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.
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:
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.
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.
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.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.
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.
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.
StatsCalculators.com -- Slick and modern design, thoroughly validated, tutorials,
step-by-step guides and examples.
Include option for data visualization and calculators for descriptive statistics, hypothesis testing, probability distributions,
confidence intervals and regression (linear, non-linear and logistic)
It's free! No ads!
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.
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...
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 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:
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.
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:
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
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
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 -- 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.
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
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
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.
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
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)
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.
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.
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.
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.
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.
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.
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-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.
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.
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.
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.
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"
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.
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.
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.
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
This is a re-implementation of John Pezullos original page above, accommodating for 2x2 or more (i.e. N-by-M) contingency tables
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
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.
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)
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.
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.
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.
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.
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.
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...
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.
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.
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.
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.
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 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.
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)
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.
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.
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.
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.
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.
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.
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.
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...
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.
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.
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.
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.
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.
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.
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]
Please send all suggestions for new pages, notifications for dead links, and other requests in an e-mail to statpages.org@gmail.com
