Why Robust Statistics?
The most commonly used statistical methods in the social sciences make
assumptions about normality and variance homogeneity. However, often
these assumptions are violated. Many social scientists believe that
current methods are robust to violations of assumptions. But this is
not necessarily the case.
With high speed computers, it is now possible to apply robust
statistical methods that were heretofore impractical to use. These
methods offer useful and viable alternatives to traditional analytic
methods, often yielding greater statistical power and increased sensitivity.
The methods also deal effectively with outliers.
These methods are not readily available on many widely used
statistical packages (e.g., SPSS). ZumaStat makes them available in a
simple point-and-click format.
ZumaStat Robust Statistics
ZumaStat provides a user friendly interface to access powerful statistical
programs on robust statistics that are available in the computer package
called R, which is available free. Most of the R functions were written by Professor
Rand Wilcox of the University of Southern California and are described in
his three books:
Wilcox, R. (2005). Introduction to Robust Estimation and
Hypothesis Testing. San Diego: Academic Press, Second edition.
Wilcox, R. (2003). Applying Contemporary Statistical
Techniques. San Diego: Academic Press.
Wilcox, R. (1999). Fundamentals of Modern Statistical
Methods. New York: Springer.
(Note: Professor Wilcox is not affiliated with ZumaStat).
These excellent books can be obtained from the respective web sites
www.academicpress.com and
www.springer-ny.com.
You don't have to know R to access these programs. You
can do so using the intuitive interface of ZumaStat or you
can use the ZumaStat programs directly from SPSS and Excel, working with the
active data sets or worksheets in these programs.
You must have R on your computer to use these programs. R
is freeware and complete instructions for obtaining and installing it are
contained in ZumaStat.
Imports Files
ZumaStat interface will work directly in SPSS or Excel, or
you can work directly from ascii files.
Robust Methods Available through ZumaStat
ZumaStat makes accessible a wide range of analytic procedures
for robust analysis. These include:
 |
Analysis of Trimmed Means:
Trimmed means focus on the mean of the distribution after a certain
percentage of cases have been trimmed from the tails of the distribution.
Such means are robust to outliers and methods for estimating standard
errors and confidence intervals are relatively robust to violations of
normality and variance homogeneity. With the R functions used
by ZumaStat, you can compare the trimmed means for two groups (for both
independent groups and dependent groups), three or more groups
(corresponding to one way analysis of variance and multiple comparisons) and you can conduct single degree of freedom contrasts relevant
to a wide range of factorial designs (for a discussion of single degree of
freedom contrasts, click
here). You can do two factor and three factor ANOVAs on trimmed
means. |
|
Analysis of
Medians: Medians are outlier resistant measures of central
tendency. With ZumaStat, you can obtain significance tests and
confidence intervals to compare medians for two groups (for both
independent groups and dependent groups), three or more groups
(corresponding to one way analysis of variance and multiple comparisons) and you can conduct single degree of freedom contrasts
of medians relevant
to a wide range of factorial designs. |
|
Analysis of
M Estimators: M estimators are robust indices of central
tendency that derive from the formal literature on robust statistics.
With ZumaStat, you can compare M estimators for two groups (for both
independent groups and dependent groups), three or more groups
(corresponding to one way analysis of variance and multiple comparisons) and you can conduct single degree of freedom contrasts relevant
to a wide range of factorial designs. |
|
Analysis of
Quantiles: The robust package permits you to compare groups for any
specified quantile (e.g., the 0.25 quantile, the 0.50 quantile (which is
the median), the 0.75 quantile). A wide range of tests for group
differences are available. The robust package also offers quantile
regression. |
|
Robust Measures of Variability: The robust package calculates the
interquartile range, the MAD for a distribution of scores, as well as many
other robust indices of variability/scale. There are tests of
variability differences between groups in the package as well.
|
|
Robust Measures of Correlation: The robust package allows you
to calculate the
percentage bend correlation, a robust index of association in the bivariate case, as well as confidence intervals for the index. In
addition, the robust package offers a bootstrapped based confidence interval
procedure for Pearson's correlation that allows for heteroscedasticity.
Half a dozed robust indices of association are available.
|
|
Robust Regression: The robust package performs several methods of robust
regression for both bivariate and multiple regression scenarios.
These include Theil-Sen regression, least trimmed squares regression,
least trimmed absolute values regression, regression based on M
estimators, and bootstrapped OLS regression for non-normal and
heteroscedastic cases, among others. |
|
Robust
Analysis of Covariance: The robust package offers robust methods of
analysis of covariance that take into account predictor-covariate
interactions vis-a-vis smoothing methods. |
|
Smoothing:
The robust package offers a variety of smoothing methods for examining the
relationships between variables. |
|
Additional Functions:
Almost all of the functions available in the Wilcox (2005) book are in
the robust package of ZumaStat. Look over this book to get a sense of
the many statistical tests that are available. |
| Point and Click R:
R is a powerful statistical package that uses functions written by
statisticians throughout the world in a programming language that is
unique to R. Use of these functions requires learning that language.
ZumaStat can be integrated with SPSS and Excel so that it automatically
passes the active data set in SPSS or Excel that you are working on to R.
|
