Sections of the StatPages.net (statpages.info and statpages.org) website
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Web Pages that Perform Statistical Calculations!
Precision Consulting
 Offers dissertation help, editing, tutoring, and coaching services on a variety of statistical
methods including ANOVA, Multiple Linear Regression, Structural Equation
Modeling, Confirmatory Factor Analysis, and Hierarchical Linear Modeling.
If you're stuck on your proposal, methodology, or statistical phase of
your dissertation, you might want to
contact them.

The web pages
listed below comprise a powerful, convenientlyaccessible, multiplatform
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 email 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, singlepopulation tests
 Sample comparisons: ttests, ANOVAs, nonparametric
comparisons
 Contingency tables, crosstabs, ChiSquare tests
 Regression, correlation, least squares
curvefitting, nonparametric correlation
 Analysis of survival data
 Bayesian Methods
 Other statistical tests and analyses
 Specialized and disciplinespecific tests and
analyses
 Power, sample size and experimental design
Other Statistical Resources...
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.
 Choosing a Statistical Test, Chapter 37 of Dr. Harvey
Motulsky's book Intuitive Biostatistics.
 "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
"standalone" 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 browserbased version of
Stratigraphics statistical software. Provides plotting, probability
distributions, summary statistics, one, two, and multiplesample analysis,
timeseries analysis, regression analysis, curvefitting, attribute estimates,
ANOVAs, Statistical Process Control, smoothing, power/samplesize
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 singleuser copy or a
corporate deployment license can be purchased. To use the Guest version, click here.
 OpenEpi Version 2.2 
OpenEpi is a free, webbased, open source, operatingsystemindependent 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 popup 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 computergenerated
analogs of popular games and processes), Analyses (collection of common
webaccessible tools for statistical data analysis), Games (interfaces and
simulations to reallife processes), Modeler (tools for distribution,
polynomial and spectral modelfitting and simulation), Graphs, Plots and
Charts (comprehensive webbased tools for exploratory data analysis),
Additional Tools (other statistical tools and resources), SOCR Wiki
(collaborative Wiki resource), Educational Materials and Handson 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
wellorganized output of results, with interpretations and graphical
displays.
 MedCalc  Two different web sites:
 ProtoGenie  a free
extensible webbased 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 standalone 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, printpreviewed
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 userdefined 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 stepbystep 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 payfor service, but they offer onemonth free trials.
 Expression Evaluators  type in any numeric
expression; the computer will evaluate it and display the results...
 Scientific Calculator (numeric
expression evaluator)
 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.
 Calculators  pages that look and act like a
pocket calculator...
 Plotters  type in any algebraic function; it
displays the graph...
 Function plotter  Lets you zoom in and out to view any
portion of the graph. (Needs Java.)
 Function plotter  Produces a small 3D plot of almost any
function or relation found in high school and undergraduate college
mathematics. Plots functions of the form y = f(x), such as y = x2 or y = 3x
+ 1, or relations of the form f(x,y) = g(x,y), such as x2 + y2 = 4. (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 webbased interface to the "R" statistical programming
language (similar to S or Splus)
 Mx 
 a matrix algebra interpreter and numerical optimizer for
exploration of matrix algebra. Many builtin 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,multifunction pages first...
 These pages contain calculations for a very wide assortment of
probability distribution functions, including Normal, Bivariate Normal,
Student t, ChiSquare, Fisher F, Bivariate Normal, Noncentral Student t,
Noncentral ChiSquare, Noncentral Fisher F, Poisson, Lognormal,
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, chisquare,
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, ChiSquare, and Binomial (density and cumulative)
probabilities; Use e.g. dnorm, qnorm, rnorm.)
 Central and tail areas for Normal, Student, F, ChiSquare,
Binomial, and Poisson distributions
 Statistical probability distribution
functions: Normal, Student t, ChiSquare, Fisher F
 Pvalues for the Popular Distributions  Binomial ,
Chisquare, Exponential , Fisher's F, KS: Two Samples , Poisson, Normal ,
Student's t, and Uniform distributions.
 Calculate pvalue from z, t, F, r, or Chi Square; or do
the reverse.
 Reverse computations: enter pvalue (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 (1tailed)
 Cumulative area under the normal curve (integral from
minus infinity to z)
 ChiSquare probabilities, and reverse, with a detailed
explanation
 ChiSquare Distribution
 ChiSquare Distribution
 Student t Distribution
 inverse (t value from p value)
 Probabilities for the Fisher F distribution
 Another Fisher F distribution pvalue calculator.
 Critical Fisher F value, given the alpha level, the
numerator and denominator d.f.
 Noncentral F value (by Laubscher's square root
approximation), given the Fvalue, numerator and denominator d.f., and the
noncentrality parameter.
 Binomial, Poisson and Gaussian distribution
probabilities
 Binomial probability calculator
 Binomial Approximation of the Normal Distribution
 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, ChiSquare, Binomial Test, Wilcoxon RankedSums Test, Wilcoxon Signed Ranks Test, and Correlation Coefficient
 Converting r to Z
 Statistical Power of: Z Test, tTest for One Sample or Two Related Samples, tTest 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:
 generates M groups of N numbers each by distributing the numbers from
1 to M*N randomly into the M groups
 generates M blocks of N numbers each by randomly shuffling the numbers
from 1 to N in each block
 generates a subset of N numbers by random selection from a list of the
numbers from 1 to M
 Combinatorial
Objects Server  generates an incredible assortment of...
 Permutations and their restrictions
 Subsets or Combinations
 Permutations or Combinations of a Multiset
 Set Partitions
 Numerical Partitions and relatives
 Binary, rooted, free and other trees
 Necklaces, Lyndon words, DeBruijn Sequences
 Irreducible and Primitive Polynomials over GF(2)
 Ideals or Linear Extensions of a Poset
 Spanning Trees and other Subgraphs of a Graph
 Unlabelled Graphs
 Pentomino Puzzles, Polyominoes, nQueens
 and other puzzles and Miscellanea
 Statiscope  a beautifullyimplemented 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, AndersonDarling 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, 1^{st} & 3^{rd} 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 DurbinWatson 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, 25^{th} percentile, median,
75^{th} 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.
 Confidence Intervals...
 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 1sided and 2sided 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 .
 SinglePopulation 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 OneSample Student t Test page  enter or
paste raw data, or enter mean, SD or SEM, and N
 Onesample Student t test for Mean vs. a Specified Value
 for up to 80 observations, and a postulated population mean.
 Another Student ttest 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 nonparametric 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 pvalue of the
frequentist test.
 Test observed vs. expected rates of occurrence of events,
based on Poisson distribution; also includes confidence intervals and
analysis of rateratios (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 rateratio, 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 MultiCounts  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 JarqueBera statistic
 Test for Homogeneity of a Population  enter form 25 to
84 values; page provides information to test whether histogram is unimodal.
 ShapiroWilk 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 KolmogorovSmirnov 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.
 ChiSquare "Goodness of Fit" test for observed vs expected
counts (NOT from Contingency Tables)...
 Measurement Errors and Error Propagation...
 Student ttest (for comparing two samples)...
 a very
general Student ttest web page  paired or unpaired, equal or
unequalvariance, from individual observations (which can be keyentered 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 twogroup 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.
 ttest, paired or unpaired
 ttest, paired or unpaired
 ttest, paired or unpaired
 ttest, 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 ttest from summary data (N, mean, SD)
 Very general ttest 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 ...
 OneWay and Factorial ANOVA for uncorrelated
samples (extension of unpaired Student ttest to more than 2
groups)...
 Oneway ANOVA, with graphical output
 Oneway ANOVA for 3 Independent Samples
 ANOVA: Testing the Means  Oneway ANOVA for three
groups, each containing up to 40 subjects.
 Oneway ANOVA for 4 Independent Samples
 Oneway ANOVA from summary data
(N, mean, and SD or SEM)  Now also does Tukey HSD posthoc test!
 Another 1way ANOVA from summary data
 Oneway ANOVA  Also produces a posthoc analysis
(which groups are different from which others), and a scatterplot of all
groups. For a description of the ANOVA, click here.
 Twoway factorial ANOVA for 2 rows by 2 columns
 Twoway factorial ANOVA for 2 rows by 3 columns.
 TwoWay ANOVA Test  for blocked designs of up to 4
groups by 6 treatments.
 TwoWay ANOVA with Replications  for blocked designs
of up to 4 groups by 6 treatments, with up to 4 replications.
 Twoway ANOVA  enter data into the web page, or read
it from a text file. For an explanation, click here.
 Twoway 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 oneway ANOVA.
 Very general nway factorial ANOVA, with interactions,
means table, interaction plots, Bonferroni posthoc multiple comparisons,
and confidence intervals. (When you get to the Rweb page, scroll
down to the Analysis Menu and select ANOVA.)
 RepeatedMeasures ANOVA for correlated samples
(extension of paired Student ttest to more than 2 matched
measurements)...
 Bartlett's Test for Equality of Multivariances  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.
 Posthoc Tests  After doing a twoway (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 posthoc 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
 Nonparametric tests (use these when the data is
not normally distributed)...
 Sign test for matched pairs
 Median test for unmatched pairs
 Wilcoxon SignedRanks test for matched pairs  a
nonparametric 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 SignedRanks 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 MannWhitney U
test, with up to 80 observations per sample.
 MannWhitney U test  a nonparametric substitute for the
unpaired Student t test when the data is not normally distributed. This page
also produces a dotplot and a histogram of the data for each group. For a
detailed description of the test, with formulas and examples, click here.
 KS Test for Equality of Two Populations  Given two sets
of frequencies (using the same grouping intervals), this page calculates the
KolmogorovSmirnov test.
 Twosample KolmogorovSmirnov Test  Enter numbers into
the web page, or read them in from text files. Also graphs the cumulative
distribution of the two samples.
 Wilcoxon SumofRanks (MannWhitney) test for comparing two
unmatched samples
 KruskalWallis test (nonparametric ANOVA) for 2 or more
groups of unpaired data  This page requires that you first
crosstabulate 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.
 KruskalWallis test  This page also produces a
scatterplot of ranks for all groups.
 Least Significant Difference between mean ranks (posthoc
test after a significant KruskalWallis test)
 Friedman test for comparing rankings (nonparametric)
 Twogroup ordinal comparisons to assess how probable it is
that the two groups come from a single ordering, using WaldWolfowitz,
Randomness Test, MannWhitney, and KolmogorovSmirnov
 Twogroup paired comparisons, using Ttest, 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.
 ChiSquare tests...
 Quick ChiSquare  Manual entry (tab or comma delimited) or Copy/paste Excel data directly.
Calculates Expected Cell Values, ChiSquare and Pvalue for any 2D Contingency Table.
 2by2 table analysis
(Chisquare, 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 2by2 table, by Fisher Exact, and by Chi Square (with
and without Yates' correction), with a good explanation
 for 2by2 table
 2by2 table analysis (Chi Square, Fisher Exact,
difference in proportions, risk ratio, odds ratio, theta, logodds ratio,
Poisson test)
 Diagnostic Test Evaluation  from a 2x2 crosstab 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 2byN 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.
 Chisquare Test for Relationship  for up to a 6by6
crosstab.
 for anysize table
 another for anysize table
 Exhaustive analysis of 2by2 tables, with Pearson
Chisquare, Likelyhood Ratio ChiSquare, Yates Chisquare, Mantel Haenszel
Chisquare, Odds Ratio, Log Odds Ratio, YulesQ, YulesY, Phisquare,
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 nonzero difference.)
 Also see the EvidenceBasedMedicine (EBM) calculator in the
"Biostatistical Calculators" section of the "Other Statistical Tests and Analyses" section of this
page.
 Threedimensional Tables (2x2x2)...
 Fisher Exact tests for contingency tables...
 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, 5by5 table or less)
 Contingency table for sequenced categories
This is a reimplementation of John Pezullos original page above, accommodating for 2x2 or more (i.e. NbyM) contingency tables
 Contingency table for sequenced categories, 5by2 table,
with exact probability calculations
 Spearman's correlation from crosstabbed data with sequenced row
and column categories
 McNemar's test to analyze a matched casecontrol 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 observedvsexpected, and observedvsuniform situations.
 Comparison of ratings or rankings by different
raters...
 ChiSquare test for equality of distributions
 ChiSquare "Goodness of Fit" test for observed vs expected
counts (NOT from Contingency Tables)...
 Straight Lines and Correlation Coefficients...
 Least squares regression. (nice interface)
 Linear correlation and regression (nicely designed)
 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 2parameter 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.
 Calculate partial correlation coefficients
r_{bc.a}, r_{ac.b}, r_{ab.c} from r_{ab},
r_{ac}, r_{bc}
 WebStat (an integrated (Java)
applet) can perform simple regression analysis
 Correlation Tests...
 Spearman's rank correlation (nonparametric)...
 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 nonparametric
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 ttests, 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
NbyN 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 interrelationships between three partial correlation
coefficients.
 Beyond Simple 2parameter Curvefitting...
 Very general nonlinear leastsquares
curve fitter  almost any function you can write up to 8 nonlinear
parameters, up to 10 independent variables.
 MyCurveFit.com  an
easytouse curvefitting page. Offers 13 predefined functions (no
initial guesses required), along with the ability to fit a general
nonlinear function you provide (along with initial guesses). Displays the
results graphically, along with the formula of the fitted curve.
Several types of unequal datapoint 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 nonlinear
leastsquares curvefitter  with an enormous list of predefined 2D
and 3D functions, and extensive graphical and statistical output.
 Another nonlinear leastsquares curve fitter  with
graphical output! Choose one of 15 predefined nonlinear functions of one
variable and up to three parameters.
 3D
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
3D 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 commonlyoccurring
nonlinear functions (gaussians, sigmoidals, rationals, sinusoidals, etc.),
and then ranks them according to goodnessoffit.
 Compare
the fit of two models to your data. Which model fits better? Enter
goodnessoffit (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 curvefitter 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 pointandclick 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)
 Cox Proportional Hazards Survival
Regression Analysis
 A faster version of Cox
Proportional Hazards Analysis
 CoxReg, advanced Cox
Proportional Hazards Regression Analysis
 Regression by Prevalence  when you have data on the
number of occurrences and nonoccurrences 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 DurbinWatson 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 onelagapart &
twolagapart autocorrelations. A related page: Time Series' Statistics calculates these statistics, and
also the overall mean & variance, and the first & second partial
autocorrelations.
 KaplanMeier 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 logrank test. Uses the R statistical engine on the ShinyApps
server to provide very highquality output. Written by Soren Merser.
 KaplanMeier Survival Plot  for one or more groups. Draws
KM curves with optional confidence bands (ordinary, log, or loglog 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).
 KaplanMeier 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 (KaplanMeier)  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
proportionalhazards regression analysis and return the regression
coefficients, their standard errors, hazard (risk) ratio, and their confidence
intervals, and the baseline survivor curve, along with goodnessoffit
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, logrank test,
and a predicted survival plot for specified covariable patterns. Uses
the R statistical engine on the ShinyApps server to provide very
highquality 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 exponentialshaped
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 newlydeveloped 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 observedvsexpected, and observedvsuniform situations.
 Analysis of
"1degree 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
 2by2 table analysis (ChiSquare,
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.
 Diagnostic Test Calculator  This calculator can determine diagnostic test characteristics
(sensitivity, specificity, likelihood ratios)
and/or determine the posttest probability of disease given given the pretest 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. Payfor plans also provide an autooptimizer,
optimization comparison, manual optimizer, and control of survey analysis.
 Queueing Theory Calculator  Performs classic calculations
for singleserver or multiserver queues (queue length, waiting time,
etc.).
 Interactive CrossValidation  Performs the "leaveoneout"
crossvalidation inference for: central tendency, leastsquares lines,
onedimensional multinomial tables, twodimensional contingency tables with
structural zeroes, ksample problems, and blockandtreatment designs. The web
page is welldocumented, 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 pvalues when performing
multiple comparisons (has an excellent discussion of this topic)
 Multiple comparisons correction (Bonferroni adjustment)
 Number
Needed to Treat, based on a 2by2 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 Casecontrol Studies
 NetMul: a browser interface to a program that performs:
 Principal Coordinate Analysis (PCO)
 coinertia analysis
 discriminant analysis and within or betweenclass 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 postoptimality analysis of
smallsize linear programming problems (constrained optimization).
 Martindale's Reference Desk  Calculators OnLine 
Statistics (the granddaddy of all compendia of calculating web pages)
 Biostatistical Calculators:
 EvidenceBased Medicine (EBM) calculator  From Warren
Goff's interestinglynamed 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, PreOdds, PostProb), and Harm (RR, OR NNH).
Can also compare two different tables.
 Diagnostic Test Evaluation  from a 2x2 crosstab 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 followup, the calculator provides estimates for several different scenarios.
 Compute
EC_{anything} from EC_{50}_{ }(assuming a
standard "Hilltype" doseresponse relationship). Very useful in
doseresponse studies.
 Thorough analysis of 2by2 table relevant to Predictions and
Diagnostic Tests  sensitivity, specificity, prevalence, diagnostic
accuracy, PPV, posttest 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, 244872 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, SNAPPE, 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: MS105E / ANSI/ASQC Z1.4, ISO 2859
(sampling plans for attribute data), MS414 / ANSI/ASQC Z1.9 (sampling plans
for measurement data, and MS1235C (sampling inspection plans for
continuous production, Procedure CSP1).
 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 MS105E, Continuous Sampling CSP1, Western
Electric Rules, and System Reliability for consecutivetype systems)

 Queuing Theory
Calculator  a remarkably powerful web calculator that can solve a wide
variety of queueing problems: singleserver, multipleserver, infiniteserver,
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 705 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 singlelevel buildings, and Wind Loading Analysis for lowrise 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.
 Singleperiod Inventory Analysis  computes the optimal
inventory level over a single cycle, from upto28 pairs of (number of
possible item to sell, and their associated nonzero 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 realtime data
retrieval system. Includes economic regression analysis.
 BlackScholes 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 upto6x6
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, MiddleoftheRoad, 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 upto6x6 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 evidencebased 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 upto10 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 1sample tests (normal and binomialbased). This site also
provides calculators for noninferiority 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/samplesize 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 chisquare and Poisson tests, and an
amazing variety of ANOVAs  1, 2, and 3way; randomized completeblock; Latin
and GrecoLatin squares; 1stage, 2stage, and factorial nested designs;
crossover; splitplot; stripplot; 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 standalone
application.
Here's a collection of online power calculator web pages for specific kinds
of tests:
 For onegroup tests (comparing the sample to a specified
value) or for paired twogroup tests...
 For designing surveys (sample size and confidence
intervals for proportions, based on sample size, with or without corrections
for finite populations:
 For twogroup tests...
 Comparing means for two independent samples...
 Difference between two proportions (as, for example, by a Chi Square
test on a 2by2 crosstab)...
 For ANOVAs and other multigroup comparisons...
 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 interrelationships between three partial correlation coefficients
 Samplesize 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 f^{2}), and
the desired statistical power level. If you know the effect size as
R^{2}, you can calculate f^{2} from R^{2} with this
calculator.
 Power/Samplesize 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 R^{2}, and the sample size.
 Posthoc power for multiple regression  calculates the
observed power for your study, given the observed alpha level, the number of
predictors, the observed R^{2}, and the sample size.
 Power calculations for logistic regression with binary exposure and covariables.
 Other power calculations...
 Retrospective power analysis
(after doing the test) Before doing a retrospective power
analyses, check out Richard Stevens' humorous web page to see if you really
need to do one.
 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 2population 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,
timetoevent, or a numerical quantity).
 Survival Analysis  computes power, sample size, or
detectableeffect 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:
 Links to printable copies (in Adobe Acrobat PDF format) of
many power tables including: Z Test, tTest for One Sample or Two Related Samples, tTest 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 Aoptimal designs
over continuous spaces. Factors may be continuous, fixedlevel, or
qualitative. The site can handle inequality and equality (e.g., mixture)
constraints; provides color plots; performs oneclick,
runorderrandomization; allows design import/export interoperable with most
3rdparty analysis software; provides OLS and BLUP fits; and includes an
extensive Classical Design Library(tm), including factorial,
fractionalfactorial, BoxBehnken, centralcomposite, PlackettBurman,
orthogonal array, and uniform designs. All designs may be evaluated under
the I, D, and A, and Soptimality criteria, as well as for the maximum
distance between nearestneighbor pairs of design points (maximin
criterion). The My WebDOE(tm) feature allows users to store their designs,
evaluations, and fits online. There is no need for userprovided
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, Splitplot, 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 firstorder carryover
(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
 Samplesize calculations for parallelgroup
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,
10:110,1989]
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