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.

[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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[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?

[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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