CANCELLING: Chi-square and effect size W

[Peters Gj (PSYCHOLOGY)]

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

## Phd. Student                              ## Visit:
   Department of Work and Social Psychology     Room 3.004
   Faculty of Psychology                        Universiteitssingel 5
   University of Maastricht                     6229 ES Maastricht
                                                The Netherlands
________________________________________________________________________
____

-----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

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
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SIGNOFF SPSSX-L
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[Ornelas, Fermin-2]

Can you send me your spread sheet, I am curious about this problem.

Fermin Ornelas, Ph.D.
Management Analyst III, AZ DES
1789 W. Jefferson Street
Phoenix, AZ 85032
Tel: [phone]
E-mail: [hidden email]


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Peters Gj (PSYCHOLOGY)
Sent: Tuesday, December 04, 2007 11:11 AM
To: [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

## Phd. Student                              ## Visit:
   Department of Work and Social Psychology     Room 3.004
   Faculty of Psychology                        Universiteitssingel 5
   University of Maastricht                     6229 ES Maastricht
                                                The Netherlands
________________________________________________________________________
____

-----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

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD

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=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD