Chi-square and effect size W

[Peters Gj (PSYCHOLOGY)]

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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[Marta Garcia-Granero]

Hi Gjalt-Jorn

Although you already have found a solution on your own, you should also
try G*Power, a freeare sample size, power and effect size calculator
that computes w (as well as other measures of effect size).

Best regards,
Marta García-Granero

> [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!]
>

=====================
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[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