CMHtest: Generalized Cochran-Mantel-Haenszel Tests
In vcdExtra: 'vcd' Extensions and Additions
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Provides generalized Cochran-Mantel-Haenszel tests of association of two possibly ordered factors,
optionally stratified other factor(s). With strata, CMHtest calculates these tests for
each level of the statifying variables and also provides overall tests controlling for the
strata.
For ordinal factors, more powerful tests than the test for general association
(independence) are obtained by assigning scores to the row and columm categories.
Usage
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CMHtest(x, ...)
## S3 method for class 'formula'
CMHtest(formula, data = NULL, subset = NULL, na.action = NULL, ...)
## Default S3 method:
CMHtest(x, strata = NULL,
rscores = 1:R, cscores = 1:C,
types = c("cor", "rmeans", "cmeans", "general"),
overall=FALSE, details=overall, ...)
## S3 method for class 'CMHtest'
print(x, digits = max(getOption("digits") - 2, 3), ...)
Arguments
x
A 2+ way contingency table in array form, or a class "table" object
with optional category labels specified in the dimnames(x) attribute.
formula
a formula specifying the variables used to create a contingency table from data.
This should be a one-sided formula when data is in array form, and a two-sided formula
with a response Freq if data is a data frame with a cell frequency variable.
For convenience, conditioning formulas can be specified indicating strata.
data
either a data frame, or an object of class "table" or "ftable".
subset
an optional vector specifying a subset of observations to be used.
na.action
a function which indicates what should happen when the data contain NAs.
Ignored if data is a contingency table
strata
For a 3- or higher-way table, the names or numbers of the factors
to be treated as strata. By default, the first 2 factors are treated
as the main table variables, and all others considered stratifying factors.
rscores
Row scores. Either a set of numbers (typically integers, 1:R)
or the string "midrank" for standardized midrank scores,
or NULL to exclude tests that depend on row scores.
cscores
Column scores. Same as for row scores.
types
Types of CMH tests to compute: Any one or more of
c("cor", "cmeans", "rmeans", "general"),
or "ALL" for all of these.
overall
logical. Whether to calculate overall tests, controlling for
the stratifying factors.
details
logical. Whether to include computational details in the result
...
Other arguments passed to default method.
digits
Digits to print.
Details
The standard χ^2 tests for association in a two-way table
treat both table factors as nominal (unordered) categories.
When one or both factors of a two-way table are
quantitative or ordinal, more powerful tests of association
may be obtained by taking ordinality into account using
row and or column scores to test for linear trends or differences
in row or column means.
The CMH analysis for a two-way table produces generalized Cochran-Mantel-Haenszel statistics
(Landis etal., 1978).
These include the CMH correlation statistic ("cor"),
treating both factors as ordered.
For a given statum, with equally spaced row and column scores,
this CMH statistic reduces to (n-1) r^2,
where r is the Pearson correlation between X and Y.
With "midrank" scores, this CMH statistic is analogous
to (n-1) r_S^2, using the Spearman rank correlation.
The ANOVA (row mean scores and column mean scores) statistics,
treat the columns and rows respectively as ordinal,
and are sensitive to mean shifts over columns or rows.
These are transforms of the F statistics from one-way ANOVAs
with equally spaced scores and to Kruskal-Wallis tests with
"midrank" scores.
The CMH general association statistic treat both factors as unordered,
and give a test closely related to the Pearson χ^2 test.
When there is more than one stratum, the overall general CMH statistic
gives a stratum-adjusted Pearson χ^2,
equivalent to what is calculated by mantelhaen.test.
For a 3+ way table, one table of CMH tests is produced for each
combination of the factors identified as strata.
If overall=TRUE, an additional table is calculated for
the same two primary variables, controlling for (pooling over)
the strata variables.
These overall tests implicitly assume no interactions between the
primary variables and the strata and they will have low power in the
presence of interactions.
Value
An object of class "CMHtest" , a list with the following 4 components:
table
A matrix containing the test statistics, with columns
Chisq, Df and Prob
names
The names of the table row and column variables
rscore
Row scores
cscore
Column scores
If details==TRUE, additional components are included.
If there are strata, the result is a list of "CMHtest" objects.
If overall=TRUE another component, labeled ALL
is appended to the list.
Author(s)
Michael Friendly
References
Stokes, M. E. & Davis, C. S. & Koch, G., (2000).
Categorical Data Analysis using the SAS System, 2nd Ed.,
Cary, NC: SAS Institute,
pp 74-75, 92-101, 124-129.
Details of the computation are given at:
http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_freq_a0000000648.htm
Cochran, W. G. (1954), Some Methods for Strengthening the Common χ^2 Tests,
Biometrics, 10, 417-451.
Landis, R. J., Heyman, E. R., and Koch, G. G. (1978).
Average Partial Association in Three-way Contingency Tables:
A Review and Discussion of Alternative Tests,
International Statistical Review, 46, 237-254.
Mantel, N. (1963), Chi-square Tests with One Degree of Freedom: Extensions of the Mantel-Haenszel Procedure,"
Journal of the American Statistical Association, 58, 690-700.
See Also
cmh_test provides the CMH test of general association;
lbl_test provides the CMH correlation test of linear by linear association.
mantelhaen.test provides the overall general
Cochran-Mantel-Haenszel chi-squared test of the null that two nominal variables are conditionally independent
in each stratum, assuming that there is no three-way interaction
Examples
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data(JobSat, package="vcdExtra")
CMHtest(JobSat)
CMHtest(JobSat, rscores="midrank", cscores="midrank")
# formula interface
CMHtest(~ ., data=JobSat)
# A 3-way table (both factors ordinal)
data(MSPatients, package="vcd")
CMHtest(MSPatients)
# also calculate overall tests, controlling for Patient
CMHtest(MSPatients, overall=TRUE)
# compare with mantelhaen.test
mantelhaen.test(MSPatients)
# formula interface
CMHtest(~ ., data=MSPatients, overall=TRUE)
# using a frequency data.frame
CMHtest(xtabs(Freq~ses+mental, data=Mental))
# or, more simply
CMHtest(Freq~ses+mental, data=Mental)
# conditioning formulae
CMHtest(Freq~right+left|gender, data=VisualAcuity)
CMHtest(Freq ~ attitude+memory|education+age, data=Punishment)
# Stokes etal, Table 5.1, p 92: two unordered factors
parties <- matrix(
c(221, 160, 360, 140,
200, 291, 160, 311,
208, 106, 316, 97), nrow=3, ncol=4, byrow=TRUE)
dimnames(parties) <- list(party=c("Dem", "Indep", "Rep"),
neighborhood=c("Bayside", "Highland", "Longview", "Sheffield"))
CMHtest(parties, rscores=NULL, cscores=NULL)
# compare with Pearson chisquare
chisq.test(parties)
Example output
Loading required package: vcd
Loading required package: MASS
Loading required package: grid
Loading required package: colorspace
Loading required package: gnm
Cochran-Mantel-Haenszel Statistics for income by satisfaction
AltHypothesis Chisq Df Prob
cor Nonzero correlation 2.9830 1 0.084144
rmeans Row mean scores differ 4.4774 3 0.214318
cmeans Col mean scores differ 3.1036 3 0.375931
general General association 5.9034 9 0.749549
Cochran-Mantel-Haenszel Statistics for income by satisfaction
AltHypothesis Chisq Df Prob
cor Nonzero correlation 2.9726 1 0.084685
rmeans Row mean scores differ 4.1200 3 0.248799
cmeans Col mean scores differ 3.3108 3 0.346144
general General association 5.9034 9 0.749549
Cochran-Mantel-Haenszel Statistics for income by satisfaction
AltHypothesis Chisq Df Prob
cor Nonzero correlation 2.9830 1 0.084144
rmeans Row mean scores differ 4.4774 3 0.214318
cmeans Col mean scores differ 3.1036 3 0.375931
general General association 5.9034 9 0.749549
$`Patients:Winnipeg`
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
in stratum Patients:Winnipeg
AltHypothesis Chisq Df Prob
cor Nonzero correlation 51.424 1 7.4426e-13
rmeans Row mean scores differ 55.393 3 5.6601e-12
cmeans Col mean scores differ 53.631 3 1.3450e-11
general General association 64.318 9 1.9580e-10
$`Patients:New Orleans`
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
in stratum Patients:New Orleans
AltHypothesis Chisq Df Prob
cor Nonzero correlation 28.863 1 7.7667e-08
rmeans Row mean scores differ 30.594 3 1.0347e-06
cmeans Col mean scores differ 29.054 3 2.1818e-06
general General association 43.428 9 1.7990e-06
$`Patients:Winnipeg`
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
in stratum Patients:Winnipeg
AltHypothesis Chisq Df Prob
cor Nonzero correlation 51.424 1 7.4426e-13
rmeans Row mean scores differ 55.393 3 5.6601e-12
cmeans Col mean scores differ 53.631 3 1.3450e-11
general General association 64.318 9 1.9580e-10
$`Patients:New Orleans`
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
in stratum Patients:New Orleans
AltHypothesis Chisq Df Prob
cor Nonzero correlation 28.863 1 7.7667e-08
rmeans Row mean scores differ 30.594 3 1.0347e-06
cmeans Col mean scores differ 29.054 3 2.1818e-06
general General association 43.428 9 1.7990e-06
$ALL
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
Overall tests, controlling for all strata
AltHypothesis Chisq Df Prob
cor Nonzero correlation 80.086 1 3.5848e-19
rmeans Row mean scores differ 83.923 3 4.4189e-18
cmeans Col mean scores differ 81.116 3 1.7685e-17
general General association 101.21 9 8.9683e-18
Cochran-Mantel-Haenszel test
data: MSPatients
Cochran-Mantel-Haenszel M^2 = 101.21, df = 9, p-value < 2.2e-16
$`Patients:Winnipeg`
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
in stratum Patients:Winnipeg
AltHypothesis Chisq Df Prob
cor Nonzero correlation 51.424 1 7.4426e-13
rmeans Row mean scores differ 55.393 3 5.6601e-12
cmeans Col mean scores differ 53.631 3 1.3450e-11
general General association 64.318 9 1.9580e-10
$`Patients:New Orleans`
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
in stratum Patients:New Orleans
AltHypothesis Chisq Df Prob
cor Nonzero correlation 28.863 1 7.7667e-08
rmeans Row mean scores differ 30.594 3 1.0347e-06
cmeans Col mean scores differ 29.054 3 2.1818e-06
general General association 43.428 9 1.7990e-06
$ALL
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
Overall tests, controlling for all strata
AltHypothesis Chisq Df Prob
cor Nonzero correlation 80.086 1 3.5848e-19
rmeans Row mean scores differ 83.923 3 4.4189e-18
cmeans Col mean scores differ 81.116 3 1.7685e-17
general General association 101.21 9 8.9683e-18
Cochran-Mantel-Haenszel Statistics for ses by mental
AltHypothesis Chisq Df Prob
cor Nonzero correlation 37.156 1 1.0907e-09
rmeans Row mean scores differ 40.297 5 1.3012e-07
cmeans Col mean scores differ 40.666 3 7.6971e-09
general General association 45.958 15 5.4003e-05
Cochran-Mantel-Haenszel Statistics for ses by mental
AltHypothesis Chisq Df Prob
cor Nonzero correlation 37.156 1 1.0907e-09
rmeans Row mean scores differ 40.297 5 1.3012e-07
cmeans Col mean scores differ 40.666 3 7.6971e-09
general General association 45.958 15 5.4003e-05
$`gender:male`
Cochran-Mantel-Haenszel Statistics for right by left
in stratum gender:male
AltHypothesis Chisq Df Prob
cor Nonzero correlation 1554.6 1 0
rmeans Row mean scores differ 1556.3 3 0
cmeans Col mean scores differ 1556.6 3 0
general General association 3303.3 9 0
$`gender:female`
Cochran-Mantel-Haenszel Statistics for right by left
in stratum gender:female
AltHypothesis Chisq Df Prob
cor Nonzero correlation 3691.3 1 0
rmeans Row mean scores differ 3709.4 3 0
cmeans Col mean scores differ 3724.0 3 0
general General association 8095.8 9 0
$`education:elementary|age:15-24`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:elementary|age:15-24
AltHypothesis Chisq Df Prob
cor Nonzero correlation 3.5652 1 0.059002
rmeans Row mean scores differ 3.5652 1 0.059002
cmeans Col mean scores differ 3.5652 1 0.059002
general General association 3.5652 1 0.059002
$`education:secondary|age:15-24`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:secondary|age:15-24
AltHypothesis Chisq Df Prob
cor Nonzero correlation 0.077731 1 0.7804
rmeans Row mean scores differ 0.077731 1 0.7804
cmeans Col mean scores differ 0.077731 1 0.7804
general General association 0.077731 1 0.7804
$`education:high|age:15-24`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:high|age:15-24
AltHypothesis Chisq Df Prob
cor Nonzero correlation 0.089524 1 0.76478
rmeans Row mean scores differ 0.089524 1 0.76478
cmeans Col mean scores differ 0.089524 1 0.76478
general General association 0.089524 1 0.76478
$`education:elementary|age:25-39`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:elementary|age:25-39
AltHypothesis Chisq Df Prob
cor Nonzero correlation 8.5433 1 0.003468
rmeans Row mean scores differ 8.5433 1 0.003468
cmeans Col mean scores differ 8.5433 1 0.003468
general General association 8.5433 1 0.003468
$`education:secondary|age:25-39`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:secondary|age:25-39
AltHypothesis Chisq Df Prob
cor Nonzero correlation 0.92897 1 0.33513
rmeans Row mean scores differ 0.92897 1 0.33513
cmeans Col mean scores differ 0.92897 1 0.33513
general General association 0.92897 1 0.33513
$`education:high|age:25-39`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:high|age:25-39
AltHypothesis Chisq Df Prob
cor Nonzero correlation 0.472 1 0.49207
rmeans Row mean scores differ 0.472 1 0.49207
cmeans Col mean scores differ 0.472 1 0.49207
general General association 0.472 1 0.49207
$`education:elementary|age:40-`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:elementary|age:40-
AltHypothesis Chisq Df Prob
cor Nonzero correlation 11.606 1 0.00065737
rmeans Row mean scores differ 11.606 1 0.00065737
cmeans Col mean scores differ 11.606 1 0.00065737
general General association 11.606 1 0.00065737
$`education:secondary|age:40-`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:secondary|age:40-
AltHypothesis Chisq Df Prob
cor Nonzero correlation 6.0457 1 0.01394
rmeans Row mean scores differ 6.0457 1 0.01394
cmeans Col mean scores differ 6.0457 1 0.01394
general General association 6.0457 1 0.01394
$`education:high|age:40-`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:high|age:40-
AltHypothesis Chisq Df Prob
cor Nonzero correlation 3.0436 1 0.081055
rmeans Row mean scores differ 3.0436 1 0.081055
cmeans Col mean scores differ 3.0436 1 0.081055
general General association 3.0436 1 0.081055
Cochran-Mantel-Haenszel Statistics for party by neighborhood
AltHypothesis Chisq Df Prob
general General association 273.81 6 3.3158e-56
Pearson's Chi-squared test
data: parties
X-squared = 273.92, df = 6, p-value < 2.2e-16
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Provides generalized Cochran-Mantel-Haenszel tests of association of two possibly ordered factors,
optionally stratified other factor(s). With strata, CMHtest calculates these tests for
each level of the statifying variables and also provides overall tests controlling for the
strata.
For ordinal factors, more powerful tests than the test for general association (independence) are obtained by assigning scores to the row and columm categories.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 | CMHtest(x, ...)
## S3 method for class 'formula'
CMHtest(formula, data = NULL, subset = NULL, na.action = NULL, ...)
## Default S3 method:
CMHtest(x, strata = NULL,
rscores = 1:R, cscores = 1:C,
types = c("cor", "rmeans", "cmeans", "general"),
overall=FALSE, details=overall, ...)
## S3 method for class 'CMHtest'
print(x, digits = max(getOption("digits") - 2, 3), ...)
|
Arguments
x |
A 2+ way contingency table in array form, or a class |
formula |
a formula specifying the variables used to create a contingency table from |
data |
either a data frame, or an object of class |
subset |
an optional vector specifying a subset of observations to be used. |
na.action |
a function which indicates what should happen when the data contain |
strata |
For a 3- or higher-way table, the names or numbers of the factors to be treated as strata. By default, the first 2 factors are treated as the main table variables, and all others considered stratifying factors. |
rscores |
Row scores. Either a set of numbers (typically integers, |
cscores |
Column scores. Same as for row scores. |
types |
Types of CMH tests to compute: Any one or more of
|
overall |
logical. Whether to calculate overall tests, controlling for the stratifying factors. |
details |
logical. Whether to include computational details in the result |
... |
Other arguments passed to default method. |
digits |
Digits to print. |
Details
The standard χ^2 tests for association in a two-way table treat both table factors as nominal (unordered) categories. When one or both factors of a two-way table are quantitative or ordinal, more powerful tests of association may be obtained by taking ordinality into account using row and or column scores to test for linear trends or differences in row or column means.
The CMH analysis for a two-way table produces generalized Cochran-Mantel-Haenszel statistics (Landis etal., 1978).
These include the CMH correlation statistic ("cor"),
treating both factors as ordered.
For a given statum, with equally spaced row and column scores,
this CMH statistic reduces to (n-1) r^2,
where r is the Pearson correlation between X and Y.
With "midrank" scores, this CMH statistic is analogous
to (n-1) r_S^2, using the Spearman rank correlation.
The ANOVA (row mean scores and column mean scores) statistics,
treat the columns and rows respectively as ordinal,
and are sensitive to mean shifts over columns or rows.
These are transforms of the F statistics from one-way ANOVAs
with equally spaced scores and to Kruskal-Wallis tests with
"midrank" scores.
The CMH general association statistic treat both factors as unordered,
and give a test closely related to the Pearson χ^2 test.
When there is more than one stratum, the overall general CMH statistic
gives a stratum-adjusted Pearson χ^2,
equivalent to what is calculated by mantelhaen.test.
For a 3+ way table, one table of CMH tests is produced for each
combination of the factors identified as strata.
If overall=TRUE, an additional table is calculated for
the same two primary variables, controlling for (pooling over)
the strata variables.
These overall tests implicitly assume no interactions between the primary variables and the strata and they will have low power in the presence of interactions.
Value
An object of class "CMHtest" , a list with the following 4 components:
table |
A matrix containing the test statistics, with columns
|
names |
The names of the table row and column variables |
rscore |
Row scores |
cscore |
Column scores |
If details==TRUE, additional components are included.
If there are strata, the result is a list of "CMHtest" objects.
If overall=TRUE another component, labeled ALL
is appended to the list.
Author(s)
Michael Friendly
References
Stokes, M. E. & Davis, C. S. & Koch, G., (2000). Categorical Data Analysis using the SAS System, 2nd Ed., Cary, NC: SAS Institute, pp 74-75, 92-101, 124-129. Details of the computation are given at: http://support.sas.com/documentation/cdl/en/statug/63033/HTML/default/viewer.htm#statug_freq_a0000000648.htm
Cochran, W. G. (1954), Some Methods for Strengthening the Common χ^2 Tests, Biometrics, 10, 417-451.
Landis, R. J., Heyman, E. R., and Koch, G. G. (1978). Average Partial Association in Three-way Contingency Tables: A Review and Discussion of Alternative Tests, International Statistical Review, 46, 237-254.
Mantel, N. (1963), Chi-square Tests with One Degree of Freedom: Extensions of the Mantel-Haenszel Procedure," Journal of the American Statistical Association, 58, 690-700.
See Also
cmh_test provides the CMH test of general association;
lbl_test provides the CMH correlation test of linear by linear association.
mantelhaen.test provides the overall general
Cochran-Mantel-Haenszel chi-squared test of the null that two nominal variables are conditionally independent
in each stratum, assuming that there is no three-way interaction
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 | data(JobSat, package="vcdExtra")
CMHtest(JobSat)
CMHtest(JobSat, rscores="midrank", cscores="midrank")
# formula interface
CMHtest(~ ., data=JobSat)
# A 3-way table (both factors ordinal)
data(MSPatients, package="vcd")
CMHtest(MSPatients)
# also calculate overall tests, controlling for Patient
CMHtest(MSPatients, overall=TRUE)
# compare with mantelhaen.test
mantelhaen.test(MSPatients)
# formula interface
CMHtest(~ ., data=MSPatients, overall=TRUE)
# using a frequency data.frame
CMHtest(xtabs(Freq~ses+mental, data=Mental))
# or, more simply
CMHtest(Freq~ses+mental, data=Mental)
# conditioning formulae
CMHtest(Freq~right+left|gender, data=VisualAcuity)
CMHtest(Freq ~ attitude+memory|education+age, data=Punishment)
# Stokes etal, Table 5.1, p 92: two unordered factors
parties <- matrix(
c(221, 160, 360, 140,
200, 291, 160, 311,
208, 106, 316, 97), nrow=3, ncol=4, byrow=TRUE)
dimnames(parties) <- list(party=c("Dem", "Indep", "Rep"),
neighborhood=c("Bayside", "Highland", "Longview", "Sheffield"))
CMHtest(parties, rscores=NULL, cscores=NULL)
# compare with Pearson chisquare
chisq.test(parties)
|
Example output
Loading required package: vcd
Loading required package: MASS
Loading required package: grid
Loading required package: colorspace
Loading required package: gnm
Cochran-Mantel-Haenszel Statistics for income by satisfaction
AltHypothesis Chisq Df Prob
cor Nonzero correlation 2.9830 1 0.084144
rmeans Row mean scores differ 4.4774 3 0.214318
cmeans Col mean scores differ 3.1036 3 0.375931
general General association 5.9034 9 0.749549
Cochran-Mantel-Haenszel Statistics for income by satisfaction
AltHypothesis Chisq Df Prob
cor Nonzero correlation 2.9726 1 0.084685
rmeans Row mean scores differ 4.1200 3 0.248799
cmeans Col mean scores differ 3.3108 3 0.346144
general General association 5.9034 9 0.749549
Cochran-Mantel-Haenszel Statistics for income by satisfaction
AltHypothesis Chisq Df Prob
cor Nonzero correlation 2.9830 1 0.084144
rmeans Row mean scores differ 4.4774 3 0.214318
cmeans Col mean scores differ 3.1036 3 0.375931
general General association 5.9034 9 0.749549
$`Patients:Winnipeg`
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
in stratum Patients:Winnipeg
AltHypothesis Chisq Df Prob
cor Nonzero correlation 51.424 1 7.4426e-13
rmeans Row mean scores differ 55.393 3 5.6601e-12
cmeans Col mean scores differ 53.631 3 1.3450e-11
general General association 64.318 9 1.9580e-10
$`Patients:New Orleans`
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
in stratum Patients:New Orleans
AltHypothesis Chisq Df Prob
cor Nonzero correlation 28.863 1 7.7667e-08
rmeans Row mean scores differ 30.594 3 1.0347e-06
cmeans Col mean scores differ 29.054 3 2.1818e-06
general General association 43.428 9 1.7990e-06
$`Patients:Winnipeg`
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
in stratum Patients:Winnipeg
AltHypothesis Chisq Df Prob
cor Nonzero correlation 51.424 1 7.4426e-13
rmeans Row mean scores differ 55.393 3 5.6601e-12
cmeans Col mean scores differ 53.631 3 1.3450e-11
general General association 64.318 9 1.9580e-10
$`Patients:New Orleans`
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
in stratum Patients:New Orleans
AltHypothesis Chisq Df Prob
cor Nonzero correlation 28.863 1 7.7667e-08
rmeans Row mean scores differ 30.594 3 1.0347e-06
cmeans Col mean scores differ 29.054 3 2.1818e-06
general General association 43.428 9 1.7990e-06
$ALL
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
Overall tests, controlling for all strata
AltHypothesis Chisq Df Prob
cor Nonzero correlation 80.086 1 3.5848e-19
rmeans Row mean scores differ 83.923 3 4.4189e-18
cmeans Col mean scores differ 81.116 3 1.7685e-17
general General association 101.21 9 8.9683e-18
Cochran-Mantel-Haenszel test
data: MSPatients
Cochran-Mantel-Haenszel M^2 = 101.21, df = 9, p-value < 2.2e-16
$`Patients:Winnipeg`
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
in stratum Patients:Winnipeg
AltHypothesis Chisq Df Prob
cor Nonzero correlation 51.424 1 7.4426e-13
rmeans Row mean scores differ 55.393 3 5.6601e-12
cmeans Col mean scores differ 53.631 3 1.3450e-11
general General association 64.318 9 1.9580e-10
$`Patients:New Orleans`
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
in stratum Patients:New Orleans
AltHypothesis Chisq Df Prob
cor Nonzero correlation 28.863 1 7.7667e-08
rmeans Row mean scores differ 30.594 3 1.0347e-06
cmeans Col mean scores differ 29.054 3 2.1818e-06
general General association 43.428 9 1.7990e-06
$ALL
Cochran-Mantel-Haenszel Statistics for New Orleans Neurologist by Winnipeg Neurologist
Overall tests, controlling for all strata
AltHypothesis Chisq Df Prob
cor Nonzero correlation 80.086 1 3.5848e-19
rmeans Row mean scores differ 83.923 3 4.4189e-18
cmeans Col mean scores differ 81.116 3 1.7685e-17
general General association 101.21 9 8.9683e-18
Cochran-Mantel-Haenszel Statistics for ses by mental
AltHypothesis Chisq Df Prob
cor Nonzero correlation 37.156 1 1.0907e-09
rmeans Row mean scores differ 40.297 5 1.3012e-07
cmeans Col mean scores differ 40.666 3 7.6971e-09
general General association 45.958 15 5.4003e-05
Cochran-Mantel-Haenszel Statistics for ses by mental
AltHypothesis Chisq Df Prob
cor Nonzero correlation 37.156 1 1.0907e-09
rmeans Row mean scores differ 40.297 5 1.3012e-07
cmeans Col mean scores differ 40.666 3 7.6971e-09
general General association 45.958 15 5.4003e-05
$`gender:male`
Cochran-Mantel-Haenszel Statistics for right by left
in stratum gender:male
AltHypothesis Chisq Df Prob
cor Nonzero correlation 1554.6 1 0
rmeans Row mean scores differ 1556.3 3 0
cmeans Col mean scores differ 1556.6 3 0
general General association 3303.3 9 0
$`gender:female`
Cochran-Mantel-Haenszel Statistics for right by left
in stratum gender:female
AltHypothesis Chisq Df Prob
cor Nonzero correlation 3691.3 1 0
rmeans Row mean scores differ 3709.4 3 0
cmeans Col mean scores differ 3724.0 3 0
general General association 8095.8 9 0
$`education:elementary|age:15-24`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:elementary|age:15-24
AltHypothesis Chisq Df Prob
cor Nonzero correlation 3.5652 1 0.059002
rmeans Row mean scores differ 3.5652 1 0.059002
cmeans Col mean scores differ 3.5652 1 0.059002
general General association 3.5652 1 0.059002
$`education:secondary|age:15-24`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:secondary|age:15-24
AltHypothesis Chisq Df Prob
cor Nonzero correlation 0.077731 1 0.7804
rmeans Row mean scores differ 0.077731 1 0.7804
cmeans Col mean scores differ 0.077731 1 0.7804
general General association 0.077731 1 0.7804
$`education:high|age:15-24`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:high|age:15-24
AltHypothesis Chisq Df Prob
cor Nonzero correlation 0.089524 1 0.76478
rmeans Row mean scores differ 0.089524 1 0.76478
cmeans Col mean scores differ 0.089524 1 0.76478
general General association 0.089524 1 0.76478
$`education:elementary|age:25-39`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:elementary|age:25-39
AltHypothesis Chisq Df Prob
cor Nonzero correlation 8.5433 1 0.003468
rmeans Row mean scores differ 8.5433 1 0.003468
cmeans Col mean scores differ 8.5433 1 0.003468
general General association 8.5433 1 0.003468
$`education:secondary|age:25-39`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:secondary|age:25-39
AltHypothesis Chisq Df Prob
cor Nonzero correlation 0.92897 1 0.33513
rmeans Row mean scores differ 0.92897 1 0.33513
cmeans Col mean scores differ 0.92897 1 0.33513
general General association 0.92897 1 0.33513
$`education:high|age:25-39`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:high|age:25-39
AltHypothesis Chisq Df Prob
cor Nonzero correlation 0.472 1 0.49207
rmeans Row mean scores differ 0.472 1 0.49207
cmeans Col mean scores differ 0.472 1 0.49207
general General association 0.472 1 0.49207
$`education:elementary|age:40-`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:elementary|age:40-
AltHypothesis Chisq Df Prob
cor Nonzero correlation 11.606 1 0.00065737
rmeans Row mean scores differ 11.606 1 0.00065737
cmeans Col mean scores differ 11.606 1 0.00065737
general General association 11.606 1 0.00065737
$`education:secondary|age:40-`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:secondary|age:40-
AltHypothesis Chisq Df Prob
cor Nonzero correlation 6.0457 1 0.01394
rmeans Row mean scores differ 6.0457 1 0.01394
cmeans Col mean scores differ 6.0457 1 0.01394
general General association 6.0457 1 0.01394
$`education:high|age:40-`
Cochran-Mantel-Haenszel Statistics for attitude by memory
in stratum education:high|age:40-
AltHypothesis Chisq Df Prob
cor Nonzero correlation 3.0436 1 0.081055
rmeans Row mean scores differ 3.0436 1 0.081055
cmeans Col mean scores differ 3.0436 1 0.081055
general General association 3.0436 1 0.081055
Cochran-Mantel-Haenszel Statistics for party by neighborhood
AltHypothesis Chisq Df Prob
general General association 273.81 6 3.3158e-56
Pearson's Chi-squared test
data: parties
X-squared = 273.92, df = 6, p-value < 2.2e-16
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