How do you determine if a particular cell of an i x j contingency table is statistically significant among all other cells?

Question

I have a contingency table which is not fixed, it varies depending on on the data.

I want to know how significant a particular cell is compared with the other cells. Is there a method of doing this?

score 3 · Accepted Answer · answered Feb 26 '11 at 04:23

The term "statistically significant" is a bit arbitrary, because it is defined relative to a null hypothesis. The basic way to test this is to use your "null hypothesis" to define a set of Expected values for each cell.

The standard way to measure the error is $r_i^2=\frac{(O_i-E_i)^2}{E_i}$ (O=observed count, E=expected count under the null hypothesis), which is the "partition" of the chi-square.

Another alternative is to use $d_i=O_i log(\frac{O_i}{E_i})$ ("entropy" statistic).

Both are approximately equal in large tables, with big expected values.

The "significant cells" have large values of these two values

score 0 · Answer 2 · answered Feb 23 '11 at 15:24

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I am not sure if I understand the first part of your question - everything varies depending on the data, does it not?

There are ways to partition chi-square; I am not near my references, but this article seems apropos http://www.jstor.org/pss/2283933

If you know in advance which cell you will want to test, you can simply combine the other rows or columns.

answered Feb 23 '11 at 15:24

Peter Flom

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Thank you for the reference. However i currently do not have access to jstor. Thank you for the idea as well about partitioning the chi-square. – dixi Feb 24 '11 at 02:32

How do you determine if a particular cell of an i x j contingency table is statistically significant among all other cells?

2 Answers2