Chi square column comparison in SPSS

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by tutkuoztel » Fri Sep 25, 2020 11:14 am

Hello there,

I ran a 2 x 3 crosstabulation chi square test on spss and compared the column proportions. I know that the different subscripts depict a significant difference proportions among the columns. But in the attached file, I have a column which has both of the subscript letters (I marked where it is, it writes "a,b").

I am having kind of a hard time understanding this. what does this "a,b" tell me? can it be that that one column is not statistically significant from either of the other two columns? Can it be even possible since the other two columns are statistically different from one another (as depicted "a" and "b")?

another question I want to ask is how to report these significant results. Although I clicked the "bonferroni p-values", none of my tables gave me such a p value that corresponded to the significant difference between the column proportions.

Any help would be much appreciated!

Thank you so much in advance, tutku
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by jonathon » Sat Sep 26, 2020 7:26 am

hi,

wait a second ... is this question to do with jamovi?! :P

yeah i'm not sure what the subscripts are either.

jonathon
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by MAgojam » Sat Sep 26, 2020 8:20 pm

Hi, @tutkuoztel.
Your output probably corresponds to an SPSS syntax like this:
Code: Select all
CROSSTABS
  / TABLES = Binarized_Accuracy BY Experimental_Condition
  / FORMAT = AVALUE TABLES
  / STATISTICS = CHISQ
  / CELLS = COUNT EXPECTED ROW COLUMN ASRESID BPROP
  / COUNT ROUND CELL.

with the PROP option, pairwise comparisons of column proportions are calculated and indicates which pairs of columns (for a given row) are significantly different.
Significant differences are indicated in the contingency table with APA-style formatting using subscript letters and are calculated at significance level .05.
With BPROP also the possibility to adjust the p-values ​​(Bonferroni method), pairwise comparisons of column proportions make use of the Bonferroni correction, which adjusts the observed significance level for the fact that multiple comparisons are made.
As a footnote to the contingency table, this should be reported:
"Each subscript letter denotes a subset of Experimental Condition categories whose column proportions do not differ significantly from each other at level .05".
tutkuoztel wrote: what does this "a,b" tell me? can it be that that one column is not statistically significant from either of the other two columns? Can it be even possible since the other two columns are statistically different from one another (as depicted "a" and "b")?

Your interpretation is correct, it could be that the column (EC = 0) is not statistically significant from either of the other two columns. It might also be possible since the other two columns are statistically different from each other.

Since there is an association between two nominal variables (or whether one can influence the other), but what could this association be.
There are a few different ways to perform a so-called post-hoc analysis. A nice article explaining some of them can be found in an article by Sharpe (2015).
https://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1269&context=pare
Many authors suggest examining so-called adjusted residuals, or Pearson residuals, or standardized adjusted residuals. These standardized residues can then be used to check whether the observed and expected value in the population may actually be different.
In your contingency table, the adjusted residuals appear to be higher for level (1) of Experimental Condition. At a 95% confidence level, if the value is greater than 1.96 or less than -1.96, it could be considered significantly different, but since we are doing this for each cell, we actually have a big risk in taking the wrong decision. To adjust for this multiple test, we would have to adjust the significance level by dividing the original level of 0.05 by the number of tests we perform (in this case the number of cells [R x C]). We should therefore consider a significance of 0.05 / 6 = 0.00833, which would correspond to a critical value of 2.63826 (or less than -2.63826).
This is known as the Bonferroni correction. To determine this critical value and the adjusted p-value for the z-value = 2.52435 (sig.0ff) for Experimental Condition level (1), take a look at this screenshot of some formulas in Excel.
p-value adjusted.PNG
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Cheers,
Maurizio
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by tutkuoztel » Tue Sep 29, 2020 10:35 am

Dear @MAgojam,

thank you so much for your support and help. I recently read in IBM's webpage that cells involving more than one subscript depicts a significant difference from all those other cells which are represented by those subscripts. I leave the link below:

https://www.ibm.com/support/knowledgecenter/en/SSLVMB_24.0.0/spss/tables/sig_tests_colprop_ex.html

Do you think I miss something? Or is my case that I outlined in my above post differs from that is described in the link?

Thank you so much, tutku

ps: I am aware that this post has nothing to do with jamovi, but when I saw the "statistics discussions" title, it made me think that I could post stuff from other platforms than Jamovi as well. sorry for the misunderstanding, I will not repeat it :)

best regards, tutku
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by MAgojam » Wed Sep 30, 2020 1:39 am

Hi, @tutkuoztel.
If from the menu you select Analyze> Tables> Custom Tables ... with your data, in output you get as in this screenshot:
Capture.PNG
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Pairs of columns are compared in each set of tests, and Bonferroni adjustments are used to adjust the significance values. For each significant pair, the key of the smaller category is placed under the category with the larger proportion. (as reported on the link page).

If you select Analyze> Descriptive Statistics> Cross Tables from the ...
for your output data, (see footnote to contingency table) this should be reported:
"Each subscript letter denotes a subset of Experimental Condition categories whose column proportions do not differ significantly from each other at level .05".

Cheers,
Maurizio
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