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How does SPSS compute the Bonferroni adjusted alpha used in their >2x2 Chi-square tests?

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How does SPSS compute the Bonferroni adjusted alpha used in their >2x2 Chi-square tests?

Emet Schneiderman
My question concerns how SPSS v22 does Bonferroni corrections for chi-square tests on contingency tables > 2x2 (nominal data). For example when doing the post-hoc pair-wise comparisons between the 4 groups (in columns), are the adjustments based on just the row or the whole matrix? For the former, the adjusted alpha level (threshold) would be 0.0083, (.05/6); for the latter it would seem to be .00167 (.05/30). Which are they using to declare that a p-value is significant, while preserving the experiment-wise alpha of 0.05? Their documentation is unclear on this issue.
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Re: How does SPSS compute the Bonferroni adjusted alpha used in their >2x2 Chi-square tests?

Jon Peck
You can find the adjustment formula in the Algorithms documentation under CROSSTABS.  It is based on the subtable in the column proportions test.

On Thu, Oct 13, 2016 at 8:39 AM, Emet Schneiderman <[hidden email]> wrote:
My question concerns how SPSS v22 does Bonferroni corrections for chi-square
tests on contingency tables > 2x2 (nominal data). For example when doing the
post-hoc pair-wise comparisons between the 4 groups (in columns), are the
adjustments based on just the row or the whole matrix? For the former, the
adjusted alpha level (threshold) would be 0.0083, (.05/6); for the latter it
would seem to be .00167 (.05/30). Which are they using to declare that a
p-value is significant, while preserving the experiment-wise alpha of 0.05?
Their documentation is unclear on this issue.



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Jon K Peck
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Re: How does SPSS compute the Bonferroni adjusted alpha used in their >2x2 Chi-square tests?

Emet Schneiderman
<quote author="Jon Peck">
You can find the adjustment formula in the Algorithms documentation under
CROSSTABS.  It is based on the subtable in the column proportions test.

Jon - Thanks for pointing me to the documentation.  If I understand it correctly, the Bonferroni corrections are computed on a row by row basis, and do not account for the total number of rows in the contingency table (i.e., treated as independent). For example with a 6x4 contingency table (6 response levels in the rows and 4 groups in columns),  there are 6 possible pairwise comparisons per row, so the adjusted alpha level (threshold) would be 0.00833, (.05/6).  Is this your understanding?
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Re: How does SPSS compute the Bonferroni adjusted alpha used in their >2x2 Chi-square tests?

Jon Peck
You can get the same result from the CTABLES column proportions test if you specify APA-style significance indication.  In the CTABLES output, you get a bit more explanation.

Note: Values in the same row and subtable not sharing the same subscript are significantly different at p< .05 in the two-sided test of equality for column proportions. Cells with no subscript are not included in the test. Tests assume equal variances.
Tests are adjusted for all pairwise comparisons within a row of each innermost subtable using the Bonferroni correction.

CTABLES now (V24) offers more choices and information.
You can choose between Bonferroni and Benjamini-Hockberg FDR,
and you can get the actual significance levels if you choose a separate table for the results.
You can also specify the significance levels you want and can get non-APA style indicators,
which I find more understandable.


On Fri, Oct 14, 2016 at 10:41 AM, Emet Schneiderman <[hidden email]> wrote:
You can find the adjustment formula in the Algorithms documentation under
CROSSTABS.  It is based on the subtable in the column proportions test.

Jon - Thanks for pointing me to the documentation.  If I understand it
correctly, the Bonferroni corrections are computed on a row by row basis,
and do not account for the total number of rows in the contingency table
(i.e., treated as independent). For example with a 6x4 contingency table (6
response levels in the rows and 4 groups in columns),  there are 6 possible
pairwise comparisons per row, so the adjusted alpha level (threshold) would
be 0.00833, (.05/6).  Is this your understanding?



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Jon K Peck
[hidden email]

===================== 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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