Effect size Excel sheets (WAS: CANCELLING: Chi-square and effect size W)

[Peters Gj (PSYCHOLOGY)]

Dear all,

I received some requests for the Excel sheets I mentioned in my previous
mails (see below).

I have put them at my site, albeit perhaps without the necessary
explanations. I hope they're of use to anybody though :-)

http://gjyp.nl?section=statistics

(it's at the bottom; the first two are about something else)

By the way, apparently, if I understood correctly, W is actually kind of
evil as it can become bigger than 1 depending on the number of
columns/rows in a table, making it not necessarily comparable across
different tables (although this also goes for Cohen's d apparently?
[1]). Cramer's V apparently corrects this, so this seems to be a more
reliable effect size measure. When the table is 2x2, Cramer's V = W (=
Phi), and then it doesn't matter, so even then reporting Cramer's V is
better.

(getting ready for the rain of corrections for what must be outrageous
oversimplifications :-))

Kind regards,

Gjalt-Jorn

(if you have any questions, just mail me at [hidden email])


[1] Kirk, R (2007) Effect magnitude: a different focus. Journal of
statistical planning & inference 137, 1634-1646



-----Original Message-----
From: Peters Gj (PSYCHOLOGY)
Sent: dinsdag 4 december 2007 19:11
To: SPSS mailing list <[hidden email]>
Subject: CANCELLING: Chi-square and effect size W

Hey all,

I'm very sorry, I googled a bit further and I found a document by
somebody called Karl Wuensch which looks very promising (e.g. includes
examples) at http://core.ecu.edu/psyc/wuenschk/docs30/Power-N.doc.
Another of his documents
(http://core.ecu.edu/psyc/wuenschk/docs30/EffectSizeConventions.doc)
stated that:

Size     W     OR
Small    .1    1.49
Medium   .3    3.45
Large    .5    9

Which answers my question; and I think his first document
('Power-N.doc') will be able to help me gain the necessary understanding
to actually use these measures without screwing up :-)

I am sorry for having sent the e-mail prematurely! I hope it did not
cause too much inconvenience!

Kind regards,

Gjalt-Jorn
________________________________________________________________________
____
Gjalt-Jorn Ygram Peters

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________________________________________________________________________
____

-----Original Message-----
From: Peters Gj (PSYCHOLOGY)
Sent: dinsdag 4 december 2007 18:57
To: SPSS mailing list <[hidden email]>
Subject: Chi-square and effect size W

Dear SPSSX list,

[this e-mail is about statistics rather than SPSS; if it is considered
off-topic, please inform me and I'll find a group that's more
appropriate. I post it here because it's about something that SPSS
doesn't seem to do, and most people here seem to find statistics
interesting, not only SPSS]

I am writing a paper in which I report (among other things) bivariate
psychological findings. Contrary to conventions in this field, I am
planning to not report the 'default statistics' (e.g. t, F, Chi^2) but
effect sizes (I am aware of the fact that many of these have problems of
their own, but am statistically too illiterate to do any better at the
moment).

I have searched Google and the limited literature I have at my disposal
(actually mainly Cohen's 1992 Power Primer) and if I understand
correctly, something called 'w' can be used to express the effect size
corresponding to a chi-square.

I can't find this thing in SPSS, so I resorted to calculate it myself.

If I understood correctly, it is calculated similar to chi-square: for
each cell, take the _proportion_ (as opposed to frequency) in that cell,
subtract the proportion one expected given H0, and divide by expected
proportion given H0; then take the square root of the sum for all cells:

w = SQRT ( (Pfound - Pexpected) / Pexpected) )

I played around a bit with Excel (ahum) and it seems that if you divide
Chi-square by the total number of observations in the original table,
then take the square root, you get w, too.

So far so good, I thought (I hope you're still with me :-)).

However, for 2x2 tables, I want to use odds ratios (OR) as effect size
measure; but I need to know values corresponding to 'small', 'medium'
and 'large' (I know this 'labelling' is not ideal). I know these for w
(.2, .3 & .5, according to Cohen). So I adjusted my Excel sheet to, for
any given 2x2 table, calculate both w and the OR, and started to create
tables that gave w's of .2, .3 and .5, so that I could use the
corresponding OR in the paper.

Yet, it appears that different tables, with the same corresponding w,
have different corresponding ORs . . .

Now, my question is, could anybody please tell me where I screw up?

I would be very grateful for any help/pointers anybody can give me!

[I will send anybody who's interested the Excel file of course; I also
have Excel files to calculate Cohen's d and Omega-squared, all three use
exported SPSS output files to automatically make a list of all
t-tests/anova's/chi-squares and calculate the effect sizes, so if
anybody wants it, just drop me a line!]

Thank you in advance and kind regards,

Gjalt-Jorn Peters

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