*! version 1 2010-10-12
help emhVersion 1.0 2010-10-12

Title

emh -- Extended Mantel-Haenszel Statistics

Syntax

emh
var1 var2
[if] [in]
[weight]
[, options]

Main
strata(varlist) stratify on varlist

correlation Correlation Statistic; the default

anova ANOVA (Mean Scores) Statistic

general General Association Statistic

transformation(scoretype) use transformation scores, e.g., ranks

by is allowed; see [D] by.

fweights are allowed; see weight.

Only one of correlation, anova and general is permitted at a time.

Description

emh calculates extended Mantel-Haenszel chi-square test statistics (also known as
Cochran-Mantel-Haenszel Statistics) for stratified tables. Tables are
defined by var1 and var2, both which must be numeric. Stratification
is optional.

Options

Main

strata(varlist) specifies variables on which to stratify the analysis.
Stratification variables may be numeric, string or a mix of the two.

correlation Correlation Statistic--tests for a linear association
between var1 and var2. Suitable when both are at least ordinal.

anova ANOVA (Row Mean-score Differences) Statistic--tests for a difference in
means of var1 between groups that are defined by var2. Suitable when
var1, the response variable, is at least ordinal. var2, the predictor variable, may be
nominal (unordered).

general General Association Statistic--most general form of association; of
interest especially when both var1 and var2 are nominal.

transformation(scoretype) When correlation is specified, transforms
both var1 and var2; when anova is specified, transforms
the response variable (var1). This option is ignored when general
is specified. Available scoretypes are table (untransformed--the default),
integer, rank, ridit, modridit (standardized midranks),
savage (Savage scores), mood (Mood scores), median (above or at-or-below
median), vdw (van der Waerden scores) and klotz (Klotz scores).

Remarks

emh computes chi-square test statistics for association of row and column
variables in unstratified or stratified tables. A good introduction to the use
of these statistics is Chapters 2 through 7 of M. E. Stokes, C. S. Davis and
G. G. Koch, Categorical Data Analysis Using the SAS(R) System Second Edition.
Cary, North Carolina: SAS Institute, 2000.

emh uses tabulate internally. The number of levels of var1 and var2 are
limited to what tabulate can accept. In order to accommodate an analysis
with many levels of either or both of these variables, e.g., with continuous
variables, matsize and memory might need to be set larger.

Computing extended Mantel-Haenszel statistics involves inverting a pooled covariance
matrix. For some datasets, the matrix might be singular. When
this occurs, a warning is displayed, and the chi-square statistic and associated
p-value are set to missing. Such occurrences are more likely when requesting the General
Association statistic for a dataset with many levels of row and column
variables and with a substantial amount of missing data.

Some transformation types available in emh have an established use in
unstratified two-group mean score-difference analysis, e.g., Mood test, van der
Waerden test, Klotz test. Their use does not appear so well known in stratified
analysis of multi-group (>2) datasets. In this context, such transformations might
not display the desired sensitivity to location or scale difference. In general,
users should exercise care in choosing whether and how to employ various scoring schemes.

Examples

. sysuse auto

. emh rep78 price, s(foreign)

Saved results

emh saves the following in r():

Scalars

r(chi2) chi-square test statistic

r(df) degrees of freedom for chi-square statistic

r(p) p-value for reported chi-square statistic and degrees of freedom

Macros

r(scoretype) short-name for score type, as specified in transformation(scoretype)

r(ScoreType) formal name for score type, as displayed in output

Author

J. Coveney E-mail jcoveney@bigplanet.com
if you observe any problems.

Also see

Help: [ST] epitab;
vanelteren (if installed), somersd (if installed),
[R] tabulate twoway