|
Size: 2048
Comment:
|
Size: 2295
Comment:
|
| Deletions are marked like this. | Additions are marked like this. |
| Line 43: | Line 43: |
| The !MAHPLO macro is run using the call below. There are four inputs: the number of observations in the group (NOBS), the name of the group variable (gp), the value or name of the group (gpval) and the variables that are to be tested (vars). In the example below we wish to test the multivariate Normality of data comprising six observations, for females (gender=2) based on three variables, x1 to x3. | The !MAHPLO macro is run using the call below. There are four inputs: the number of observations in the group (NOBS), the name of the group variable (gp), the value or name of the group (gpval) and the variables that are to be tested (vars). In the SPSS data example [attachment:iris.sav given here] we wish to test the multivariate Normality of data comprising 26 observations, for females (gender=2) based on three variables, x1 to x3. |
| Line 45: | Line 45: |
| !MAHPLO NOBS=6 gp=gender gpval=2 vars=x1 x2 x3. | !MAHPLO NOBS=26 gp=gender gpval=2 vars=x1 x2 x3. |
| Line 47: | Line 47: |
__Reference__ Burdenski, T. (2000). Evaluating univariate, bivariate, and multivariate Normality using graphical and statistical procedures. ''Multiple Linear Regression Viewpoints'', '''26(2)''', 15-28. |
SPSS macro version of Budenski's program for a graphical plot to assess multivariate Normality
The !MAHPLO macro below plots Mahalanobis distances of each observation in a particular group against its hypothesised chi-square value assuming multivariate Normality. The plot should form a straight line.
DEFINE !MAHPLO (NOBS !TOKENS(1)
/gp !tokens(1)
/gpval !tokens(1)
/vars !cmdend).
list variables=all/cases=9999/format=numbered .
COMMENT 'y' is a variable automatically created by the program,
COMMENT and does not have to modified for different data sets.
select if (!gp eq !gpval) .
compute y=$casenum .
print formats y(F5) .
regression variables=y !vars/
descriptive=mean stddev corr/
dependent=y/enter !vars/
save=mahal(mahal) .
sort cases by mahal(a) .
execute .
list variables=y !vars mahal/cases=9999/format=numbered .
COMMENT In the next TWO lines, for a given data set put the
COMMENT actual n in place of the number '41' used for the
COMMENT example data set.
loop #i=1 to !NOBS .
compute p=($casenum - .5) / !NOBS.
COMMENT In the next line, change '3' to whatever is the number
COMMENT of variables.
COMMENT The p critical value of chi square for a given case
COMMENT is set as [the case number (after sorting) - .5] / the
COMMENT sample size].
if (!gp eq !gpval) chisq=idf.chisq(p,3) .
end loop .
print formats p chisq (F8.5) .
list variables=y p mahal chisq/cases=9999/format=numbered .
GRAPH
/SCATTERPLOT(BIVAR)=mahal WITH chisq
/MISSING=LISTWISE .
!ENDDEFINE.The !MAHPLO macro is run using the call below. There are four inputs: the number of observations in the group (NOBS), the name of the group variable (gp), the value or name of the group (gpval) and the variables that are to be tested (vars). In the SPSS data example [attachment:iris.sav given here] we wish to test the multivariate Normality of data comprising 26 observations, for females (gender=2) based on three variables, x1 to x3.
!MAHPLO NOBS=26 gp=gender gpval=2 vars=x1 x2 x3.
Reference
Burdenski, T. (2000). Evaluating univariate, bivariate, and multivariate Normality using graphical and statistical procedures. Multiple Linear Regression Viewpoints, 26(2), 15-28.