Weibull, Uniform (continuous and discrete), Triangular, Geometric, and Hypergeometric:**These pages each compute probabilities for the four most common probability distributions**:- Normal, t,
Chi-Square, and Binomial (density and cumulative) probabilities; (When you get to the
**Rweb**page, scroll down to the**Analysis Menu**and select**Probability**.) - 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 (Java)
- Statistical probability distribution functions: Normal, Student t, Chi-Square, Fisher F (JavaScript)
- Reverse computations: enter p-value (and, if necessary, sample sizes and/or degrees of freedom); program will compute z, t, F, Chi Square, and correlation coefficient (JavaScript)

- Normal, t,
Chi-Square, and Binomial (density and cumulative) probabilities; (When you get to the
**These pages each compute probabilities for a specific distributions**:- Normal distribution areas, with nice graphical interpretations (Java)
- A very attractive page for Normal distribution (and inverse), with detailed explanations (Java)
- 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 -- the probability of a studentized range being less than or equal to value x with v degrees of freedom from r sample
- Probabilities for the Fisher F distribution
- Binomial probability calculator (JavaScript)
- Binomial Approximation of the Normal Distribution (JavaScript)
- Cumulative frequency for the Binomial distribution
- Probabilities for Gamma, complete Beta, and Incomplete Beta distributions (JavaScript)
- Multinomial Distribution (Java)

- This page contains links to
printable copies (in Adobe Acrobat PDF format) of many statistical tables including
some for which no "calculating pages" are available
- Normal 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 for a large number of distributions
- Normal, Student t, Chi-Square, Binomial, Random Digits (Java)
- Random integers -- generates any number of random integers, uniformly distributed between any two limits
- Random fractional numbers -- generates any number of random numbers, each a fraction between 0 and 1 with 8 digits after the decimal point
- Random Permutations -- generates N sets of random permutations of integers from 1 to M
- Another random permutation generator
- Research Randomizer -- generates one or more sets of random numbers from a specified range, with or without repeats, sorted or unsorted.
- Block Randomizer -- assigns subjects randomly to different groups, with multiple blocking to ensure that imbalances are kept under control if the study is terminated prematurely
- Random
assignment of subjects to one or more groups (Java) -- three
variations:
- generates M groups of N numbers each by distributing the numbers from 1 to M*N randomly into the M groups
- generates M blocks of N numbers each by randomly shuffling the numbers from 1 to N in each block
- generates a subset of N numbers by random selection from a list of the numbers from 1 to M

- Combinatorial Objects Server --
generates an incredible assortment of...
- Permutations and their restrictions
- Subsets or Combinations
- Permutations or Combinations of a Multiset
- Set Partitions
- Numerical Partitions and relatives
- Binary, rooted, free and other trees
- Necklaces, Lyndon words, DeBruijn Sequences
- Irreducible and Primitive Polynomials over GF(2)
- Ideals or Linear Extensions of a Poset
- Spanning Trees and other Subgraphs of a Graph
- Unlabelled Graphs
- Pentomino Puzzles, Polyominoes, n-Queens
- and other puzzles and Miscellanea

- Statiscope -- a beautifully-implemented page for calculating and displaying a large number of descriptive statistics from a set of numbers you enter (Java)
- WebStat (an integrated applet) can generate summary statistics, as well as histograms, stem and leaf plots, boxplots, dotplots, parallel coordinate plots, means plots, scatterplots, QQ plots, and time series plots (Java)
- Descriptive Sampling Statistics -- Enter up to 80 numbers; this page will calculate the mean, variance, SD, CV, skewness and kurtosis. (JavaScript)
- Rweb -
extensive tabular and graphical descriptive summarization: mean, quartiles,
histograms, scatterplot matrices (with smoothers), QQ plots (normal and pairwise), time
series, box plots. (When you get to the
**Rweb**page, scroll down to the**Analysis Menu**and select**Summary**.) - The Data Applet provides descriptive statistics, histograms, boxplots, and scatterplots (Java)
- A variety of descriptive statistics and a stem and leaf display
- Descriptive statistics, stem plot, and histogram
- 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.
- Combine Subgroups -- calculate the mean and SD of a combination of groups from the N, mean and SD of each group.
- Computes summary statistics for one variable, draws a crude histogram, and sorts a list of values. Given pairs of values, it computes the least squares regression line and Pearson correlation coefficient.
- Basic
descriptive statistics (mean, sum of squares, variance, standard deviation, minimum,
25
^{th}percentile, median, 75^{th}percentile, and maximum for up to 500 numbers (Java) - Multinomial Distributions -- Enter up to 12 values and their corresponding probabilities, and this page will calculate Expected Value, Variance, Standard Deviation, & Coefficient of Variation (JavaScript)
- Paired Data Sets Statistics -- Enter up to 28 sample paired data sets, and this page will calculate means, variances, and covariance (JavaScript)
- Histogram -- Enter up to 80 numbers, and this page will display a histogram. (JavaScript)
- Histogram from a set of numbers, lets you dynamically alter the interval width and see the effect immediately (Java)
- Histogram -- type in or upload a data set or give a URL; submit; returns a colored histogram that you can copy from the page; also does polygons and cumulative
- Point Pattern Analysis -- used to describe and help analyze point patterns. It consists of 14 different analysis routines for a variety of basic descriptive statistics: nearest neighbor analysis, K-function, space-time Knox, Join-Count statistics, Global Moran’s I and Geary’s c, general Getis-Ord’s G, local K-function, and more.
- 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. To view the resulting files requires a VRML viewer.
- Compute and plot a Kernel Density Estimate from a set of points, using Epanechnikov, triangular, biweight or Gaussian kernels
- Compute Poisson change-point, that is: estimate when, in a long sequence of occurrences, the occurrence rate underwent a sudden change
- Boxplot -- type in or upload a data set, or give a URL; submit; returns a colored boxplot that you can copy from the page
- Parallel Boxplot -- type in or upload a bivariate data set with a continuous variable and a group indicator; submit; returns a colored parallel boxplots that you can copy from the page
- Q-Q Plot -- type in or upload a data set, or give a URL; submit; returns a colored q-q plot that you can copy from the page
- Plot up to 10 x,y data points (Java)

- 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) (JavaScript) (also available as an Excel spreadsheet)
- 95% C.I. around an observed proportion
- Bayesian "credible" intervals around an observed proportion. Somewhat comparable to the "classic" confidence intervals, but tend to be somewhat narrower.
- 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
- http://department.obg.cuhk.edu.hk/ResearchSupport/Binomial_Test.asp -- whether the number of "successes" differed from what you would have expected, based on the number of trials and the expected probability of success
- 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 (Java)
- 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, based on Poisson distribution; also includes confidence intervals and analysis of rate-ratios (such as Standardized Mortality Ratio, Morbidity Ratio, and Comparative Mortality Figure)
- Similar to above, but used to study the distribution of accidents and events at the individual level
- Exact confidence intervals around a rate-ratio, using Liddell's method (also contains a number of common approximations, for comparison) (JavaScript)
- Test observed vs expected proportions, based on the Binomial distribution
- Binomial Test -- whether the number of "successes" differ from what was expected based on the number of trials and the probability of success.
- Similar to above, but deals with the probability of a particular sample size, given an observed 'x' number positive (or white, or car crashes) vs. an expected 'U' proportion positive
- Runs Test for Randomness -- Enter up to 80 numbers, and this page will calculate a runs test to see if the numbers form a random sequence (JavaScript)
- Analyze observed proportions in samples from finite populations, based on the Hypergeometric distribution
- Test for Normality -- Enter up to 80 numbers, and this page will test for normality based on the Jarque-Bera statistic (JavaScript)

- Chi-Square "Goodness of Fit" test for observed vs expected
counts (NOT from Contingency Tables)...
- Chi Square test -- takes observed values, and expected values that can be specified as expected occurrences, or percentages or fractions of the total. Data can be typed in or copied and pasted.
- Chi-Square test
- Chi-Square test
- Chi-Square test (for up to 8 categories) (JavaScript)

- Measurement Errors and Error Propagation...

- Student t-test (for comparing two samples)...
- a very general Student t-test web page -- paired or unpaired, equal- or unequal-variance, from individual observations (which can be key-entered or copy/pasted) or summary data (N, Mean, SD or SEM). Includes explanations and advice on carrying out this type of test.
- t-test, paired or unpaired
- t-test, paired or unpaired
- t-test, paired or unpaired (JavaScript)
- 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 (Java)
- A general 2-sample comparison calculator, for paired, unpaired, equal-variance, obtaining its p-values from table lookup or from resampling
- Unpaired t-test from summary data (N, mean, SD) (Java)
- Another Unpaired t-test from summary data
- Very general t-test program for comparing measured quantities, observed counts, and proportions between two unpaired samples; also produces risk ratio, odds ratio, number needed to treat, and population analysis. (JavaScript)
- Test differences between two observed proportions, based on the Binomial distribution

- ANOVA (Analysis of Variance) -- comparison of two
**or more**samples ...- Factorial ANOVA for uncorrelated samples (extension of
**unpaired**Student t-test to more than 2 groups)...- One-way factorial ANOVA, with graphical output
- One-way factorial ANOVA for 3 Independent Samples (JavaScript)
- One-way factorial ANOVA for 4 Independent Samples (JavaScript)
- One-way factorial ANOVA from summary data (N, mean, and SD or SEM) (JavaScript)
- Another 1-way factorial ANOVA from summary data
- Two-way factorial ANOVA for 2 rows by 2 columns (JavaScript)
- Two-way factorial ANOVA for 2 rows by 3 columns (JavaScript)
- Two-way factorial ANOVA for 2 rows by 2 columns, from summary data (N, mean, SD) (Java)
- Very general
n-way factorial ANOVA, with interactions, means table, interaction plots, Bonferroni
post-hoc multiple comparisons, and confidence intervals. (When you get to the
**Rweb**page, scroll down to the**Analysis Menu**and select**ANOVA**.)

- Repeated-Measures ANOVA for correlated samples (extension of
**paired**Student t-test to more than 2 matched measurements)... - Post-Tests -- After doing a two-way (or other) ANOVA, post tests compare individual pairs of groups. This calculator does not perform the ANOVA calculations, but takes the output from an ANOVA (residual means square error, degrees of freedom) performs a post test between any pairs of cells that you select (using cell means and N's), at whatever alpha you specify.
- Tukey LSD (Least Significant Difference), using the standard table produced by an ANOVA
- Scheffe Least Significant Difference, using data from a standard ANOVA table and the N's for the two groups being compared

- Factorial ANOVA for uncorrelated samples (extension of
- 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 -- This page takes case-by-case pairs of matched data
- Another Wilcoxon Signed-Ranks test for matched pairs -- This page takes summarized, tabulated data: how many cases had differences of +1, +2, +3, etc., and -1, -2, -3, etc.
- 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 -- This page requires that you first cross-tabulate your data into a matrix, with a row for every group and a column for every different numeric value that any subject had; the cell of the matrix tell how many subjects (if any) in that group had exactly that numeric value.
- Least Significant Difference between mean ranks (post-hoc test after a significant Kruskal-Wallis test)
- Friedman test for comparing rankings (non-parametric)
- 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 (JavaScript)
- Two-group paired comparisons, using T-test, Wilcoxon, Signs test, and McNemar test (JavaScript)
- 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, based on the normal approximation to the binomial distribution

- Sequential Analysis -- each subject's data (usually paired
comparisons) is tested as it becomes available, and a decision is made to accept or to
reject the null hypothesis or to keep testing.
- by Paired Preferences -- Each pair of observations is compared and rated qualitatively as "preferring A" or "preferring B"
- by Paired Differences -- Each pair of numbers is subtracted to obtain a difference

- WebStat (an integrated (Java) applet) can perform Z-tests and T-tests (one- and two-sample) for population means, and Chi-square and Fisher-F tests for population variances

- Chi-Square tests...
- for 2-by-2 table (JavaScript)
- 2-by-2 table analysis
(Chi-square, sensitivity, odds ratio, relative risk, difference in proportions, number
needed to treat, etc.)
**with confidence intervals**(JavaScript) - 2-by-2 table analysis (Chi Square, Fisher Exact, difference in proportions, risk ratio, odds ratio, theta, log-odds ratio, Poisson test)
- for 2-by-2 table, with odds ratio, relative risk, etc. with confidence intervals (the results page is very nicely formatted for printing out)
- for 2-by-N table, where the two rows represent dichotomies like lived/died, present/absent, yes/no. This can test for a trend in the probability of an event when you have counts of the two categories over a set of time intervals.
- for table up to about 30 cells
- for up to 10-by-10 tables. This page also has a section for comparing observed with explicitly-specified frequencies. (JavaScript)
- for any-size table
- another for any-size table
- another for
any-size table (When you get to the
**Rweb**page, scroll down to the**Analysis Menu**and select**Two Way**.) - Exhaustive analysis of 2-by-2 tables, with Pearson Chi-square, Likelyhood Ratio Chi-Square, Yates Chi-square, Mantel Heanszel Chi-square, Odds Ratio, Log Odds Ratio, Yules-Q, Yules-Y, Phi-square, Pearson correlation, and McNemar Test (JavaScript)

- Three-dimensional Tables (2x2x2)...
- Three-dimensional 2x2x2 table
- Log-Linear Analysis for a 2x2x2 Table of Cross-Categorized Frequency Data (JavaScript) [Calculates the values of G2 for first- and second-order interaction effects for a table of observed frequency data cross-classified according to three categorical variables, A, B, and C, each of which has two levels or subcategories (a1, a2; b1, b2; c1, c2)]

- Fisher Exact tests for contingency tables...
- Fisher exact (2x2)
- Fisher exact (2x2) (JavaScript)
- Fisher exact (2x2) (JavaScript)
- Fisher Exact, with good Help discussion (JavaScript)
- Fisher Exact (2x5) (JavaScript)

- Exact unconditional
homogeneity/independence tests for 2-by-2 tables

(said to be more powerful than the Fisher exact test!) - Contingency table for sequenced categories (Ordinal by Ordinal, 5-by-5 table or less) (JavaScript)
- Contingency table for sequenced categories, 5-by-2 table, with exact probability calculations (JavaScript)
- 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 for comparing the way two raters scored each of a number of items, using case-by-case data entry
- Another Cohen's Kappa, for case-by-case data
- Another Cohen's Kappa, using already-tabulated data
- Kappa for nominal data as concordance between multiple raters -- Each of several raters puts each of several entities into one of several categories
- Intraclass correlation for concordance between multiple raters, using a data matrix that tells how each rater scored each case

- Chi-Square test for equality of distributions
- Chi-Square "Goodness of Fit" test for observed vs expected
counts (NOT from Contingency Tables)...
- Chi Square test -- takes observed values, and expected values that can be specified as expected occurrences, or percentages or fractions of the total. Data can be typed in or copied and pasted.
- Chi-Square test
- Chi-Square test
- Chi-Square test (for up to 8 categories) (JavaScript)
- Chi-Square test for up to 10 categories. This page also has a section for up to a 10-by-10 contingency table. (JavaScript)

- Straight Lines and Correlation Coefficients...
- Least squares regression line and Pearson correlation coefficient. (Java)
- Variations on straight-line fitting, when X and Y have error
- Least squares regression. (nice interface)
- Linear correlation and regression (nicely designed) (JavaScript)
- Draw a scatterplot, and compute various statistics
- Correlation and regression calculator -- input two sets of numbers (or upload a file); computes the means, variances, covariance, correlation coefficient and regression coefficients; also gives a scatterplot with the two regression lines
- The Data Applet provides descriptive statistics, histograms, boxplots, and scatterplots (Java)
- Least squares straight line (also allows some simple transformations), with an interesting tutorial on the topic
- 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 r
_{bc.a}, r_{ac.b}, r_{ab.c}from r_{ab}, r_{ac}, r_{bc}(JavaScript) - WebStat (an integrated (Java) applet) can perform simple regression analysis

- Correlation Tests...
- Spearman's rank correlation (non-parametric)...
- 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 (tests whether the slopes are different, and whether the lines are vertically distinct)
- Biserial and point-biserial correlation analysis
- Biserial correlation coefficient from summary data (N, mean, SD) of the X and Y variables
- Point-biserial correlation analysis
- Manipulation of a correlation matrix -- you enter the N-by-N correlation matrix, the page computes all Partial Correlation Coefficients, all Standardized Partial Regression Coefficients, and the Multiple Correlation Coefficient for each variable.
- A versatile page for calculating the significance of a correlation (rho<>0), significance of the difference between two correlations, power and sample size requirements for correlations testing, and the inter-relationships between three partial correlation coefficients.
- Sobel's test to determine the extent to which an intermediate variable ("mediator") carries the influence of an independent variable (predictor) on a dependent variable (outcome). (JavaScript)

- Beyond Simple 2-parameter Curve-fitting...
- Very general non-linear least squares curve-fitter (almost any function -- even functions that are non-linear in the parameters!). Also does least-absolute-value fitting. (JavaScript)
- Linear, parabolic, or cubic fit, with graphics (Java) (newer version here)
- Multivariate linear or univariate polynomial regression, with graphical output. Has a good discussion of the relevant mathematics and computational accuracy.
- Univariate and
multiple regression, with
**very**extensive graphical output (histograms, scatterplots, scatterplot matrices) and residual analysis (QQ, histogram, residuals vs dependent or predictors). Very intuitive point-and-click interface, dynamically customized for your data. (When you get to the**Rweb**page, scroll down to the**Analysis Menu**and select**Regression**.) - Automatic Multiple Regression,
**(*** TEMPORARILY OFFLINE ***)**automatically builds a model or regression equation! You merely supply the dependent and independent variables and it does the rest. It will find which variables are important enough to include in the model, determine the proper transformation of each of those variables, then look for 2-way and 3-way interaction terms important enough to include in the model, and transform them appropriately. - Multiple regression, if you already have the correlation coefficient matrix between all
independent and dependent variables...
- for 2 independent variables (JavaScript)
- for 3 independent variables (JavaScript)
- for 4 independent variables (JavaScript)

- Fit any of five families of curves (linear, polynomial, exponential, descending exponential, Gaussian) and draw a graph (Java)
- Curve fitting, smoothing, parameter estimating, data correlating and forecasting utility (Java)
- Logistic Regression, if the dependent variable is restricted to two values (such as whether an event did or did not occur) (JavaScript)
- Regression and GLM Calculator -- performs linear, Poisson, binomial and Gamma regression, with canonical, identity, logit, log, probit, inverse, cloglog, and sqrt link functions
- Cox Proportional Hazards Survival Regression Analysis (JavaScript)
- A faster version of Cox Proportional Hazards Analysis (JavaScript)
- Regression by Prevalence -- when you have data on the number of occurrences and non-occurrences of something over a set of time intervals. Tests whether the probability of the occurrence shows a trend over time.
- Test Bias Assessment Program, computes statistics to help you decide if test scores predict a criterion differently across subgroups (Java)

- Cox Proportional Hazards Survival Regression Analysis (JavaScript)
- A faster version of Cox Proportional Hazards Analysis (JavaScript)
- 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.

- Bayes' theorem calculations -- takes prior probabilities and conditional probabilities, and calculates revised probabilities. (great for solving certain kinds of brain teaser puzzles) (JavaScript)
- Bayesian calculations for diagnostic tests -- computes interrelationships among true pos, true neg, false pos, false neg, prevalence, sensitivity, specificity, predictive values, and likelihood ratios. (JavaScript)
- Calculate the post-test probability of an outcome (disease) from prior probability (prevalence) of the disease, and from the sensitivity and specificity of the test (Java)
- Sequential Experimental Design for testing the probability ratios (JavaScript)
- 2-by-2 table analysis (Chi-Square, sensitivity, odds ratio, relative risk, etc. with confidence intervals (JavaScript)
- for 2-by-2 table, with odds ratio, relative risk, etc. with confidence intervals (the results page is very nicely formatted for printing out!)
- Wald's Sequential Probability Ratio's -- for designing a sequential experiment in which a decision is made after each observation either to accept the null hypothesis, accept the alternate hypothesis, or acquire more observations.

- Bonferroni adjustment of critical p-values when performing multiple comparisons (has an excellent discussion of this topic)
- 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 (Java)
- Clustering Calculator generates tree structures of data clustering, and much more (Java)
- Misclassification Bias in Prevalence Studies (Java)
- Selection Bias in Case-control Studies (Java)
- 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.

- A Web-Based SAS Code Developer for Experimental Designs

Martindale's Reference Desk - Calculators On-Line - Statistics (the grand-daddy of all compendia of calculating web pages)

- Biostatistical Calculators...
- Number Needed to Treat -- Explanation, examples, tables, and an interactive nomogram
- Number Needed to Treat, also Normal, Student t, Chi-Square, Binomial, and Random Digits
- Clinical Significance Calculator -- For two groups (control and treatment), enter the group size and incidence rate; the page will calculate absolute and relative risk reductions, odds ratio, and number needed to treat, along with 95% confidence intervals for each result
- Thorough analysis of 2-by-2 table relevant to Predictions and Diagnostic Tests -- sensitivity, specificity, prevalence, diagnostic accuracy, PPV, post-test probabilities, likelihood ratio 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 (based on a logistic model)
- LODS - Logistic Organ Dysfunction System calculator (JavaScript)
- APACHE-II Score for acute physiology and chronic health evaluation (JavaScript)
- 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 -- estimates amount of workforce improvement from implementing a valid selection procedure in an organization. Computes institutional expectancies under three different models.
- Investment Derivative Calculations -- A very elaborate online calculator and real-time data retrieval system. Includes economic regression analysis.

Check out the large number of power and sample size calculators at the UCLA Statistics website. Many of them are included below.

- For one-group tests (comparing the sample to a specified value) or for
**paired**two-group tests...- Comparing a mean to a specified value (JavaScript) (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 (JavaScript) (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

- For designing surveys (sample size and confidence intervals for
proportions, based on sample size, with or without corrections for finite populations:
- 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 (Java)
- Sample size or confidence interval of a proportion

- For two-group tests...
- Comparing means for two independent samples...
- Same-size samples (JavaScript) (also available at another website)
- Equal- or unequal-size samples
- Same-size samples; equal or unequal variances (Java)
- 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 (JavaScript)
- Equal- or unequal-size samples
- T independent samples (JavaScript) (also available at another website)

- Difference between two rates of occurrence of events
- Survival outcome analysis -- computes power or sample size in a two group design with a survival outcome; allows for unequal sample sizes, loss to follow-up rates for each group, cross overs, and specifying the patient entry distribution into the study

- Comparing means for two independent samples...
- For ANOVAs and other multi-group comparisons...
- Sample size needed for comparison of 2 or more groups, knowing the SD's with a group, and the expected difference between groups
- Sample size computation for multiple comparisons -- said to be more "realistic" than ordinary ANOVA sample size calculations (explained on the web page)
- ANOVA - power and sample
size analyses for many models:
- Pushbutton interface for:
- Bar-graph interface for:
- "Roll your own" for:

- Two-way ANOVA power calculation (Java)
- Simplified power analysis for multi-way ANOVA designs

- For regressions and correlation tests...
- Power or sample size for comparing an observed correlation coefficient with a specified value
- A versatile page for calculating the significance of a correlation (rho<>0), significance of the difference between two correlations, power and sample size requirements for correlations testing, and the inter-relationships between three partial correlation coefficients
- Power calculations for logistic regression with a continuous exposure variable and an additional continuous covariate or confounding variable. Also accommodates measurement error in the exposure variable. Has graphical output.

- Other power calculations...
- Retrospective power analysis (after doing the test) (JavaScript)
- Power calculations for clinical trials and scientific experiments
- Survival outcome analysis -- computes power or sample size in a two group design with a survival outcome; allows for unequal sample sizes, loss to follow-up rates for each group, cross overs, and specifying the patient entry distribution into the study
- Exact power for the Fisher exact test (Java)
- A large, well-organized collection of of power and sample size calculators, containing many of the above links
- Find sample size, power and minimal detectable difference for a:

- Links to printable copies (in Adobe Acrobat PDF format) of many power tables including: Z Test, t-Test for One Sample or Two Related Samples, t-Test for Two Independent Samples, Analysis of Variance, Correlation Coefficient, and Required Sample Size for various tests
- Wald's Sequential Probability Ratio's -- for designing a sequential experiment in which a decision is made after each observation either to accept the null hypothesis, accept the alternate hypothesis, or acquire more observations.
- Experimental Design...
- EDGAR -- generates experimental designs and randomizes the position of experimental treatments in the design, so that the subsequent analysis of the data is comparatively straightforward
- Gehan/Simon Two-Stage Designs approximating the power and significance level specified in the input.
- Find Optimal/MiniMax Phase-II 2-stage designs, where H0: p=p0 and H1: p=p1>p0, subject to a fixed maximum sample size, N. Finds all the designs that satisfy Type I & II error criteria. [see Simon, Controlled Clin Trials, 10:1-10,1989]
- Compute
boundaries for a specified alpha spending function,

compute drift given power and bound, and

compute probabilities,

all based upon the Lan-DeMets method. Allows computation of boundaries at any time during the monitoring of a study. It is valid for any normal test statistic with independent increments. The information time is the ratio of accrued sample size to the total sample size for normal data.