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Sections of the StatPages.net (statpages.info and statpages.org) website
Interactive Stats
Free Software
Books & Manuals
Demos & Tutorials
Other Links
About this Website
What's New
John Pezzullo
Statistical Jokes
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© 2024 StatPages
WEB PAGES THAT PERFORM STATISTICAL CALCULATIONS!
The web pages listed below comprise a powerful, conveniently-accessible,
multi-platform statistical software package. There are also links to online
statistics books, tutorials, downloadable software, and related resources.
These pages are located on servers all over the world, and are the result of
much cleverness and hard work on the part of some very talented individuals. So
if you find a page useful it would be nice to send the authors a short e-mail
expressing your appreciation for their hard work and generosity in making this
software freely accessible to the world.
Table of Contents for this page...
* Selecting the right kind of analysis
* "Online Software" Package websites
* Calculators, plotters, function integrators, and interactive programming
environments
* Probability distribution functions: tables, graphs, random number generators
* Descriptive statistics, histograms, charts
* Confidence intervals, single-population tests
* 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
* Bayesian Methods
* Other statistical tests and analyses
* Specialized and discipline-specific tests and analyses
* Power, sample size and experimental design
Other Statistical Resources...
* Free statistical software packages
* Online statistics textbooks, reference manuals, and journals
* Interactive statistical demonstrations and tutorials
* Links to other statistics-related pages
* About this Project
--------------------------------------------------------------------------------
FIRST -- CHOOSE THE RIGHT TEST! [RETURN TO TABLE OF CONTENTS]
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 Biostatistics.
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.
4. Statibot (Provided by Dominik Heeb)
* Helps to find the right analysis, based on real data
* Performs the analysis on the real data
* English and German
* Free
--------------------------------------------------------------------------------
"ONLINE SOFTWARE PACKAGE" WEB SITES [RETURN TO TABLE OF CONTENTS]
As you can see from looking at the StatPages.org 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:
* Statigraphics Stratus-- a browser-based version of Stratigraphics statistical
software. Provides plotting, probability distributions, summary statistics,
one-, two-, and multiple-sample analysis, time-series analysis, regression
analysis, curve-fitting, attribute estimates, ANOVAs, Statistical Process
Control, smoothing, power/sample-size calculations, and other statistical
analyses.Also provides access to over 50 applets in which you can enter
data, compute statistics, create tables and graphs, and print out the
results. The free "Guest" version supports up to 100 rows and 10 columns of
data. For larger data sets, a single-user copy or a corporate deployment
license can be purchased. To use the Guest version, click here.
* 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.
* SciStatCalc -- a very good web site (thank you Alijah Ahmed!), with online
calculators for many of the common statistical probability functions and
significance tests, and pages that explain the concepts and formulas behind
the tests. Calculating pages provide flexible input options (type the numbers
in, or read them from a text fiile), and well--organized output of results,
with interpretations and graphical displays.
* MedCalc -- Two different web sites:
* MedCalc.org -- a collection of seven free calculating web pages: tests for
one mean or one proportion, comparisons of means or proportions, relative
risk, odds ratio, and diagnostic test evaluation.
* MedCalc.net -- a pay-for browser-based statistical system (5-day free trial
available) providing a wide range of statistical analyses (click here for
list).
* 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.
* 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.
* AppOnFly has a different approach -- the company maintains Windows computers
with a wide selection of Windows software, including utilities for accessing
PDF, ZIP, graphics and other files, web browsers, various office suites (MS
Office, Libre Office, Apache OpenOffice, WordPerfect Office), and statistical
packages (SPSS, NCSS, R), to mention a few. They then provide apps for
accessing this Windows desktop environment from any device -- computer,
smartphone, tablet (Windows, Mac OS, iOS, Android). This is a pay-for
service, but they offer one-month free trials.
--------------------------------------------------------------------------------
CALCULATORS, PLOTTERS, FUNCTION INTEGRATORS, AND INTERACTIVE PROGRAMMING
ENVIRONMENTS...[RETURN TO TABLE OF CONTENTS]
* Expression Evaluators -- type in any numeric expression; the computer will
evaluate it and display the results...
* Had2Know -- Calculators for math, statistics, finance, home and garden
remodeling, science, technology, health, and much more.
* GIGAcalculator.com -- several nice statistical tools, each accompanied by
detailed description of the underlying math and assumptions, alongside
relevant formulas.
* Stats Solver -- A diverse assambley of useful statistic online calculaters.
Informative. Step_by-step.
* UnitConverter -- Slick and easy, but includes cookies and advertising.
* Scientific Calculator -- numeric expression evaluator.
* StatsCalculator -- Neath and easy calculator. Will serve as a basic
alternative for paid tools such as Minitab.
* Statistics Calculator -- Compute a number of statistical properties of a
dataset (mean, median, harmonic mean, geometric mean, minimum, maximum,
range, variance, standard deviation)
* Inverse Symbolic Calculator -- tells you where a number came from. For
example, if you type in 1.55838744, this program will tell you that it's
really the square root of 17/7.
* Percentage Calculator -- New with more features and improved accuracy and
help.
* Calculators -- pages that look and act like a pocket calculator...
* A simple 5-function calculator with memory (Adobe Flash Player required).
* iCalcu -- four statistics calculators: Five-number summary, ANOVA and Tukey
HSD, Chi-square and Binomial Probability. They are extremely easy to use,
with intuitive examples included. More to come.
* acetabulum.dk -- 5 Statistic Online Calculators (Correlation Test, Survival
Analysais, Cox Propertional Hazard, One and Two Way ANOVA and ANOVA from
summary data, Logistic Regression).
* Margin of Error Calculator -- The margin of error calculator can be
employed to compute the MOE of a survey in accordance with the sample
proportion and size, and the desired confidence level.
* CoCalc -- an advanced RPN scientific calculator from CoHort Software. Has
log, trig, boolean, binary/hex, and basic statistics functions. Implemented
as a Java applet, so it can be run from the Web or stored on your computer
for "offline" running when not connected to the Web. Also available in a
larger-font version.
* Links to Other Online Calculators, and calculator-related resources, from
Essential Links (el.com).
* 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. (but Flash Player 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...
* Indefinite Integrals -- using the Mathematica engine
* 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)
* 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.
* More calculators -- a list free online/downloadable calculators.
--------------------------------------------------------------------------------
PROBABILITY DISTRIBUTION FUNCTIONS: TABLES, GRAPHS, RANDOM NUMBER GENERATORS...
[RETURN TO TABLE OF CONTENTS]
* 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:
* Xuru's page to calculate PDFs, CDFs, and their complementary and inverse,
along with expected values, mean, variance, skewness & kurtosis, for
binomial, geometric, negative binomial, Poisson, hypergeometric, normal,
chi-square, Student t and Fisher F distributions.
* Distribution/density calculators, plotters and random number generators
* Very sophisticated interactive page for over 65 continuous and discreet
statistical distribution functions -- Select a function from a menu, and
it will show you a graph of that function along with its properties. You
can click on the graph to select limits, and it will show you the left,
middle and right integrals.
* These pages each compute probabilities for the four most common probability
distributions:
* Normal, t, Chi-Square, and Binomial (density and cumulative)
probabilities; Use e.g. dnorm, qnorm, rnorm.)
* 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
* P-values for the Popular Distributions -- Binomial , Chi-square,
Exponential , Fisher's F, K-S: Two Samples , Poisson, Normal , Student's
t, and Uniform distributions.
* Calculate p-value from z, t, F, r, or Chi Square; or do the reverse.
* Reverse computations: enter p-value (and, if necessary, sample sizes
and/or d.f.); program will compute z, t, F, Chi Square, and correlation
coefficient
* These pages each compute probabilities and/or inverses for a specific
distributions:
* Normal distribution areas, with nice graphical interpretations
* Another very good Normal Distribution calculator, with nice graphics
* A very attractive page for Normal distribution (and inverse), with
detailed explanations
* Normal area (1-tailed)
* Cumulative area under the normal curve (integral from minus infinity to
z)
* Chi-Square probabilities, and reverse, with a detailed explanation
* Chi-Square Distribution
* Chi-Square Distribution
* Student t Distribution
* inverse (t value from p value)
* Probabilities for the Fisher F distribution
* Another Fisher F distribution p-value calculator.
* Critical Fisher F value, given the alpha level, the numerator and
denominator d.f.
* Non-central F value (by Laubscher's square root approximation), given the
F-value, numerator and denominator d.f., and the noncentrality parameter.
* Binomial, Poisson and Gaussian distribution probabilities
* Cumulative frequency for the Binomial distribution
* Probabilities for Gamma, complete Beta, and Incomplete Beta distributions
* 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...
* Random integers -- generates any number of random integers, uniformly
distributed between any two limits
* Generate tables of random integers from any specified range, or random
values from a Normal distribution with any specified mean and SD.
* Random fractional numbers -- generates any number of random numbers, each a
fraction between 0 and 1 with 8 digits after the decimal point
* Randomly assign subjects to treatment groups -- can randomly choose a group
for each subject, or randomly shuffle subjects within groups.
* 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 -- three variations:
1. generates M groups of N numbers each by distributing the numbers from 1
to M*N randomly into the M groups
2. generates M blocks of N numbers each by randomly shuffling the numbers
from 1 to N in each block
3. 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
--------------------------------------------------------------------------------
DESCRIPTIVE STATISTICS, HISTOGRAMS, CHARTS... [RETURN TO TABLE OF CONTENTS]
* Statiscope -- a beautifully-implemented page for calculating and displaying a
large number of descriptive statistics from a set of numbers you enter (Java
code)
* Xuru's page for single variable descriptive statistics: mean, median, sd,
variance, mean abs deviation, geometric mean & sd, skewness, kurtosis,
quartiles, standard errors, Anderson-Darling normality test, and some
confidence intervals of the mean and sd. You can copy and paste data directly
from a spreadsheet or a tabulated data file, or enter numbers manually.
* Descriptive Sampling Statistics -- Enter up to 80 numbers; this page will
calculate the mean, variance, SD, CV, skewness and kurtosis.
* Descriptive statistics (mean, SD, SEM, and CI of mean). Can enter or paste
raw data, or enter mean, SD or SEM, and N to get CI.
* Descriptive Statistics -- Enter up to 80 values; page calculates: N, mean,
variance, SD, CV, skewness, kurtosis, SEM, median, min, max, range, 1st & 3rd
quartiles, interquartile range, quartile deviation, coeff of quartile var,
and absolute deviation.
* Measuring for Accuracy -- Given a set of observed and predicted values, this
page calculates the SD of errors, mean absolute & relative error, and
Durbin-Watson statistic.
* Arithmetic, Geometric, and Harmonic Means -- of up to 80 values.
* 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
* A variety of descriptive statistics and a stem and leaf display
* 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. Also contains an
excellent discussion of what to do about outliers.
* Combine Subgroups -- calculate the mean and SD of a combination of groups
from the N, mean and SD of each group.
* Basic descriptive statistics (mean, sum of squares, variance, standard
deviation, minimum, 25th percentile, median, 75th percentile, and maximum for
up to 500 numbers
* Empirical Distribution Function -- from up to 42 sets of [value, frequency].
* Multinomial Distributions -- Enter up to 12 values and their corresponding
probabilities, and this page will calculate Expected Value, Variance,
Standard Deviation, & Coefficient of Variation
* Paired Data Sets Statistics -- Enter up to 28 sample paired data sets, and
this page will calculate means, variances, and covariance
* Histogram -- Enter up to 80 numbers, and this page will display a histogram.
* Histogram from a set of numbers, lets you dynamically alter the interval
width and see the effect immediately
* Determination and Removal of Outliers -- Given a set of numbers, this page
iteratively isolates potential outliers for removal.
* StatsJournal -- is a free resource for anyone who needs basic statistics
tools.
--------------------------------------------------------------------------------
CONFIDENCE INTERVALS, SINGLE-POPULATION TESTS, MEASUREMENT ERRORS... [RETURN TO
TABLE OF CONTENTS]
* Confidence Intervals...
* Exact C.I.'s for Binomial (observed proportion) and Poisson (observed
count). (Also available as an Excel spreadsheet, and as an Excel Add-In.)
* Exact and "modified Wald" C.I.'s for observed proportion or count, with a
good explanation
* Bayesian "credible" intervals around an observed proportion. Somewhat
comparable to the "classic" confidence intervals, but tend to be slightly
narrower.
* 95% or 99% C.I. for proportions for any specified sample size and
population size
* Confidence interval around an observed sample SD, assuming the data are
sampled from a Normal distribution
* Percentage: Estimation & Testing -- calculates exact binomial confidence
intervals and tests of hypothesis for population proportion, from infinite
or finite populations.
* Tolerance Intervals...
* Tolerance Intervals for the Normal Distribution. (Don't confuse tolerance
intervals with confidence intervals!) A tolerance interval for a measured
quantity is the interval in which there is a specified likelihood that a
specified fraction of the population's values lie. This page will calculate
1-sided and 2-sided tolerance intervals for any specified population
fraction, and for any specified level of confidence, from the mean and
standard deviation of a finite sample, under the assumption that the
population is normally distributed. These calculations are also available
in a downloadable Excel spreadsheet: tolintvl.xls .
* Single-Population Tests...
* Sign and Binomial test -- test an observed proportion against a proposed
population proportion
* Mean, SD, confidence interval, etc. for a set of values
* An excellent One-Sample Student t Test page -- enter or paste raw data, or
enter mean, SD or SEM, and N
* One-sample Student t test for Mean vs. a Specified Value -- for up to 80
observations, and a postulated population mean.
* Another Student t-test of a single mean (vs specified value) from N, mean,
SD
* Test for Asymmetry around zero -- Enter a set of numbers (usually a mix of
positive and negative numbers), and the program will apply a non-parametric
test (originally created by R. A. Fisher) of whether the numbers are
consistent with a population frequency distribution that is symmetrical
around zero (but does not necessarily have to be normal). It is a
frequentist test to work Darwin's experiment with matched pairs, and
experiments like it.
* Test for the mean being greater than some specified value. This unusual
test is Bayesian and frequentist at the same time. The null hypothesis
asserts some value for the mean of a population of positive numbers; the
alternative hypothesis says the mean is higher than that. This test gives a
Bayesian likelihood ratio that is also an upper bound on the p-value of the
frequentist test.
* 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)
* 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
* Compatibility of Multi-Counts -- tests whether up to 14 observed event
counts (each over the same amount of time) are consistent with a single
expected event rate.
* 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
* Testing the Variance -- of up to 80 observations against a postulated
population variance.
* 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
* Test for Homogeneity of a Population -- enter form 25 to 84 values; page
provides information to test whether histogram is unimodal.
* Shapiro-Wilk Test for Normality -- enter numbers into page, or read them
from a text file. Performs normality test, also shows a histogram of the
data. For a description of the test, along with the formulas and
programming, click here.
* Test for Normality -- enter up to 42 sets of [value, frequency]; page will
calculate skewness, kurtosis, and Liliefors test for consistency with a
normal distribution.
* Test for Uniform Distribution -- enter up to 42 sets of [value, frequency];
page will calculate the Kolmogorov-Smirnov test for consistency with a
uniform distribution.
* Testing Poisson Process -- enter up to 14 sets of [value, frequency]; page
will calculate a Chi square test for consistency with a Poisson
distribution.
* Lilliefors Test for Exponential Distribution -- tests whether a set of
observed values are consistent with an exponential distribution.
* 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
* Goodness-of-Fit for Discrete Variables -- Chi square test for up to 14 sets
of [Observed, Expected] frequencies.
* Measurement Errors and Error Propagation...
* Calculate how the standard error of one or two variables propagates through
any function of those variables
* Compute confidence intervals of a sum, difference, quotient or product of
two means, assuming both groups follow a Gaussian distribution.
--------------------------------------------------------------------------------
SAMPLE COMPARISONS: T-TESTS, ANOVAS, NON-PARAMETRIC COMPARISONS... [RETURN TO
TABLE OF CONTENTS]
* 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.
* a very polished calculator for two-group Student t test, with graphical
display of means and confidence intervals, and an interpretation of the
results. Can take individual values or summary statistics (N, mean, SD) for
each group.
* t-test, paired or unpaired
* t-test, paired or unpaired
* t-test, paired
* Paired Student t test -- enter data into the page, or read it from a text
file. This page also produces histograms of the data (each group, and
paired differences). For a detailed description of the test, with formulas
and examples, click here.
* Paired Student t Test -- on up to 42 pairs of values, along with a
postulated population mean difference.
* Testing Two Populations -- Unpaired Student t test for up to 80
observations in each sample. Also accepts a postulated difference between
the two population means, which can be different from 0.
* Unpaired t-test from summary data (N, mean, SD)
* 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.
*
* ANOVA (Analysis of Variance) -- comparison of two or more samples ...
* One-Way and Factorial ANOVA for uncorrelated samples (extension of unpaired
Student t-test to more than 2 groups)...
* One-way ANOVA, with graphical output
* ANOVA: Testing the Means -- One-way ANOVA for three groups, each
containing up to 40 subjects.
* One-way ANOVA from summary data (N, mean and SD or SEM) -- Now also does
Tukey HSD post-hoc test!
* One-way ANOVA from summary data (N, mean and SD or SEM) -- As above but
allows
* copy/paste data
* evaluate more than 10 groups
* includes Tukey-Kramers post-hoc test
* Another 1-way ANOVA from summary data
* One-way ANOVA -- Also produces a post-hoc analysis (which groups are
different from which others), and a scatterplot of all groups. For a
description of the ANOVA, click here.
* Two-Way ANOVA Test -- for blocked designs of up to 4 groups by 6
treatments.
* Two-Way ANOVA with Replications -- for blocked designs of up to 4 groups
by 6 treatments, with up to 4 replications.
* Two-way ANOVA -- enter data into the web page, or read it from a text
file. For an explanation, click here.
* Two-way factorial ANOVA for 2 rows by 2 columns, from summary data (N,
mean, SD)
* ANOVA for Condensed Data Sets -- Enter up to 10 sets of (N, mean, SD);
page calculates a one-way ANOVA.
* 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)...
* ANOVA for repeated-measures or matched measurements -- Enter three sets
of matched measurements (up to 40 points each); page calculates a
repeated-measures ANOVA.
* Bartlett's Test for Equality of Multi-variances -- for up to 14 sets of [N,
variance].
* Bartlett's test for equality/homogeneity of variances for three or more
groups. Also produces a scatter plot of all the groups. For a description
of the test, along with the formulas and programming, click here.
* Post-hoc Tests -- After doing a two-way (or other) ANOVA, post -hoc tests
(also called 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-hoc 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
* 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 -- a non-parametric substitute
for the paired Student t test when the data is not normally distributed.
This page also produces histograms of the data (each group, and paired
differences). For a detailed description of the test, with formulas and
examples, click here.
* 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.
* Comparing Two Random Variables -- by the Mann-Whitney U test, with up to 80
observations per sample.
* Mann-Whitney U test -- a non-parametric substitute for the unpaired Student
t test when the data is not normally distributed. This page also produces a
dot-plot and a histogram of the data for each group. For a detailed
description of the test, with formulas and examples, click here.
* K-S Test for Equality of Two Populations -- Given two sets of frequencies
(using the same grouping intervals), this page calculates the
Kolmogorov-Smirnov test.
* Two-sample Kolmogorov-Smirnov Test -- Enter numbers into the web page, or
read them in from text files. Also graphs the cumulative distribution of
the two samples.
* 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.
* Kruskal-Wallis test -- This page also produces a scatterplot of ranks for
all groups.
* 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
* 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
* Comparison of two proportions between two groups (each given as # successes
/ # of trials). Shows confidence intervals, and interprets the results of
the comparison.
* Paired Preferences Test -- Enter the sample size, and the two percentages
(preferring A and preferring B), and this program will calculate the T
score and significance level. This page is based on a normal approximation
to the binomial distribution, and should not be used if the sample size is
less than 30.
* Comparison of Event Rates between two groups...
* a very polished calculator for comparing two event rates (number of events
in a certain amount of time). Shows confidence intervals around each event
rate, and interprets the significance of the difference between the rates
of the two groups.
* 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
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CONTINGENCY TABLES, CROSS-TABS, CHI-SQUARE TESTS... [RETURN TO TABLE OF
CONTENTS]
* Chi-Square tests...
* Quick Chi-Square -- Manual entry (tab or comma delimited) or Copy/paste
Excel data directly. Calculates Expected Cell Values, Chi-Square and
P-value for any 2D Contingency Table.
* 2-by-2 table analysis (Chi-square, Fisher Exact Test, sensitivity, odds
ratio, relative risk, difference in proportions, number needed to treat,
etc.) with confidence intervals.
* EpiMax Table Calculator -- similar to the above, but with a clearer screen
layout.
* for 2-by-2 table, by Fisher Exact, and by Chi Square (with and without
Yates' correction), with a good explanation
* for 2-by-2 table
* 2-by-2 table analysis (Chi Square, Fisher Exact, difference in proportions,
risk ratio, odds ratio, theta, log-odds ratio, Poisson test)
* Diagnostic Test Evaluation -- from a 2x2 cross-tab of diagnostic test
results (positive or negative) vs. true disease state (present or absent),
calculates sensitivity, specificity, positive and negative likelihood
ratios and predictive values, and disease prevalence, along with their 95%
confidence intervals.
* 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.
* Chi-square Test for Relationship -- for up to a 6-by-6 cross-tab.
* for any-size table
* another for any-size table
* Exhaustive analysis of 2-by-2 tables, with Pearson Chi-square, Likelyhood
Ratio Chi-Square, Yates Chi-square, Mantel Haenszel Chi-square, Odds Ratio,
Log Odds Ratio, Yules-Q, Yules-Y, Phi-square, Pearson correlation, and
McNemar Test
* Paired Proportion Test -- for testing whether the proportion of subjects
having some characteristic is the same in two matched groups or in one
group before and after some intervention. (Also can test against a null
hypothesis specifying some non-zero difference.)
* Also see the Evidence-Based-Medicine (EBM) calculator in the
"Biostatistical Calculators" section of the "Other Statistical Tests and
Analyses" section of this page.
* Three-dimensional Tables (2x2x2)...
* Three-dimensional 2x2x2 table
* Fisher Exact tests for contingency tables...
* Fisher exact (2x2)
* Fisher Exact, with good Help discussion
* Fisher Exact (2x5)
* Fisher Exact (2x2)
* Test differences between two observed proportions, based on the Binomial
distribution
* Barnards Test (2x2) -- An exact test for 2x2 tables that is exact (like the
Fisher test), but can be more powerful than the Fisher test (more likely to
produce significance). For an explanation, click here.
* Contingency table for sequenced categories (Ordinal by Ordinal, 5-by-5 table
or less)
* Contingency table for sequenced categories This is a re-implementation of
John Pezullos original page above, accommodating for 2x2 or more (i.e.
N-by-M) contingency tables
* 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 to analyze a matched case-control study, with a good
explanation
* McNemar's test for paired contingency tables
* McNemar's test for 2x2 paired tables -- For a background explanation, with
formulas and examples, click here.
* Cochrane's Q Test -- An extension of the McNemar test to 2xN tables. For an
explanation, click here.
* Exact Bayes test for independence in r by c contingency tables -- Can also
handle comparison of observed-vs-expected, and observed-vs-uniform
situations.
* Comparison of ratings or rankings by different raters...
* Quantify agreement with kappa -- assesses how well two or more observers,
or methods, classify object/subjects into groups.
* Friedman test for comparing rankings (Ordinal by Nominal)
* Quantify agreement with kappa -- assesses how well two observers, or two
methods, classify subjects into groups. For up to a 12-by-12 table.
* Online Kappa Calculator -- calculates free-marginal and fixed-marginal
variations of birater and multirater Kappas (chance-adjusted measures of
interrater agreement).
* 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, 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
--------------------------------------------------------------------------------
REGRESSION, CORRELATION, LEAST SQUARES CURVE-FITTING, NON-PARAMETRIC
CORRELATION... [RETURN TO TABLE OF CONTENTS]
* Straight Lines and Correlation Coefficients...
* Least squares regression. (nice interface)
* Linear regression to data copy/pasted from a spreadsheet or tabular file.
* Linear Regression -- enter X and Y into the web page, or read them in from
a text file. Produces regression coefficients, coefficient of
determination, and other quantities, along with a graph of the observed
data points and fitted line. For a description of the concepts of linear
regression, click here.
* Several variations on 2-parameter linear regression (logarithmic
regression, exponential regression, and power regression)
* Simple Linear Regression -- for up to 84 points, with extensive output and
residual analysis.
* The Data Applet provides descriptive statistics, histograms, boxplots, and
scatterplots
* Scatter Diagram and Test for Outliers -- for up to 84 points.
* Bivariate Sampling Statistics -- calculates means, variances, and
covariance for up to 42 [x,y] measurements.
* WebStat (an integrated (Java) applet) can perform simple regression
analysis
* Correlation Tests...
* Spearman's rank correlation (non-parametric)...
* Spearman
* Spearman's correlation from cross-tabbed data with sequenced row and
column categories
* Calculate Pearson, Spearman or Kendall Correlation Coefficient from a N × M
2D data matrix.
* Write, copy/paste (Excel or other spreadsheet) or load data from a csv
file.
* First row may include column names. Specify which columns to test for
correlation.
* Optional specify: confidence level, continuity correction, exact p-value
and alternative hypothesis.
* Correlation test
* Pearson Correlation Coefficient -- also produces a scatterplot of the data.
For a description of correlation coefficients, click here.
* Spearman Rank Correlation Coefficient -- a non-parametric substitute for
the Pearson correlation coefficient. This page also produces a scatterplot
of the data. For a description of correlation coefficients, click here.
* Significance level corresponding to a correlation coefficient
* Testing the Correlation Coefficient -- enter up to 42 r values, along with
a postulated population r value.
* 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)
* Comparing Two Linear Regressions -- Enter two sets of [x,y] values; page
calculates two straight lines, then compares slopes and intercepts.
* Test for Several Correlation Coefficients -- enter up to 14 sets of [N, r];
page will test whether all r's are consistent with a single population r
value.
* Biserial correlation coefficient from summary data (N, mean, SD) of the X
and Y variables
* Lin's "concordance correlation coefficient" -- first proposed by Lin
(1989) for assessment of concordance in continuous data. A breakthrough in
assessing agreement between alternative methods for continuous data. Seems
to avoid the shortcomings of correlation coefficient r, paired t-tests,
least squares analysis for slope and intercept, coefficient of variation,
intraclass correlation coefficient.. It is robust on as few as 10 pairs of
data.
* 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.
* Beyond Simple 2-parameter Curve-fitting...
* Very general nonlinear least-squares curve fitter -- almost any function
you can write-- up to 8 nonlinear parameters, up to 10 independent
variables.
* Performs nonlinear least-square regression as above but will handle more
than 8 parameters and includes plotting option.
* MyCurveFit.com -- an easy-to-use curve-fitting page. Offers 13 pre-defined
functions (no initial guesses required), along with the ability to fit a
general non-linear function you provide (along with initial guesses).
Displays the results graphically, along with the formula of the fitted
curve. Several types of unequal data-point weighting are provided. Lets
you generate predicted values (interpolated and extrapolated) from the
fitted curve. Lets you save results in Excel and PDF formats.
* ZunZun non-linear least-squares curve-fitter -- with an enormous list of
pre-defined 2-D and 3-D functions, and extensive graphical and statistical
output.
* Another non-linear least-squares curve fitter -- with graphical output!
Choose one of 15 pre-defined nonlinear functions of one variable and up to
three parameters.
* 3-D Regression and Interactive Graph (by MiaBella LLC) -- a powerful web
page that fits a linear function of two predictor variables (Z = a + b*X +
c*Y), and displays a very elegant 3-D scatterchart of the {X,Y,Z} points
and the fitted plane. You can rotate the graph in three dimensions using
the mouse, and you can see the X, Y, and Z values of any point (say, an
outlier) by clicking on the point.
* Polynomial Regression -- fit polynomials of degree 2 through 10.
* Multiple Linear Regression -- fit functions of more than one predictor
variable.
* Multiple Polynomial Regression -- fit functions of one or more predictors,
each expressed as polynomials, up to the order you specify.
* Nonlinear Regression -- Automatically fits over 100 of the most
commonly-occurring non-linear functions (gaussians, sigmoidals, rationals,
sinusoidals, etc.), and then ranks them according to goodness-of-fit.
* Compare the fit of two models to your data. Which model fits better? Enter
goodness-of-fit (SSQ, or weighted SSQ) and # of data points and # of
parameters for each model. The calculator will compare the models using
Akaike's method, , then the F test.
* Fit "rational functions" (also called "Pade functions") to {X,Y} data. A
rational function is a fraction whose numerator and denominator are both
polynomials in X. They can fit a broader range of functions than
polynomials alone can -- they can fit data where the Y value "levels off"
to a horizontal line for very large or small X, and can fit functions that
have "singularities" (Y shoots to infinity at some value of x). This
curve-fitter is part of an extensive set of online calculators to solve
problems in structural engineering (bending and buckling of beams and
plates, etc.) at the Software for Structures web site.
* 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.)
* Multiple Linear Regression -- up to 16 data points and up to 4 independent
variables; calculates fitted model, and a large number of residual analysis
statistics.
* Quadratic Regression -- Fits a least squares parabola to up to 84 data
points, and provides extensive residual analysis.
* Multiple regression, if you already have the correlation coefficient matrix
between all independent and dependent variables...
* Fit any of five families of curves (linear, polynomial, exponential,
descending exponential, Gaussian) and draw a graph
* Logistic Regression, if the dependent variable is restricted to two values
(such as whether an event did or did not occur)
* Logistic Regression -- extends John C Pezzullos page (above) to handle
power models and let you calculate Predicted Probability for specific
covariable patterns.
* Cox Proportional Hazards Survival Regression Analysis
* A faster version of Cox Proportional Hazards Analysis
* Advanced Cox Proportional Hazards Regression Analysis
* Advanced Cox Proportional Hazards Regression Analysis - interactive
* 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
* Time Series Analysis...
* Autoregressive Time Series -- tools for the identification, estimation, and
forecasting based on autoregressive order obtained from a time series.
* Detecting Trend & Autocrrelation in Time Series -- Given a set of numbers,
this page tests for trend by Sign Test, and for autocorrelation by
Durbin-Watson test.
* Plot of a Time Series -- generates a graph of a time series with up to 144
points.
* Seasonal Index -- Calculates a set of seasonal index values from a set of
values forming a time series. A related page performs a Test for
Seasonality on the index values.
* Forecasting by Smoothing -- Given a set of numbers forming a time series,
this page estimates the next number, using Moving Avg & Exponential
Smoothing, Weighted Moving Avg, and Double & Triple Exponential Smoothing.
* Runs Test for Random Fluctuations -- in a time series.
* Test for Stationary Time Series -- Given a set of numbers forming a time
series, this page calculates the mean & variance of the first & second
half, and calculates one-lag-apart & two-lag-apart autocorrelations. A
related page: Time Series' Statistics calculates these statistics, and also
the overall mean & variance, and the first & second partial
autocorrelations.
--------------------------------------------------------------------------------
ANALYSIS OF SURVIVAL DATA... [RETURN TO TABLE OF CONTENTS]
* Kaplan-Meier Survival Plot and LogRank Test -- Type or copy/paste data, or
read it in from a file. Prepares tables, graphs (with 95% confidence
intervals), and statistical comparison output. Can accommodate two or more
groups, and can perform stratified log-rank test. Uses the R statistical
engine on the ShinyApps server to provide very high-quality output. Written
by Soren Merser.
* Kaplan-Meier Survival Plot -- for one or more groups. Draws K-M curves with
optional confidence bands (ordinary, log, or log-log type, at the 50, 80, 90,
or 95% conf. level). This is part of Peter Rosenmai's EurekaStatistics web
site (a blog about statistics and R).
* Kaplan-Meier Survival Plot and LogRank -- calculates survival curves (with
confidence bands), and performs a LogRank test test to comparing survival
curves between two groups.
* 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.
* CoxReg -- performs Cox Proportional Hazards Regression. You can copy/paste
data from Excel, or upload a CSV file. Produces a regression table report,
survival plot, survival table, log-rank test, and a predicted survival plot
for specified covariable patterns. Uses the R statistical engine on the
ShinyApps server to provide very high-quality output. Written by Soren
Merser.
* Compare Average Survival Time between two distributions -- Enter the number
of events and the average time to event for each of two groups. The
calculator will display the confidence interval around each mean time, and
will compare the two mean times. (Assumes an exponential-shaped survival
curve.)
--------------------------------------------------------------------------------
BAYESIAN METHODS... [RETURN TO TABLE OF CONTENTS]
* Bayesian Credibililty Analysis -- allows the credibility of a clinical trial
finding to be assessed in the light of current knowledge. This page takes the
odds ratio and its confidence interval from a clinical trial, and uses a
newly-developed Bayesian method to calculate a quantity called the critical
odds ratio (COR). If odds ratios at least as impressive as that indicated by
the COR can be justified by existing knowledge, then the results of the
clinical trial can be deemed credible.
* Etiologic Predictive Value (EPV) -- a new statistical method developed for
determining the probability of symptoms being caused by a bacteriological
finding, while taking carriers into consideration. To calculate EPV, one must
know the number of positive and negative tests among patients and healthy
controls as well as the sensitivity of the test. This enables calculating the
positive and negative EPV with a 95% confidence interval.
* Exact Bayes test for independence in r by c contingency tables -- Can also
handle comparison of observed-vs-expected, and observed-vs-uniform
situations.
* Analysis of "1-degree of freedom" data -- performs interactive frequentist
and Bayesian conditional tests for counts data having one degree of freedom.
That is, it does hypergeometric, binomial, Poisson, Bessel, and related
distributions (for double dichotomies, sign tests, a special kind of
structural zero design, etc.).
* Bayes' theorem calculations -- takes prior probabilities and conditional
probabilities, and calculates revised probabilities. (great for solving
certain kinds of brain teaser puzzles)
* Interpret P values -- Compute post test probability to take into account the
context of the experiment, as expressed by the prior probability that your
hypothesis is true.
* Bayesian calculations for diagnostic tests -- computes interrelationships
among true pos, true neg, false pos, false neg, prevalence, sensitivity,
specificity, predictive values, and likelihood ratios (requires JavaScript).
* Sequential Experimental Design for testing the probability ratios
* 2-by-2 table analysis (Chi-Square, sensitivity, odds ratio, relative risk,
etc. with confidence intervals
* 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.
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OTHER STATISTICAL TESTS AND ANALYSES... [RETURN TO TABLE OF CONTENTS]
* Diagnostic Test Calculator -- This calculator can determine diagnostic test
characteristics (sensitivity, specificity, likelihood ratios) and/or
determine the post-test probability of disease given given the pre-test
probability and test characteristics. Given sample sizes, confidence
intervals are also computed.
* 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.).
* 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).
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SPECIALIZED AND DISCIPLINE-SPECIFIC TESTS AND ANALYSES... [RETURN TO TABLE OF
CONTENTS]
* Martindale's Reference Desk - Calculators On-Line - Statistics (the
grand-daddy of all compendia of calculating web pages)
* Biostatistical Calculators:
* Evidence-Based Medicine (EBM) calculator -- From Warren Goff's
interestingly-named web site. Analyzes one or more fourfold (2x2) tables;
calculates Chi Square, CER, EER, and RR, and parameters related to
treatment (RRR, ARR, NNT, NNH, with 95% confidence intervals), diagnosis
(Sensitivity, Specificity, PPV, NPV, Prevalence, LR+, LR-, OR, Pre-Odds,
Post-Prob), and Harm (RR, OR NNH). Can also compare two different tables.
* Diagnostic Test Evaluation -- from a 2x2 cross-tab of diagnostic test
results (positive or negative) vs. true disease state (present or absent),
calculates sensitivity, specificity, positive and negative likelihood
ratios and predictive values, and disease prevalence, along with their 95%
confidence intervals.
* Risk Reduction Calculator -- Given information about the probability of an
outcome under control and experimental treatments, this calculator produces
measures of risk increase/decrease and number needed to treat or harm,
including confidence intervals. If some patients were lost to follow-up,
the calculator provides estimates for several different scenarios.
* Compute ECanything from EC50 (assuming a standard "Hill-type" dose-response
relationship). Very useful in dose-response studies.
* 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
* Scoring systems for ICU and surgical patients -- Online calculation of
scores used in general or specialized Intensive Care or Anesthesia,
including:
* Adult, General scores: SAPS II, APACHE II, SOFA, MODS , ODIN, MPM (on
admission , 24 hrs, 48 hrs , MPM Over Time) , MPM II (on admission,
24-48-72 hrs) , LODS, and TRIOS
* Adult, Specialized and Surgical Intensive Care - Preoperative evaluation:
EUROSCORE, ONTARIO, Parsonnet, System 97, QMMI, MPM, POSSUM, and
Portsmouth POSSUM
* Adult, Trauma scores: ISS/RTS/TRISS, and 24 h - ICU Trauma Score
* Adult, Therapeutic intervention, nursing ICU scores: TISS
* Pediatric, General scores: PRISM, DORA, PELOD, and PIM
* Pediatric, Specialized (Neonatal, Surgical): CRIB, SNAP, SNAP-PE, SNAP II
/ SNAPPE II
* Pediatric, Trauma Scores: Pediatric Trauma Score
* Some Calculators for Medical Purposes
* Item Analysis -- for multiple choice questionnaires
* Statistical Quality Control (SQC) Online -- Online calculators and tutorials
to perform SQC annd Statistical Process Control (SPC). Contains:
* Online versions of Military & Civilian Standard Tables: MS-105E / ANSI/ASQC
Z1.4, ISO 2859 (sampling plans for attribute data), MS-414 / ANSI/ASQC Z1.9
(sampling plans for measurement data, and MS-1235C (sampling inspection plans
for continuous production, Procedure CSP-1).
* Online Calculators for Process Capability Index (Cp), MTBF Calculator for a
system given the part (component) failure rate, and Control Charts and Runs
Rules (Switching Rules for MS-105E, Continuous Sampling CSP-1, Western
Electric Rules, and System Reliability for consecutive-type systems)
*
* Queuing Theory Calculator -- a remarkably powerful web calculator that can
solve a wide variety of queueing problems: single-server, multiple-server,
infinite-server, infinite or finite waiting room, Erlang loss model, and
machine interference model (with or without spare machines). Provides
detailed output in the form of averages, standard deviations, and frequency
distributions in the form of tables and graphs.
* Structural Engineering Calculators, from BuildingsGuide.com -- currently
includes ASCE 7-05 Code calculators for Snow Loading Analysis, Ice Loading
Analysis for WT, MT & ST shapes, for W, M, S & HP shapes, and for C & MC
shapes; Seismic Base Shear for single-level buildings, and Wind Loading
Analysis for low-rise buildings.
* Decision Making in Economics and Finance:
* ABC Inventory Classification -- an analysis of a range of items, such as
finished products or customers into three "importance" categories: A, B, and
C as a basis for a control scheme. This pageconstructs an empirical
cumulative distribution function (ECDF) as a measuring tool and decision
procedure for the ABC inventory classification.
* Inventory Control Models -- Given the costs of holding stock, placing an
order, and running short of stock, this page optimizes decision parameters
(order point, order quantity, etc.) using four models: Classical, Shortages
Permitted , Production & Consumption, Production & Consumption with
Shortages.
* Optimal Age for Replacement -- Given yearly figures for resale value and
running costs, this page calculates the replacement optimal age and average
cost.
* Single-period Inventory Analysis -- computes the optimal inventory level over
a single cycle, from up-to-28 pairs of (number of possible item to sell, and
their associated non-zero probabilities), together with the "not sold unit
batch cost", and the "net profit of a batch sold".
* Investment Derivative Calculations -- A very elaborate online calculator and
real-time data retrieval system. Includes economic regression analysis.
* Black-Scholes Calculator -- to place a value on stock options.
*
* Bardahl Calculator -- to compute the reasonable working capital needs of a
corporation.
* Probabilistic Modeling:
* Bayes' Revised Probability -- computes the posterior probabilities to
"sharpen" your uncertainties by incorporating an expert judgement's
reliability matrix with your prior probability vector. Can accommodate up
to nine states of nature.
* Decision Making Under Uncertainty -- Enter up-to-6x6 payoff matrix of
decision alternatives (choices) by states of nature, along with a
coefficient of optimism; the page will calculate Action & Payoff for
Pessimism, Optimism, Middle-of-the-Road, Minimize Regret, and Insufficient
Reason.
* Determination of Utility Function -- Takes two monetary values and their
known utility, and calculates the utility of another amount, under two
different strategies: certain & uncertain.
* Making Risky Decisions -- Enter up-to-6x6 payoff matrix of decision
alternatives (choices) by states of nature, along with subjective estimates
of occurrence probability for each states of nature; the page will
calculate action & payoff (expected, and for most likely event), min
expected regret , return of perfect information, value of perfect
information, and efficiency.
* Multinomial Distributions -- for up to 36 probabilities and associated
outcomes, calculates expected value, variance, SD, and CV.
* Revising the Mean and the Variance -- to combine subjectivity and
evidence-based estimates. Takes up to 14 pairs of means and variances;
calculates combined estimates of mean, variance, and CV.
* Subjective Assessment of Estimates -- (relative precision as a measuring
tool for inaccuracy assessment among estimates), tests the claim that at
least one estimate is away from the parameter by more than r times (i.e., a
relative precision), where r is a subjective positive number less than one.
Takes up-to-10 sample estimates, and a subjective relative precision (r<1);
the page indicates whether at least one measurement is unacceptable.
* Subjectivity in Hypothesis Testing -- Takes the profit/loss measure of
various correct or incorrect conclusions regarding the hypothesis, along
with probabilities of Type I and II errors (alpha & beta), total sampling
cost, and subjective estimate of probability that null hypothesis is true;
returns the expected net profit.
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POWER, SAMPLE SIZE AND EXPERIMENTAL DESIGN CALCULATIONS... [RETURN TO TABLE OF
CONTENTS]
Check out the PowerAndSampleSize.com web site, which contains (at last count) 19
interactive calculators for power or required sample size for many different
types of statistical tests: testing 1 mean, comparing 2 or more means, testing 1
proportion, comparing 2 or more proportions, testing odds ratios, and two
1-sample tests (normal and binomial-based). This site also provides calculators
for non-inferiority and equivalence studies. The web pages display graphs that
dynamically show how power varies with various design parameters as you change
other parameters.
Also, look at 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:
* For one-group tests (comparing the sample to a specified value) or for paired
two-group tests...
* Required sample size or power for testing one mean for equality, or
non-inferiority or superiority, or equivalence.
* Required sample size or power for a one-sample normal-based test of a mean.
* Required sample size or the statistical power when comparing the mean of a
sample to a specific value.
* Power/Sample-size for One-sample or Paired t test -- select the One-sample
t test (or paired t) option, then click the Run Selection button.
* Confidence Interval around a mean -- select the CI for one mean option,
then click the Run Selection button.
* Comparing a mean to a specified value
* Required sample size or power for a one-sample binomial test of a
proportion.
* Required sample size or power for testing one proportion for equality, or
non-inferiority or superiority, or equivalence.
* Comparing a proportion to a specified value
* Comparing a proportion to a specified value
* Power/Sample size to compare a proportion to a specific value -- select the
Test of one proportion option, then click the Run Selection button.
* Sample-size for Conf Interval around a proportion -- select the CI for one
proportion option, then click the Run Selection button.
* 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:
* Calculates sample size for given population size, confidence interval
(margin of error), confidence level, and population proportion. Also
displays margin of error for three other specified sample sizes (your
choice), and sample sizes for three other specified confidence levels.
* Find the required sample size or statistical power for comparing an
observed proportion with a specific value
* Find the sampling error in an observed proportion
* Calculate sample size required for a given confidence interval, or
confidence interval for a given sample size. Can handle finite populations.
Downloadable program also available.
* Another sample-size / confidence interval calculator for proportions in
finite samples
* Sample size or confidence interval of a proportion
* For two-group tests...
* Comparing means for two independent samples...
* Required sample size or power for testing two means for equality, or
non-inferiority or superiority or equivalence.
* Required sample size, or the statistical power when comparing the means
of two samples (can have different standard deviations)
* JavaScript based forms for simple power/sample size calculations.
* Same-size samples; equal or unequal variances
* Power/Sample-size for equal-variance or unequal-variance t-tests --
select the Two-sample t test (pooled or Satterthwaite)option, then click
the Run Selection button.
* A graphical interactive power/sample-size calculator for equal-variance
two-group test. A short tutorial here.
* Sample size for parallel-group equivalence and superiority trials, with
continuous outcome variables.
* Difference between two proportions (as, for example, by a Chi Square test
on a 2-by-2 cross-tab)...
* Required sample size or power for testing two proportions for equality,
or non-inferiority or superiority, or equivalence.
* Equal sample sizes (easy to use; with a good explanation)
* Equal sample sizes -- easy to use, with graphical display
* Equal- or unequal-size samples
* Find the required sample size or statistical power for comparing two
observed proportions
* Power/Sample-size for comparing two proportions -- select the Test
comparing two proportions option, then click the Run Selection button.
* Sample size for parallel-group equivalence and superiority trials, with
binary outcome variables.
* Test an odds ratio (from a 2x2 table) for equality, or non-inferiority or
superiority, or equivalence.
* 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
* Required sample size or power for comparing N groups, two at a time, by a
1-way ANOVA.
* Sample size computation for multiple comparisons -- said to be more
"realistic" than ordinary ANOVA sample size calculations (explained on the
web page)
* Very general power calculator -- select the Balanced ANOVA (any model)
option, then click the Run Selection button.
* Simplified power analysis for multi-way ANOVA designs
* Power/Sample-size for Chi-square tests of tables larger than 2x2 -- select
the Generic chi-square test option, then click the Run Selection button.
* Required sample size or power for compairing N proportions, two at a time,
by a 1-way ANOVA.
* For regressions and correlation tests...
* 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
* Sample-size for multiple regression -- will tell you the minimum required
sample size for your study, given the alpha level, the number of
predictors, the anticipated effect size (as f2), and the desired
statistical power level. If you know the effect size as R2, you can
calculate f2 from R2 with this calculator.
* Power/Sample-size for simple or multiple linear regression -- select the
Linear regression option, then click the Run Selection button.
* Beta level for multiple regression (i.e., the Type II error rate, which is
1 minusPower), given the observed alpha level, the number of predictors,
the observed R2, and the sample size.
* Post-hoc power for multiple regression -- calculates the observed power for
your study, given the observed alpha level, the number of predictors, the
observed R2, and the sample size.
* Power calculations for logistic regression with binary exposure- and
covariables.
* Other power calculations...
* Sample size calculator for pilot or safety studies where the goal is to
detect the occurrence of one or more events that might indicate possible
problems in study design (ambiguous inclusion criteria, misinterpretation
of questionnaire items) or product safety (occurrence of serious adverse
events, abnormal lab tests, or other safety markers). Enter the prevalence
rate you want to be able to detect (like one in a hundred), and the
probabibility you want to have of seeing at least one such event in your
sample (like 95% probability), and the page will tell you how many subjects
you need in the study.
* Online sample size calculator for pilot studies.
* Sample Size Determination -- For several situations: ANOVA and 2-population
economic sampling, correlation with acceptable absolute precision,
estimating the mean or proportion with acceptable absolute or relative
Precision, estimating the mean or proportion from finite populations, and
testing the mean or proportion based on the Null and an Alternative.
* Power calculations for clinical trials and scientific experiments -- this
page contains a table for selecting appropriate calculator, based on the
type of study (parallel, crossover, or test of association) and the type of
outcome measurement (success/failure, time-to-event, or a numerical
quantity).
* Survival Analysis -- computes power, sample size, or detectable-effect size
in a two group design with a survival outcome.
* Generic Poisson Test -- select the Generic Poisson test option, then click
the Run Selection button.
* Exact power for the Fisher exact test
* Find sample size, power and minimal detectable difference for a:
* study on the effect of one variable on another (linear regression)
* cross-over study were the outcome is a measurement (paired t-test or
non-parametric equivalent)
* parallel trial where the outcome is a measurement (unpaired t-test or
non-parametric equivalent)
* 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...
* WebDOE(tm) -- for "design of experiments". Searches for I-, D- and
A-optimal designs over continuous spaces. Factors may be continuous,
fixed-level, or qualitative. The site can handle inequality and equality
(e.g., mixture) constraints; provides color plots; performs one-click,
run-order-randomization; allows design import/export interoperable with
most 3rd-party analysis software; provides OLS and BLUP fits; and includes
an extensive Classical Design Library(tm), including factorial,
fractional-factorial, Box-Behnken, central-composite, Plackett-Burman,
orthogonal array, and uniform designs. All designs may be evaluated under
the I-, D-, and A-, and S-optimality criteria, as well as for the maximum
distance between nearest-neighbor pairs of design points (maximin
criterion). The My WebDOE(tm) feature allows users to store their designs,
evaluations, and fits on-line. There is no need for user-provided
candidatepoints.
* Design and Analysis of Comparative Experiments website by Horticulture
Research International -- provides facilities for the design and analysis
of of comparative experiments for biological and agicultural research based
on a range of experimental block and treatment structures. Constructs
simple experimental designs interactively and also constructs appropriate
statistical software for the analysis of the designs. Handles Randomised
block, Split-plot, Latin and incomplete Latin square, Trojan and incomplete
Trojan square designs.
* Tables of Latin Squares for constructing "Williams design" experiments, in
which every subject receives every treatment. These designs are balanced
for first-order carry-over (residual effects). Tables are provided for
experiments ranging from 2 to 26 treatments. Tables can also be downloaded
as a text file and as an Excel spreadsheet.
* More Latin Squares
* Sample-size calculations for parallel-group equivalence and superiority
trials with continuous or binary outcome variables.
* 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
* Type I & II error criteria. [see Simon, Controlled Clin Trials,
10:1-10,1989]
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