I did a quick (ish) calculation on paper and the first ASE came out to be 0.0394 which is not too far from what your reference says, so perhaps there is an error in our implementation.
From where is NaN coming? Presumamble it must be as a result of taking the
square root
of a negative number. This should give us a hint of the problem.
J'
On Sun, May 04, 2014 at 09:59:15PM -0700, Ben Pfaff wrote:
The CROSSTABS command can compute Goodman and Kruskal's lambda. It also
calculates the standard error of lambda according to the formula for
ASE0 given here:
http://pic.dhe.ibm.com/infocenter/spssstat/v22r0m0/index.jsp?topic=%2Fcom.ibm.spss.statistics.algorithms%2Falg_crosstabs_measures.htm
This page gives an example of the SPSS calculation:
http://www.csupomona.edu/~jlkorey/POWERMUTT/Topics/contingency_tables.html
Here is PSPP syntax that should reproduce the given on that page:
SET FORMAT F8.3.
* From
http://www.csupomona.edu/~jlkorey/POWERMUTT/Topics/contingency_tables.html.
DATA LIST LIST NOTABLE/x y w.
WEIGHT BY w.
BEGIN DATA.
1 1 424
1 2 213
1 3 59
3 1 55
3 2 188
3 3 357
END DATA.
Directional measures.
#========================================#=====#===========#========#=========#
#Category Statistic Type #Value|Asymp. Std.| Approx.|
Approx.#
# # | Error| T|
Sig.#
#----------------------------------------#-----+-----------+--------+---------#
#Nominal by Lambda Symmetric # .423| .021| 15.281|
#
#Nominal # | | |
#
# x # .497| NaN| 15.986|
#
# Dependent # | | |
#
# y # .370| NaN| 16.339|
#
# Dependent # | | |
#
#
---------------------------#-----+-----------+--------+---------#
# Goodman and x # .382| | |
#
# Kruskal tau Dependent # | | |
#
# y # .198| | |
#
# Dependent # | | |
#
#========================================#=====#===========#========#=========#
However, the asymmetrics ASEs given above are wrong. The first NaN
should be .024 and the second one should be .020 according to that
example webpage.
Worse, the ASEs given above don't match those calculated by other
software. For example, if you enter the data above into
http://vassarstats.net/newcs.html, you get the same lambda values .497
and .370 (well, to one extra digit), but ASEs .034 and .028,
respectively.
Can anyone explain how to calculate the asymptotic standard error of
lambda in a way that matches the SPSS results?
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