Re: Reformated Crosstabulation/Chi-square interpretation

On Thu, 27 Mar 2008 21:47:13 GMT, "novemrose via MathKB.com"
<u42346@uwe> wrote:

If I was interpreting the chart below what would I say about the overall
trend? This is a crosstabulation of an evaluation of the race of police
employees and the position that they hold in the police department. Of the
302 employees answering the race question, only 282 responded and of the 282,
7 of them were placed in categories by the coder and 20 are missing.

Crosstabulation
RACE
Count Hisp/Mex Hisp/Other Caucasian Other Total

Officer 146 13 52 13 224

Detective 8 1 9 1 19

Sergeant 7 0 7 0 24

Lt and above 4 1 3 0 8

Undoc code 4 0 1 2 7

Total 179 15 72 16 282

If you were seriously interpreting the table, you should
start by re-writing the table so that your statistical test
can be meaningful -- just as I suggested a couple of days
ago. Here is that exercise.

Comparing "Officer" with the three labeled categories, you
would have

Officer 146 13 52 13 224
Det-Lt. 15 2 19 1 51

- with the resulting Pearson chisquared test of 12.94,
with 3 d.f.; and the probability is p= .005 that this
configuration is chance arrangement. In particular, "Officer"
is over-represented by Hisp/Mex, and Det-Lt. range
is over-represented by Caucasian -- 19 for the latter is
about twice what would be expected by chance.


Also, lookiing at the chi-square test that was calculated (below) regarding
the chart above, what would the chi-square intrepretation indicate? What
does the "Assymp. Sig 2-sided" mean? What does the likelihood ration and

The "Asymptotic significance, two-sided" is an indication
of how rare the configuration would be by chance, given
the totals on the rows and columns. The word "asymptotic"
indicates that this is an approximate test -- In particular, it
is not always good when there are small expected values
for the cells.

The SPSS package, for one, would have warned you that the
test could be poor because there are <some count> of cells
with expectation less than 5. Having more than a quarter of
the cells that way is considered a bad sign. On the other
hand, the proliferation of numerous small rows is the main
problem with trying to draw conclusions here: Instead of having
a spurious indication of differences, because of contributions
from a tiny "expected" cell or two, the large number for
"degrees of freedom" swamps out the indication that ought
to be detected.

The 3 d.f. in my analysis carries most of the difference of
the 12 d.f. in the analysis below - The chisquared value
is 12.94 out of 17.71.



linear by linear association mean?

"Linear by linear" treats the rows and columns as
each being indexed by numbers 1, 2, 3...; the test
then assesses whether there is a "linear" relation.
Since your "RACES" do not make a sensible linear
ordering, this test is not sensible, so it is nice that it
says that there is nothing apparently there.


Basically what is the interpretation of
the chi-sqare of this same data on the chart above? Much thanks in advance:

(Given the large number of d.f.,) the associations
observed do not result in a test that is larger in value
than one would expect by chance. Of course, it is a
crappy way of testing, because the rows are too sparse.


Chi-Square Tests Value df Asymp. Sig. (2-sided)

Pearson Chi-Square 17.706a 12 .125

Likelihood Ratio 17.239 12 .141

Linear-by-Linear Assoc .937 1 .333

N of Valid Cases 282

--
Rich Ulrich

http://www.pitt.edu/~wpilib/index.html
.

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