Statistics Function Lists
Hypothesis Testing
Using Mathematica's built-in hypothesis testing functions, you
can test hypotheses concerning the mean, the variance, the difference in
two population means, and the ratio of their variances.
Analysis of Variance
The ANOVA statistics package adds analysis of variance (ANOVA) to
Mathematica's already rich statistical functionality.
It is typically used in designed experiments when the data have a numeric
response and one or more categorical variables. ANOVA tests hypotheses
about differences between two or more means by examining the ratio of
variability between conditions and variability within each condition. The
result will indicate which factors have the greatest influence on the
value of the outcome and whether any important interactions between
factors exist.
You can perform one-way or general analysis of variance with
Mathematica's
built-in ANOVA package. It allows you to select
from multiple post hoc
tests and other options to find the ones that suit you and your problem
best.
Confidence Intervals
Whether for sampled data or derived statistics, you can find confidence
intervals for various parameters such as means, differences between two
population means, variances, and ratios of the variance of two
populations.
Plotting
Mathematica's large selection of flexible two- and
three-dimensional plotting capabilities lets you generate scatter plots,
contour plots, log plots, bar charts, and more. And, in addition to
controlling such attributes as line thickness, line dashing, point size,
and colors, you can also easily customize your plots with labels, tick
marks, frames, and legends.
Descriptive and Multidescriptive Statistics
You can easily compute descriptive statistics of your data using the
built-in location, dispersion, shape, and--in the case of
multivariate data--association statistics. Standard descriptive
statistics for various built-in continuous and discrete distributions
can be calculated as well.
Statistical Distributions
Mathematica provides functions for the most commonly used
discrete, continuous, normal, and multinormal statistical distributions.
These distributions include binomial, Bernoulli, geometric,
hypergeometric, Poisson, beta, Cauchy, chi, exponential, gamma, Laplace,
Pareto, Rayleigh, Weibull, normal, Student t, chi-square, F ratio, multivariate
Student t, Wishart, Hotelling  , and others.
In addition to the statistical distributions themselves,
functions to compute their densities, means,
variances, and other related properties are also included.
Data Smoothing and Manipulation
You can select, drop, or join columns or rows of your data.
Alternatively, you can extract or drop particular elements from your
list of data. In addition, Mathematica provides several data smoothing
functions including a linear filter, moving average, and moving median
as well as functions for exponential smoothing and repeated smoothing.
Linear and Nonlinear Regression
Fit your data with Mathematica's built-in linear and nonlinear
regression capabilities. You can use Mathematica's function
Fit for basic linear regression, or you can use
the functions Regress and DesignedRegress, which not
only fit the
data but also determine commonly used statistics such as estimated error
variance, analysis of variance table, and coefficient of determination.
Numerous diagnostics for evaluating the data and the fit are also
provided.
You can use NonlinearFit for
nonlinear regression or the function NonlinearRegress if you wish
to produce a number
of regression diagnostics. In
addition, Mathematica provides functions for polynomial, spline,
and trigonometric fitting.
Mathematica provides excellent tools for numerical optimization and
nonlinear fitting. The package NMinimize offers several ways of
finding global minima, none of which calculates derivatives. The method allows
you to solve problems with an objective function that is not differentiable
or continuous. The method also allows you to find the true global minima
instead of being trapped by local minima. This feature becomes
particularly important for a statistician who wants to fit nonlinear data.
NMinimize offers excellent results for nonlinear fitting.
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