Web
Pages that Perform
Statistical Calculations!
( StatPages.org )
(Updated 08/31/2011 -- Added a link to a Ukrainian translation of my
non-linear least squares curve-fitting page)
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.
All of these resources are freely accessible, once you can get onto the
Internet.
FREE
dial-up Internet access is
available
from NetZero.
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. Please let me know
of
any dead links, computational errors, or other problems you might
encounter
(e-mail me at johnp71@aol.com).
Table of Contents for
this
page...
- Selecting the right
kind of analysis
- "Online Software" Package
websites
- Calculators,
plotters, function
integrators, and interactive programming environments
- Probability distribution
functions: tables,
graphs, random number generators
- Descriptive
statistics, histograms,
charts
- Confidence intervals,
single-population
tests
- Sample comparisons:
t-tests, ANOVAs,
non-parametric comparisons
- Contingency tables,
cross-tabs, Chi-Square
tests
- Regression,
correlation, least squares
curve-fitting, non-parametric correlation
- Analysis of survival data
- Bayesian Methods
- Other statistical tests and
analyses
- Specialized and
discipline-specific
tests and analyses
- Power, sample size and
experimental design
Other Statistical Resources...
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
Biotatistics.
- "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.net web site, there are
many
"stand-alone" web pages that are each designed to perform only a single
test
or calculation. In addition, some talented individuals and groups have
created
coherent website that perform an entire suite of calculations,
with
a logical organization and consistent user interface. Each of these web
sites
is really a fairly complete online statistical software package in
itself.
Here are some of these "comprehensive" statistical analysis web sites:
- OpenEpi
Version 2.2 --
OpenEpi is a free, web-based, open source, operating-system-independent
series of programs for use in public health and medicine, providing a
number of epidemiologic and statistical tools. Version 2 (4/25/2007)
has a new interface that presents results without using pop-up windows,
and has better installation methods so that it can be run without an
internet connection. Version 2.2 (2007/11/09) lets users run the
software in English, French, Spanish, or Italian.
- SOCR --
Statistics Online
Computational Resource. A very comprehensive collection of
online
calculators and other interactive resources, including: Distributions
(interactive graphs and calculators), Experiments (virtual
computer-generated analogs of popular games and processes), Analyses
(collection of common web-accessible tools for statistical data
analysis), Games (interfaces and simulations to real-life processes),
Modeler (tools for distribution, polynomial and spectral model-fitting
and simulation), Graphs, Plots and Charts (comprehensive web-based
tools for exploratory data analysis), Additional Tools (other
statistical tools and resources), SOCR Wiki (collaborative Wiki
resource), Educational Materials and Hands-on Activities (varieties of
SOCR educational materials), SOCR Statistical Consulting and
Statistical Computing Libraries.
- ProtoGenie
-- a free
extensible web-based environment for research design and data
collection for surveys, experiments, clinical trials, time series,
cognitive and vision research, and methods courses. Lets you specify
groups and define measurement and treatment events and their
sequencing. The goal is to let users move smoothly from research design
and data collection to interim and final statistical analysis.
- Statlets
-- an "online statistical computing center" providing access to over 50
applets in which you can enter data, compute statistics, create tables
and graphs, and print out the results. Provides basic plotting,
probability distributions, summary statistics, one-sample analysis,
time-series analysis, two-sample comparisons, regression analysis,
attribute estimates, ANOVAs, and Statistical Process Control. This
public version supports up to 50 rows and 8 columns of data. For larger
data sets, a single-user copy or a corporate deployment license can be
purchased.
- The
Calcugator
-- a calculator, plotting engine, and programming environment. Also
available as a free stand-alone downloadable program. Simple to use;
rivals programs like MATLAB, with 200 functions/operators to perform
real, integer, rational, complex, boolean, statistical, vector, array
and matrix computations. Both the input and output of the program are
displayed on standard windows which can be further edited, saved,
merged, print-previewed and printed. Allows rapid creation of 2D and 3D
plots of functions, polar and parametric displays, bar, pie, pareto and
xy charts. All plots can be configured using the mouse (zooming,
panning, selecting). Titles and labels are supported, and all figures
created by the Calcugator can be exported into popular file formats or
pasted into an editable window. As a programming environment it has a
simple and compact language with identical syntax to Java/C/C++, and
allows user-defined functions.
- SISA
(Simple
Interactive Statistical Analysis) -- SISA allows you to do
statistical analysis directly on the Internet. Click on one of the
procedure names below, fill in the form, click the button, and the
analysis will take place on the spot. Study the user friendly guides to
statistical procedures to see what procedure is appropriate for your
problem.
- The
WebMath page performs
a large number of numeric calculations and symbolic algebraic
manipulations of the type that might arise in high school / college
algebra and calculus, including some elementary statistical
calculations. In doing so, it provides a detailed step-by-step
explanation of how it arrived at the answer.
- Expression Evaluators
-- type in any
numeric expression; the computer will evaluate it and display the
results...
- Calculators
-- pages that look and act
like a pocket calculator...
- Plotters --
type in any algebraic
function; it displays the graph...
- Function
plotter -- Lets you zoom in and out to view any portion of
the
graph. (Needs Java.)
- Function
plotter -- Produces a small 3D plot of almost any function
or
relation found in high school and undergraduate college mathematics.
Plots functions of the form y = f(x), such as y = x2 or y = 3x + 1, or
relations of the form f(x,y) = g(x,y), such as x2 + y2 = 4. (No Java
needed.)
- Linear
Programming Grapher-- Enter a linear function of two
variables to
be minimized, and any number of linear inequality expressions, and the
page will instantly solve it and display a graph showing the feasible
region and the constraints.
- Simplex
Tool -- Similar to the Linear Programming Grapher, but works
with
functions of more than two variables, and doesn't graph the results.
- Integrators
-- type in any function;
the computer displays the indefinite integral function (if one exists)
and/or the value of the definite integral (area under the curve)
between two endpoints...
- Interactive Programming
Environments
-- These pages implement various mathematical programming languages.
You can enter commands or entire programs (type or copy/paste) into the
web page, and they will be executed immediately.
- Rweb
--
an interactive web-based interface to the "R" statistical programming
language (similar to S or S-plus)
- SHAZAM
-- a
programming environment for econometricians, statisticians, and others
who use statistical techniques. Its primary strength is estimating and
testing many types of regression models. Provides a flexible command
language and capabilities for programming procedures. Has an interface
to the GNUPLOT package for high quality graphics.
- Mx
-- a matrix algebra interpreter and numerical optimizer for
exploration of matrix algebra. Many built-in fit fuctions for
structural equation modeling and other statistical modeling. Has
fitting fuctions like those in LISREL, LISCOMP, EQS and CALIS, along
with facilities for maximum likelihood estimation of parameters from
missing data structures, under normal theory. Users can easily
specify complex 'nonstandard' models, define their own fit functions,
and perform optimization subject to linear and nonlinear equality or
boundary constraints.
- Probability Integrals
-- these pages
take the place of a handbook of statistical functions. They're arranged
with the most comprehensive,multi-function pages first...
- These pages contain calculations for a very
wide
assortment of probability distribution functions, including
Normal,
Bivariate Normal, Student t, Chi-Square, Fisher F, Bivariate Normal,
Noncentral Student t, Non-central Chi-Square, Non-central Fisher F,
Poisson, Log-normal, Exponential, Beta, Gamma, Logistic, Binomial,
Negative Binomial, Multinomial, Cauchy, Gumbel, Laplace, Pareto,
Weibull, Uniform (continuous and discrete), Triangular, Geometric, and
Hypergeometric:
- Xuru's
page to
calculate PDFs, CDFs, and their complementary and inverse, along with
expected values, mean, variance, skewness & kurtosis, for
binomial,
geometric, negative binomial, Poisson, hypergeometric, normal,
chi-square, Student t and Fisher F distributions.
- Distribution/density
calculators, plotters and random number generators
- Very
sophisticated interactive page for over 65 continuous and discreet
statistical distribution functions -- Select a function from
a
menu, and it will show you a graph of that function along with its
properties. You can click on the graph to select limits, and it will
show you the left, middle and right integrals.
- These pages each compute probabilities for
the four most
common probability distributions:
- Normal,
t, Chi-Square, and Binomial (density and cumulative) probabilities;
(When you get to the Rweb page, scroll down to the Analysis
Menu and select Probability.)
- Central
and tail areas for Normal, Student, F, Chi-Square, Binomial, and
Poisson distributions
- Statistical
probability
distribution functions: Normal, Student t, Chi-Square, Fisher F
- P-values
for the Popular Distributions -- Binomial , Chi-square,
Exponential
, Fisher's F, K-S: Two Samples , Poisson, Normal , Student's t, and
Uniform distributions.
- Calculate
p-value from z, t, F, r, or Chi Square; or do the reverse.
- Reverse
computations: enter p-value (and, if necessary, sample sizes
and/or
d.f.); program will compute z, t, F, Chi Square, and correlation
coefficient
- These pages each compute probabilities
and/or inverses
for a specific distributions:
- Normal
distribution areas, with nice graphical interpretations
- Another
very good Normal Distribution calculator, with nice graphics
- A
very
attractive page for Normal distribution (and inverse), with detailed
explanations
- Normal
area (1-tailed)
- Cumulative
area
under the normal curve (integral from minus infinity to z)
- Chi-Square
probabilities, and reverse, with a detailed explanation
- Chi-Square
Distribution
- Chi-Square
Distribution
- Student
t Distribution
- Student
t
Distribution and its inverse
(t
value from p value)
- Probabilities
for the Fisher F distribution
- Another Fisher
F
distribution p-value calculator.
- Critical
Fisher
F value, given the alpha level, the numerator and denominator
d.f.
- Non-central
F
value (by Laubscher's square root approximation),
given the
F-value, numerator and denominator d.f., and the noncentrality
parameter.
- Binomial,
Poisson and Gaussian distribution probabilities
- 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, Chi-Square,
Binomial
Test, Wilcoxon
Ranked-Sums Test, Wilcoxon
Signed Ranks Test, and Correlation
Coefficient
- Converting
r to Z
- Statistical Power of: Z
Test, t-Test
for One Sample or Two Related Samples, t-Test
for Two Independent Samples, Analysis
of Variance, and Correlation
Coefficient
- Required
Sample Size for various tests
- Random Number Generators...
- Random
integers -- generates any number of random integers,
uniformly
distributed between any two limits
- Generate
tables of random integers from any specified range, or random
values from a Normal distribution with any specified mean and SD.
- Random
fractional numbers -- generates any number of random numbers,
each
a fraction between 0 and 1 with 8 digits after the decimal point
- Randomly
assign subjects to treatment groups -- can randomly choose a
group
for each subject, or randomly shuffle subjects within groups.
- Research
Randomizer
-- generates one or more sets of random numbers from a specified range,
with or without repeats, sorted or unsorted.
- Block
Randomizer
-- assigns subjects randomly to different groups, with multiple
blocking to ensure that imbalances are kept under control if the study
is terminated prematurely
- Random
assignment of subjects to one or more groups -- three
variations:
- generates M groups of N numbers each by
distributing the
numbers from 1 to M*N randomly into the M groups
- generates M blocks of N numbers each by randomly
shuffling the numbers from 1 to N in each block
- generates a subset of N numbers by random
selection from
a list of the numbers from 1 to M
- Combinatorial
Objects Server -- generates an incredible assortment of...
- Permutations and their restrictions
- Subsets or Combinations
- Permutations or Combinations of a Multiset
- Set Partitions
- Numerical Partitions and relatives
- Binary, rooted, free and other trees
- Necklaces, Lyndon words, DeBruijn Sequences
- Irreducible and Primitive Polynomials over GF(2)
- Ideals or Linear Extensions of a Poset
- Spanning Trees and other Subgraphs of a Graph
- Unlabelled Graphs
- Pentomino Puzzles, Polyominoes, n-Queens
- and other puzzles and Miscellanea
- Statiscope
-- a beautifully-implemented page for calculating and displaying a
large number of descriptive statistics from a set of numbers you enter
- WebStat
(an integrated applet) can generate summary statistics, as well as
histograms, stem and leaf plots, boxplots, dotplots, parallel
coordinate plots, means plots, scatterplots, QQ plots, and time series
plots
- Xuru's page
for
single variable descriptive statistics: mean, median, sd,
variance,
mean abs deviation, geometric mean & sd, skewness, kurtosis,
quartiles, standard errors, Anderson-Darling normality test, and some
confidence intervals of the mean and sd. You can copy and paste data
directly from a spreadsheet or a tabulated data file, or enter numbers
manually.
- Descriptive
Sampling Statistics -- Enter up to 80 numbers; this page will
calculate the mean, variance, SD, CV, skewness and kurtosis.
- Descriptive
statistics (mean, SD, SEM, and CI of mean). Can enter or
paste raw
data, or enter mean, SD or SEM, and N to get CI.
- Descriptive
Statistics -- Enter up to 80 values; page calculates: N,
mean,
variance, SD, CV, skewness, kurtosis, SEM, median, min, max, range, 1st
& 3rd quartiles, interquartile range,
quartile
deviation, coeff of quartile var, and absolute deviation.
- Measuring
for Accuracy -- Given a set of observed and
predicted values,
this page calculates the SD of errors, mean absolute & relative
error, and Durbin-Watson statistic.
- Arithmetic,
Geometric, and Harmonic Means -- of up to 80 values.
- Rweb
- extensive tabular and graphical descriptive summarization:
mean,
quartiles, histograms, scatterplot matrices (with smoothers), QQ plots
(normal and pairwise), time series, box plots. (When you get to the Rweb
page, scroll down to the Analysis Menu and select Summary.)
- The
Data Applet provides descriptive statistics, histograms,
boxplots,
and scatterplots
- A
variety of descriptive statistics and a stem and leaf display
- Detect
Outliers -- this calculator performs Grubbs' test, also
called the
ESD method (extreme studentized deviate), to determine whether one of
the values in the list you enter is a signficant outlier from the rest.
Also contains an excellent discussion of what to do
about
outliers.
- Combine
Subgroups -- calculate the mean and SD of a combination of
groups
from the N, mean and SD of each group.
- Basic
descriptive statistics (mean, sum of squares, variance,
standard
deviation, minimum, 25th percentile, median, 75th
percentile, and maximum for up to 500 numbers
- Empirical
Distribution Function -- from up to 42 sets of [value,
frequency].
- Multinomial
Distributions -- Enter up to 12 values and their
corresponding
probabilities, and this page will calculate Expected Value, Variance,
Standard Deviation, & Coefficient of Variation
- Paired
Data Sets Statistics -- Enter up to 28 sample paired data
sets, and
this page will calculate means, variances, and covariance
- Histogram
-- Enter up to 80 numbers, and this page will display a
histogram.
- Histogram
from a set of numbers, lets you dynamically alter the
interval
width and see the effect immediately
- Determination
and Removal of Outliers -- Given a set of numbers, this page
iteratively isolates potential outliers for removal.
- Generate
a
VRML file to view 3-dimensional (x,y,z) data. To view the
resulting
files requires a VRML
viewer.
- Compute
and plot a Kernel Density Estimate from a set of points,
using
Epanechnikov, triangular, biweight or Gaussian kernels
- Compute
Poisson change-point, that is: estimate when, in a long
sequence of
occurrences, the occurrence rate underwent a sudden change
- Confidence Intervals...
- for
the
difference between two means, given N, mean, SD for each group
- Exact C.I.'s for
Binomial (observed
proportion) and Poisson (observed count). (Also available as
an Excel spreadsheet, and
as an Excel Add-In.)
- Exact
and "modified Wald" C.I.'s for observed proportion or count,
with a
good explanation
- Confidence
interval around a proportion, given the population size, the
sample
size, the sample percentage and the confidence level. Has interesting
animation, plus a good explanation of the concepts. A
related
page has no animation, but can be printed out.
- Bayesian
"credible" intervals around an observed proportion. Somewhat
comparable to the "classic" confidence intervals, but tend to be
somewhat narrower.
- 95%
or 99%
C.I. for proportions for any specified sample size and population size
- Confidence
interval around an observed sample SD, assuming the data are
sampled from a Normal distribution
- Percentage:
Estimation & Testing -- calculates exact binomial
confidence
intervals and tests of hypothesis for population proportion, from
infinite or finite populations.
- Tolerance Intervals...
- Tolerance
Intervals for the Normal
Distribution. (Don't confuse tolerance
intervals with confidence
intervals!) A tolerance interval for a measured
quantity is the
interval in which there is a specified likelihood that a specified fraction
of the population's values lie. This page will calculate
1-sided
and 2-sided tolerance intervals for any specified population fraction,
and for any specified level of confidence, from the mean and standard
deviation of a finite sample, under the assumption that the population
is normally distributed. These calculations are also
available in a
downloadable Excel spreadsheet: tolintvl.xls
.
- Single-Population Tests...
- Sign
and Binomial test -- test an observed proportion against a
proposed
population proportion
- Mean,
SD,
confidence interval, etc. for a set of values
- An
excellent One-Sample Student t Test page -- enter or paste
raw
data, or enter mean, SD or SEM, and N
- One-sample
Student t test for Mean vs. a Specified Value -- for up to
80
observations, and a postulated population mean.
- Another
Student t-test of a single mean (vs specified value) from N, mean, SD
- Test
for
Asymmetry around zero -- Enter a set of numbers (usually a
mix of
positive and negative numbers), and the program will apply a
non-parametric test (originally created by R. A. Fisher) of whether the
numbers are consistent with a population frequency distribution that is
symmetrical around zero (but does not necessarily have to be normal).
It is a frequentist test to work Darwin's experiment with matched
pairs, and experiments like it.
- Test
for the mean being greater than some specified value. This
unusual
test is Bayesian and frequentist at the same time.
The null
hypothesis asserts some value for the mean of a population of positive
numbers; the alternative hypothesis says the mean is higher than that.
This test gives a Bayesian likelihood ratio that is also an upper bound
on the p-value of the frequentist test.
- Test
observed vs. expected rates of occurrence of events, based on
Poisson distribution; also includes confidence intervals and analysis
of rate-ratios (such as Standardized Mortality Ratio, Morbidity Ratio,
and Comparative Mortality Figure)
- Similar
to above, but used to study the distribution of accidents and events at
the individual level
- Exact
confidence intervals around a rate-ratio, using Liddell's
method
(also contains a number of common approximations, for comparison)
- Test
observed vs expected proportions, based on the Binomial
distribution
- Binomial
Test -- whether the number of "successes" differ from what
was
expected based on the number of trials and the probability of success.
- Similar
to above, but deals with the probability of a particular sample size,
given an observed 'x' number positive (or white, or car crashes) vs. an
expected 'U' proportion positive
- Compatibility
of Multi-Counts -- tests whether up to 14 observed event
counts
(each over the same amount of time) are consistent with a single
expected event rate.
- Runs
Test for Randomness -- Enter up to 80 numbers, and this page
will
calculate a runs test to see if the numbers form a random sequence
- Testing
the Variance -- of up to 80 observations against a postulated
population variance.
- Analyze
observed proportions in samples from finite populations,
based on
the Hypergeometric distribution
- Test
for Normality -- Enter up to 80 numbers, and this page will
test
for normality based on the Jarque-Bera statistic
- Test
for Homogeneity of a Population -- enter form 25 to 84
values; page
provides information to test whether histogram is unimodal.
- Test
for Normality -- enter up to 42 sets of [value, frequency];
page
will calculate skewness, kurtosis, and Liliefors test for consistency
with a normal distribution.
- Test
for Uniform Distribution -- enter up to 42 sets of [value,
frequency]; page will calculate the Kolmogorov-Smirnov test for
consistency with a uniform distribution.
- Testing
Poisson Process -- enter up to 14 sets of [value, frequency];
page
will calculate a Chi square test for consistency with a Poisson
distribution.
- Lilliefors
Test for Exponential Distribution -- tests whether a set of
observed values are consistent with an exponential distribution.
- Chi-Square "Goodness of
Fit" test for
observed vs expected counts (NOT from Contingency
Tables)...
- Measurement Errors and
Error Propagation...
- Student t-test
(for comparing two
samples)...
- a
very
general Student t-test web page -- paired or unpaired, equal-
or
unequal-variance, from individual observations (which can be
key-entered or copy/pasted) or summary data (N, Mean, SD or SEM).
Includes explanations and advice on carrying out this type of test.
- t-test,
paired
or unpaired
- t-test, paired
or unpaired
- t-test, paired
or unpaired
- t-test,
paired
- Paired
Student t Test -- on up to 42 pairs of values, along with a
postulated population mean difference.
- Testing
Two Populations -- Unpaired Student t test for up to 80
observations in each sample. Also accepts a postulated difference
between the two population means, which can be different from 0.
- Unpaired
t-test from summary data (N, mean, SD)
- Very
general t-test program for comparing measured quantities, observed
counts, and proportions between two unpaired samples; also
produces
risk ratio, odds ratio, number needed to treat, and population
analysis.
- ANOVA (Analysis of
Variance) --
comparison of two or more samples ...
- One-Way and Factorial
ANOVA for
uncorrelated samples (extension of unpaired Student
t-test to
more than 2 groups)...
- One-way
ANOVA, with graphical output
- One-way
ANOVA for 3 Independent Samples
- ANOVA:
Testing the Means -- One-way ANOVA for three groups, each
containing up to 40 subjects.
- One-way
ANOVA for 4 Independent Samples
- One-way
ANOVA from summary data
(N, mean, and SD or SEM)
- Another
1-way ANOVA from summary data
- Two-way
factorial ANOVA for 2 rows by 2 columns
- Two-way
factorial ANOVA for 2 rows by 3 columns.
- Two-Way
ANOVA Test -- for blocked designs of up to 4 groups by 6
treatments.
- Two-Way
ANOVA with Replications -- for blocked designs of up to 4
groups by
6 treatments, with up to 4 replications.
- Two-way
factorial ANOVA for 2 rows by 2 columns, from summary data (N, mean, SD)
- ANOVA
for Condensed Data Sets -- Enter up to 10 sets of (N, mean,
SD);
page calculates a one-way ANOVA.
- Very
general n-way factorial ANOVA, with interactions, means
table,
interaction plots, Bonferroni post-hoc multiple comparisons, and
confidence intervals. (When you get to the Rweb
page, scroll
down to the Analysis Menu and select ANOVA.)
- Repeated-Measures
ANOVA for
correlated samples (extension of paired Student
t-test to more
than 2 matched measurements)...
- Bartlett's
Test for Equality of Multi-variances -- for up to 14 sets of
[N,
variance].
- Post-hoc
Tests -- After doing a two-way (or other) ANOVA, post -hoc
tests
(also called post tests) compare individual pairs of groups. This
calculator does not perform the ANOVA calculations, but takes the
output from an ANOVA (residual means square error, degrees of freedom)
performs a post-hoc test between any pairs of cells that you select
(using cell means and N's), at whatever alpha you specify.
- Tukey
LSD (Least Significant Difference), using the standard table
produced by an ANOVA
- Scheffe
Least Significant Difference, using data from a standard
ANOVA
table and the N's for the two groups being compared
- Non-parametric tests
(use these when
the data is not normally distributed)...
- Sign
test for matched pairs
- Median
test for unmatched pairs
- Wilcoxon
Signed-Ranks test for matched pairs -- This page takes
case-by-case
pairs of matched data
- Another
Wilcoxon Signed-Ranks test for matched pairs -- This page
takes
summarized, tabulated data: how many cases had differences of +1, +2,
+3, etc., and -1, -2, -3, etc.
- Comparing
Two Random Variables -- by the Mann-Whitney U test, with up
to 80
observations per sample.
- 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.
- Wilcoxon
Sum-of-Ranks (Mann-Whitney) test for comparing two unmatched samples
- Kruskal-Wallis
test (non-parametric ANOVA) for 2 or more groups of unpaired data
-- This page requires that you first cross-tabulate your data into a
matrix, with a row for every group and a column for every different
numeric value that any subject had; the cell of the matrix tell how
many subjects (if any) in that group had exactly that numeric value.
- Least
Significant Difference between mean ranks (post-hoc test
after a
significant Kruskal-Wallis test)
- Friedman
test for comparing rankings (non-parametric)
- Two-group
ordinal comparisons to assess how probable it is that the two groups
come from a single ordering, using Wald-Wolfowitz, Randomness
Test,
Mann-Whitney, and Kolmogorov-Smirnov
- Two-group
paired comparisons, using T-test, Wilcoxon, Signs test, and
McNemar
test
- McNemar's
test for the paired comparison of proportions (or for matched pairs of
labels)
- Comparison of proportions
between two
groups...
- Comparison
of Binomial proportions
- 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.
- 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.
- WebStat
(an integrated (Java) applet)
can perform
Z-tests and T-tests (one- and two-sample) for population means, and
Chi-square and Fisher-F tests for population variances
- Chi-Square tests...
- 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. Also see Andrew Mackinnon's DAG_Stat
-- an Excel spreadsheet that contains even more quantities
(with
confidence intervals) that can be derived from a 2x2 table).
- EpiMax
Table Calculator -- similar to the above, but with a clearer
screen
layout.
- for
2-by-2 table, by Fisher Exact, and by Chi Square (with and
without
Yates' correction), with a good explanation
- for
2-by-2 table
- 2-by-2
table analysis (Chi Square, Fisher Exact, difference in
proportions, risk ratio, odds ratio, theta, log-odds ratio, Poisson
test)
- for
2-by-N table, where the two rows represent dichotomies like
lived/died, present/absent, yes/no. This can test for a trend in the
probability of an event when you have counts of the two categories over
a set of time intervals.
- Chi-square
Test for Relationship -- for up to a 6-by-6 cross-tab.
- for
any-size table
- another
for any-size table
- another
for any-size table (When you get to the Rweb
page, scroll
down to the Analysis Menu and select Two
Way.)
- Exhaustive
analysis of 2-by-2 tables, with Pearson Chi-square,
Likelyhood
Ratio Chi-Square, Yates Chi-square, Mantel Haenszel Chi-square, Odds
Ratio, Log Odds Ratio, Yules-Q, Yules-Y, Phi-square, Pearson
correlation, and McNemar Test
- Paired
Proportion Test -- for testing whether the proportion of
subjects
having some characteristic is the same in two matched groups or in one
group before and after some intervention. (Also can test against a null
hypothesis specifying some non-zero difference.)
- Also see the Evidence-Based-Medicine (EBM) calculator
in the
"Biostatistical Calculators" section of the "Other
Statistical Tests and Analyses" section of this page.
- Three-dimensional Tables
(2x2x2)...
- Fisher Exact tests
for contingency
tables...
- Test
differences between two observed proportions, based on the
Binomial
distribution
- Contingency table for
sequenced
categories (Ordinal by Ordinal, 5-by-5 table or less)
- Contingency
table for sequenced categories, 5-by-2 table, with exact
probability calculations
- Spearman's
correlation from cross-tabbed data with sequenced row and column
categories
- McNemar's
test to analyze a matched case-control study, with a good
explanation
- McNemar's
test for paired contingency tables
- Exact
Bayes test for independence in r by c contingency tables --
Can
also handle comparison of observed-vs-expected, and observed-vs-uniform
situations.
- Comparison of ratings or
rankings by
different raters...
- Chi-Square
test for equality of distributions
- Chi-Square "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.
- Several variations on 2-parameter linear regression (logarithmic
regression, exponential
regression, and power
regression)
- Simple
Linear Regression -- for up to 84 points, with extensive
output and
residual analysis.
- The
Data Applet provides descriptive statistics, histograms,
boxplots,
and scatterplots
- Scatter
Diagram and Test for Outliers -- for up to 84 points.
- Bivariate
Sampling Statistics -- calculates means, variances, and
covariance
for up to 42 [x,y] measurements.
- Calculate
partial correlation coefficients rbc.a,
rac.b,
rab.c from rab, rac,
rbc
- WebStat
(an integrated (Java) applet)
can perform
simple regression analysis
- Correlation Tests...
- Spearman's rank correlation (non-parametric)...
- Correlation
test
- Significance
level corresponding to a correlation coefficient
- 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
- 95%
Confidence Interval around an observed correlation coefficient.
- Comparison
of two correlation coefficients
- Comparison
of two or more correlation coefficients
- Comparison
of two sets of (X,Y) data to see if they are consistent with the same
straight line (tests whether the slopes are different, and
whether
the lines are vertically distinct)
- Comparing
Two Linear Regressions -- Enter two sets of [x,y] values;
page
calculates two straight lines, then compares slopes and intercepts.
- Test
for Several Correlation Coefficients -- enter up to 14 sets
of [N,
r]; page will test whether all r's are consistent with a single
population r value.
- Biserial
correlation coefficient from summary data (N, mean, SD) of
the X
and Y variables
- Lin's
"concordance correlation coefficient" -- first
proposed by
Lin (1989) for assessment of concordance in continuous data. A
breakthrough in assessing agreement between alternative methods for
continuous data. Seems to avoid the shortcomings of correlation
coefficient r, paired t-tests, least squares analysis for slope and
intercept, coefficient of variation, intraclass correlation
coefficient.. It is robust on as few as 10 pairs of data.
- Manipulation
of a correlation matrix -- you enter the N-by-N correlation
matrix,
the page computes all Partial Correlation Coefficients, all
Standardized Partial Regression Coefficients, and the Multiple
Correlation Coefficient for each variable.
- A
versatile page for calculating the significance of a correlation
(rho<>0), significance of the difference between two
correlations, power and sample size requirements for correlations
testing, and the inter-relationships between three partial correlation
coefficients.
- Beyond Simple 2-parameter
Curve-fitting...
- Very general
nonlinear least-squares
curve fitter -- almost any function you can write-- up to 8
nonlinear parameters, up to 10 independent variables. Also available in
Ukrainian !
- ZunZun non-linear
least-squares curve-fitter -- with an enormous list of
pre-defined
2-D and 3-D functions, and extensive graphical and statistical output.
- Another
non-linear least-squares curve fitter -- with graphical
output!
Choose one of 15 pre-defined nonlinear functions of one variable and up
to three parameters.
- Polynomial
Regression -- fit polynomials of degree 2 through 10.
- Multiple
Linear
Regression -- fit functions of more than one predictor
variable.
- Multiple
Polynomial Regression -- fit functions of one or more
predictors,
each expressed as polynomials, up to the order you specify.
- Nonlinear
Regression -- Automatically fits over 100 of the most
commonly-occurring non-linear functions (gaussians, sigmoidals,
rationals, sinusoidals, etc.), and then ranks them according to
goodness-of-fit.
- Compare
the fit of two models to your data. Which model fits better?
Enter
goodness-of-fit (SSQ, or weighted SSQ) and # of data points and # of
parameters for each model. The calculator will compare the models using
Akaike's method, , then the F test.
- Fit
"rational functions" (also called "Pade functions") to {X,Y}
data.
A rational function is a fraction whose numerator and
denominator
are both polynomials in X. They can fit a broader range of functions
than polynomials alone can -- they can fit data where the Y value
"levels off" to a horizontal line for very large or small X, and can
fit functions that have "singularities" (Y shoots to infinity at some
value of x). This curve-fitter is part of an extensive set of online
calculators
to solve problems in structural engineering (bending and
buckling
of beams and plates, etc.) at the Software for
Structures web
site.
- Univariate
and multiple regression, with very extensive
graphical output
(histograms, scatterplots, scatterplot matrices) and residual analysis
(QQ, histogram, residuals vs dependent or predictors). Very
intuitive point-and-click interface, dynamically customized for your
data. (When you get to the Rweb page, scroll down
to the Analysis
Menu and select Regression.)
- Automatic
Multiple Regression, (New
Web Address!)
automatically builds a model or regression equation! You merely supply
the dependent and independent variables and it does the rest. It will
find which variables are important enough to include in the model,
determine the proper transformation of each of those variables, then
look for 2-way and 3-way interaction terms important enough to include
in the model, and transform them appropriately.
- Multiple
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
- Regression
by Prevalence -- when you have data on the number of
occurrences
and non-occurrences of something over a set of time intervals. Tests
whether the probability of the occurrence shows a trend over time.
- Test
Bias
Assessment Program, computes statistics to help you decide if
test
scores predict a criterion differently across subgroups
- Time Series Analysis...
- Autoregressive
Time Series -- tools for the identification, estimation, and
forecasting based on autoregressive order obtained from a time series.
- Detecting
Trend & Autocrrelation in Time Series --
Given a set of
numbers, this page tests for trend by Sign Test, and for
autocorrelation by Durbin-Watson test.
- Plot
of a Time Series -- generates a graph of a time series with
up to
144 points.
- Seasonal
Index -- Calculates a set of seasonal index values from a set
of
values forming a time series. A related page performs a Test
for Seasonality on the index values.
- Forecasting
by Smoothing -- Given a set of numbers forming a time series,
this
page estimates the next number, using Moving Avg & Exponential
Smoothing, Weighted Moving Avg, and Double & Triple Exponential
Smoothing.
- Runs
Test for Random Fluctuations -- in a time series.
- Test
for Stationary Time Series -- Given a set of numbers
forming a
time series, this page calculates the mean & variance of the
first
& second half, and calculates one-lag-apart &
two-lag-apart
autocorrelations. A related page: Time
Series' Statistics calculates these statistics, and also the
overall mean & variance, and the first & second partial
autocorrelations.
- Kaplan-Meier
Survival Plot (with 95% Conf.Intervals) and LogRank Test
-- Type or copy/paste data, or read it in from a file.
Prepares
tables, graphs, and statistical comparison output. Can perform
stratified log-rank test.
- Life
Table
(Kaplan-Meier) -- Enter the number died and censored at each time
period, and the page calculates the cumulative survival probability and
95% confidence intervals. Also graphs the survival curve, and exports
the data, so you can create a better graph using another program.
- Cox Proportional
Hazards Survival
Regression Analysis -- specify each subject's observation
time and
status (last seen alive or dead), and any number of independent
variables (predictors, confounders, and other covariates). This web
page will perform a proportional-hazards regression analysis and return
the regression coefficients, their standard errors, hazard (risk)
ratio, and their confidence intervals, and the baseline survivor curve,
along with goodness-of-fit information. You can also use a faster version by Ronald
Brand (Leiden
University), or an enhanced
version by Kevin Sullivan (Emory University) that has
illustrative
examples and explanatory material.
- Comparison
of Two Survival Distributions, using data from a data file in
your
computer (many different file types are supported). A graph is returned
to your browser with the two survival curves plotted, along with the
estimated relative risk, standard error and p-value.
- Bayesian
Credibililty Analysis --
allows the credibility of a clinical trial finding to be assessed in
the light of current knowledge. This page takes the odds ratio and its
confidence interval from a clinical trial, and uses a newly-developed
Bayesian method to calculate a quantity called the critical
odds
ratio (COR). If odds ratios at least as impressive as
that
indicated by the COR can be justified by existing knowledge, then the
results of the clinical trial can be deemed credible.
- Etiologic
Predictive
Value (EPV) -- a new statistical method developed for
determining
the probability of symptoms being caused by a bacteriological finding,
while taking carriers into consideration. To calculate EPV, one must
know the number of positive and negative tests among patients and
healthy controls as well as the sensitivity of the test. This enables
calculating the positive and negative EPV with a 95% confidence
interval.
- Exact
Bayes test for independence in r by c contingency tables --
Can
also handle comparison of observed-vs-expected, and observed-vs-uniform
situations.
- Analysis
of
"1-degree of freedom" data -- performs interactive
frequentist and
Bayesian conditional tests for counts data having one degree of
freedom. That is, it does hypergeometric, binomial, Poisson, Bessel,
and related distributions (for double dichotomies, sign tests, a
special kind of structural zero design, etc.).
- Bayes' theorem
calculations -- takes
prior probabilities and conditional probabilities, and calculates
revised probabilities. (great for solving certain kinds of brain teaser
puzzles)
- Interpret
P values -- Compute post test probability to take into
account the
context of the experiment, as expressed by the prior probability that
your hypothesis is true.
- Bayesian
calculations for diagnostic tests -- computes
interrelationships
among true pos, true neg, false pos, false neg, prevalence,
sensitivity, specificity, predictive values, and likelihood ratios.
- Sequential
Experimental Design for testing the probability ratios
- 2-by-2 table analysis
(Chi-Square,
sensitivity, odds ratio, relative risk, etc. with confidence intervals
- Wald's
Sequential Probability Ratio's -- for designing a sequential
experiment in which a decision is made after each observation either to
accept the null hypothesis, accept the alternate hypothesis, or acquire
more observations.
- ReliCheck
-- an online
reliability analysis tool that allows users to check the reliability of
the scores on their survey. The free option provides reliability score,
statistical strength of survey, general item analysis, and a
statistical summary of the survey. Pay-for plans also provide an
auto-optimizer, optimization comparison, manual optimizer, and control
of survey analysis.
- Queueing
Theory Calculator -- Performs classic calculations for
single-server or multi-server queues (queue length, waiting time, etc.).
- Universal
Inventory/Test Scorer will instantly and automatically score
ANY
objective test or personality inventory/questionnaire. For
any
particular questionnaire, you create a text file that describes the
scores associated with each possible answer to each question
(True/False, A/B/C/D/E, Likert Scale, etc.). It is available as a Java
implementation and as JavaScript implementation. These will run online,
or can be downloaded to be run locally on your computer (offline from
the Internet).
- Interactive
Cross-Validation -- Performs the "leave-one-out"
cross-validation
inference for: central tendency, least-squares lines, one-dimensional
multinomial tables, two-dimensional contingency tables with structural
zeroes, k-sample problems, and block-and-treatment designs. The web
page is well-documented, with about a dozen examples worked out and
explained.
- Fittestmodel
--an
online forum, on which statistical evidence can be presented that is
always replicable, testable and extendible at the 'click of a button'.
The name Fittestmodel encompasses both the goal and
the means
of science, namely to find the fittestmodel by fitting, testing and
modelling. Users may discuss statistical evidence online or query for
results based on search criteria such as dataseries, methods or
criteria that measure the 'quality' of results. Publicly available
datasets from various sources may be combined into new statistical
evidence and statistical techniques will be added on a continuous
basis, by user request or otherwise.
- Bonferroni
adjustment of critical p-values when performing multiple comparisons
(has an excellent discussion of this topic)
- Multiple
comparisons correction (Bonferroni adjustment)
- Number
Needed
to Treat, based on a 2-by-2 table
- Detect
Outliers -- this calculator performs Grubbs' test, also
called the
ESD method (extreme studentized deviate), to determine whether one of
the values in the list you enter is a signficant outlier from the rest.
- Selection
Bias Calculator for Prevalence Estimates
- Calculate and plot an ROC
Curve
(for grouped predictor data)
- Clustering
Calculator generates tree structures of data clustering, and
much
more
- Misclassification
Bias in Prevalence Studies
- Predictive
Value from Sensitivity, Specificity and Prevalence, (when
analyzing
a clinical test), with a nice explanation
- Selection
Bias in Case-control Studies
- NetMul:
a browser interface to a program that performs:
- Principal Coordinate Analysis (PCO)
- co-inertia analysis
- discriminant analysis and within- or between-class
analyses
- analyses on distance matrices or neighboring graphs.
- Simultaneous
Equations and Matrix Inversion -- up to 10 equations (or
10x10
matrix).
- Linear
Optimization with Tools for Sensitivity Regions -- This page
finds
the optimal solution, and does a post-optimality analysis of small-size
linear programming problems (constrained optimization).
- Martindale's
Reference Desk - Calculators On-Line - Statistics
(the
grand-daddy of all compendia of calculating web pages)
- Biostatistical Calculators:
- Evidence-Based
Medicine (EBM) calculator -- From Warren Goff's interestingly-named web site.
Analyzes
one or more fourfold (2x2) tables; calculates Chi Square, CER, EER, and
RR, and parameters related to treatment (RRR, ARR, NNT, NNH, with 95%
confidence intervals), diagnosis (Sensitivity, Specificity, PPV, NPV,
Prevalence, LR+, LR-, OR, Pre-Odds, Post-Prob), and Harm (RR, OR NNH).
Can also compare two different tables.
- Clinical
Significance Calculator -- For two groups (control and
treatment),
enter the group size and incidence rate; the page will
calculate
absolute and relative risk reductions, odds ratio, and number needed to
treat, along with 95% confidence intervals for each result
- Compute
ECanything
from EC50 (assuming
a standard "Hill-type"
dose-response relationship). Very useful in dose-response studies.
- Thorough
analysis of 2-by-2 table relevant to Predictions and Diagnostic Tests
-- sensitivity, specificity, prevalence, diagnostic accuracy, PPV,
post-test probabilities, likelihood ratio tests
- Calculation
of posttest probability from Likelihood Ratio and pretest probability
- Conversion
of Sensitivity and Specificity to Likelihood Ratios
- Calculator
to predict the probability of a successful outcome to lumbar disc
surgery (based on a logistic model)
- LODS - Logistic
Organ Dysfunction
System calculator
- Scoring
systems for ICU and surgical patients -- Online calculation
of
scores used in general or specialized Intensive Care or Anesthesia,
including:
- Adult, General scores: SAPS II,
APACHE
II, SOFA,
MODS
, ODIN,
MPM (on
admission
, 24
hrs, 48
hrs , MPM
Over Time) ,
MPM II (on
admission, 24-48-72
hrs)
, LODS,
and TRIOS
- Adult, Specialized and Surgical
Intensive Care -
Preoperative evaluation: EUROSCORE,
ONTARIO,
Parsonnet,
System
97, QMMI,
MPM,
POSSUM,
and Portsmouth
POSSUM
- Adult, Trauma scores: ISS/RTS/TRISS,
and 24
h - ICU Trauma
Score
- Adult, Therapeutic intervention, nursing
ICU scores: TISS
- Pediatric, General scores: PRISM,
DORA,
PELOD,
and PIM
- Pediatric, Specialized (Neonatal,
Surgical): CRIB,
SNAP,
SNAP-PE,
SNAP
II / SNAPPE II
- Pediatric, Trauma Scores: Pediatric
Trauma Score
- Calculators
for Clinical Formulas -- A-a
Gradient, Anion
Gap, Body
Surface Area, Body Mass Index, Estimated
Creatinine Clearance, Fractional
Excretion of Sodium, Heart
Disease
Risk, Ingested
Substance Blood Level, Pregnancy
Due
Date , Serum
Osmolality , and Weights
and
Measures (converts lbs. to kgs. and F to C)
- Item
Analysis -- for
multiple choice questionnaires
- Statistical
Quality Control
(SQC) Online -- Online
calculators and tutorials to perform SQC annd Statistical Process
Control (SPC). Contains:
-
- Queuing
Theory
Calculator -- a remarkably powerful web calculator that can
solve a
wide variety of queueing problems: single-server, multiple-server,
infinite-server, infinite or finite waiting room, Erlang loss model,
and machine interference model (with or without spare machines).
Provides detailed output in the form of averages, standard deviations,
and frequency distributions in the form of tables and graphs.
- Structural
Engineering Calculators, from BuildingsGuide.com
--
currently includes ASCE 7-05 Code calculators for Snow
Loading Analysis, Ice Loading Analysis for WT,
MT & ST shapes, for W,
M, S & HP shapes, and for C
& MC shapes; Seismic
Base Shear for single-level buildings, and Wind
Loading Analysis for low-rise buildings.
- Single-Case
analysis tools -- an online calculator that can do a number
of
tests and analyses that are especially useful in "single-case" or
"single-system" research: Time Series (handles A-B and
multiple-baseline designs, and calculates correlations and the
C-statistic, with p-value), Autocorrelation, Chi Square, Testing
Significance of Difference: t-test and Mann-Whitney U, Binomial
Expansion, and Bayesian Analysis. Also contains a good overview
of single-case methods.
- Decision Making in
Economics and Finance:
-
- ABC
Inventory Classification -- an analysis of a range of items,
such
as finished products or customers into three "importance" categories:
A, B, and C as a basis for a control scheme. This pageconstructs an
empirical cumulative distribution function (ECDF) as a measuring tool
and decision procedure for the ABC inventory classification.
- Inventory
Control Models -- Given the costs of holding stock, placing
an
order, and running short of stock, this page optimizes decision
parameters (order point, order quantity, etc.) using four models:
Classical, Shortages Permitted , Production & Consumption,
Production & Consumption with Shortages.
- Optimal
Age for Replacement -- Given yearly figures for resale value
and
running costs, this page calculates the replacement optimal age and
average cost.
- Single-period
Inventory Analysis -- computes the optimal inventory level
over a
single cycle, from up-to-28 pairs of (number of possible item to sell,
and their associated non-zero probabilities), together with the "not
sold unit batch cost", and the "net profit of a batch sold".
- Investment
Derivative
Calculations -- A very elaborate online calculator and
real-time
data retrieval system. Includes economic regression analysis.
- Black-Scholes
Calculator -- to place a value on stock options.
- Bardahl
Calculator -- to compute the reasonable working capital needs
of a
corporation.
- Probabilistic Modeling:
- Bayes'
Revised Probability -- computes the posterior probabilities
to
"sharpen" your uncertainties by incorporating an expert judgement's
reliability matrix with your prior probability vector. Can accommodate
up to nine states of nature.
- Decision
Making Under Uncertainty -- Enter up-to-6x6 payoff matrix of
decision alternatives (choices) by states of nature, along
with a
coefficient of optimism; the page will calculate Action &
Payoff
for Pessimism, Optimism, Middle-of-the-Road, Minimize Regret, and
Insufficient Reason.
- Determination
of Utility Function -- Takes two monetary values and their
known
utility, and calculates the utility of another amount, under two
different strategies: certain & uncertain.
- Making
Risky Decisions -- Enter up-to-6x6 payoff matrix of decision
alternatives (choices) by states of nature, along with subjective
estimates of occurrence probability for each states of nature; the page
will calculate action & payoff (expected, and for most likely
event), min expected regret , return of perfect information, value of
perfect information, and efficiency.
- Multinomial
Distributions -- for up to 36 probabilities and associated
outcomes, calculates expected value, variance, SD, and CV.
- Revising
the Mean and the Variance -- to combine subjectivity and
evidence-based estimates. Takes up to 14 pairs of means and variances;
calculates combined estimates of mean, variance, and CV.
- Subjective
Assessment of Estimates -- (relative precision as a
measuring
tool for inaccuracy assessment among estimates), tests the claim that
at least one estimate is away from the parameter by more than r times
(i.e., a relative precision), where r is a subjective positive number
less than one. Takes up-to-10 sample estimates, and a subjective
relative precision (r<1); the page indicates whether at least
one
measurement is unacceptable.
- Subjectivity
in Hypothesis Testing -- Takes the profit/loss measure of
various
correct or incorrect conclusions regarding the hypothesis, along with
probabilities of Type I and II errors (alpha & beta),
total
sampling cost, and subjective estimate of probability that null
hypothesis is true; returns the expected net profit.
Check out the very general and elegant
power/sample-size
calculator by Russel Lenth (U of Iowa). It handles tests of
means
(one
or two samples), tests of proportions (one or two samples), linear
regression,
generic chi-square and Poisson tests, and an amazing variety of ANOVAs
--
1-, 2-, and 3-way; randomized complete-block; Latin and Greco-Latin
squares;
1-stage, 2-stage, and factorial nested designs; crossover; split-plot;
strip-plot; and more! This calculator is implemented in Java, and can
be
run as a web page, or can be
downloaded
to your computer to run offline as a stand-alone application.
Here's a collection of online power calculator web pages for specific
kinds
of tests:
- 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.
- Compute
the sample size, given the population size, the confidence
interval
and the confidence level. A related "advanced"
page
also allows you to specify the postulated proportion (rather than
assuming 50%).
- Find the required sample
size or statistical
power for comparing an observed proportion with a specific
value
- Confidence
Interval Calculator to compute the margin of error and
confidence
interval given the population size, sample size, sample percentage, and
confidence level. An animated
version is also available, which displays the calculation of
the
confidence interval graphically.
- Find the sampling
error in an observed proportion
- Calculate
sample size required for a given confidence interval, or confidence
interval for a given sample size. Can handle finite
populations.
Downloadable program also available.
- Another
sample-size / confidence interval calculator for proportions in finite
samples
- Sample
size or confidence interval of a proportion
- For two-group tests...
- Comparing means for two independent samples...
- Difference between two proportions (as, for example,
by a
Chi Square test on a 2-by-2 cross-tab)...
- For ANOVAs and other
multi-group
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 inter-relationships between three partial correlation
coefficients
- Sample-size
for multiple regression -- will tell you the minimum required
sample size for your study, given the alpha level, the number of
predictors, the anticipated effect size (as f2),
and the
desired statistical power level. If you know the effect size as R2,
you can calculate f2 from R2
with this
calculator.
- Power/Sample-size
for simple or multiple linear regression -- select the Linear
regression option, then click the Run Selection
button.
- Beta
level for multiple regression (i.e., the Type II
error rate,
which is 1 minusPower), given the observed alpha level, the number of
predictors, the observed R2, and the sample
size.
- Post-hoc
power for multiple regression -- calculates the observed
power for
your study, given the observed alpha level, the number of predictors,
the observed R2, and the sample size.
- Power
calculations for logistic regression with a continuous
exposure
variable and an additional continuous covariate or confounding
variable. Also accommodates measurement error in the exposure variable.
Has graphical output.
- Other power calculations...
- Retrospective
power analysis (after
doing the test) Before doing a retrospective power
analyses,
check out Richard
Stevens' web page to see if you really need to do one.
- Sample
Size Determination -- For several situations: ANOVA and
2-population economic sampling, correlation with acceptable absolute
precision, estimating the mean or proportion with acceptable absolute
or relative Precision, estimating the mean or proportion from finite
populations, and testing the mean or proportion based on the Null and
an Alternative.
- Power
calculations for clinical trials and scientific experiments
-- this
page contains a table for selecting appropriate calculator, based on
the type of study (parallel, crossover, or test of association) and the
type of outcome measurement (success/failure, time-to-event, or a
numerical quantity).
- Survival
Analysis -- computes power, sample size, or detectable-effect
size
in a two group design with a survival outcome.
- Generic
Poisson Test -- select the Generic Poisson test option,
then click the Run Selection button.
- Exact
power for the Fisher exact test
- Find sample size, power and minimal detectable
difference
for a:
- Links
to printable copies (in Adobe Acrobat PDF format) of many
power
tables including: Z
Test, t-Test
for One Sample or Two Related Samples, t-Test
for Two Independent Samples, Analysis
of Variance, Correlation
Coefficient, and Required
Sample Size for various tests
- Wald's
Sequential Probability Ratio's -- for designing a sequential
experiment in which a decision is made after each observation either to
accept the null hypothesis, accept the alternate hypothesis, or acquire
more observations.
- Experimental Design...
- WebDOE(tm)
-- for "design of experiments". Searches for I-, D- and A-optimal
designs over continuous spaces. Factors may be continuous, fixed-level,
or qualitative. The site can handle inequality and equality (e.g.,
mixture) constraints; provides color plots; performs one-click,
run-order-randomization; allows design import/export interoperable with
most 3rd-party analysis software; provides OLS and BLUP fits; and
includes an extensive Classical Design Library(tm), including
factorial, fractional-factorial, Box-Behnken, central-composite,
Plackett-Burman, orthogonal array, and uniform designs. All designs may
be evaluated under the I-, D-, and A-, and S-optimality criteria, as
well as for the maximum distance between nearest-neighbor pairs of
design points (maximin criterion). The My WebDOE(tm) feature allows
users to store their designs, evaluations, and fits on-line. There is
no need for user-provided candidatepoints.
- Design
and Analysis of Comparative Experiments website by Horticulture
Research International -- provides facilities for the design
and
analysis of of comparative experiments for biological and agicultural
research based on a range of experimental block and treatment
structures. Constructs simple experimental designs interactively and
also constructs appropriate statistical software for the analysis of
the designs. Handles Randomised block, Split-plot, Latin and incomplete
Latin square, Trojan and incomplete Trojan square designs.
- Tables of Latin
Squares for
constructing "Williams design" experiments, in which every subject
receives every treatment. These designs are balanced for first-order
carry-over (residual effects). Tables are provided for experiments
ranging from 2 to 26 treatments. Tables can also be downloaded as a text file and as an Excel
spreadsheet.
- Sample-size calculations for parallel-group
equivalence and superiority trials with continuous or binary outcome
variables.
- EDGAR
-- generates experimental designs and randomizes the position of
experimental treatments in the design, so that the subsequent analysis
of the data is comparatively straightforward
- Type I & II error criteria. [see Simon,
Controlled Clin
Trials, 10:1-10,1989]
- Compute
boundaries for a specified alpha spending function,
compute
drift given power and bound, and
compute probabilities,
all based upon the Lan-DeMets
method. Allows computation of boundaries at any time during
the
monitoring of a study. It is valid for any normal test statistic with
independent increments. The information time is the ratio of accrued
sample size to the total sample size for normal data.
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