[Bruce Weaver]

Hi David. Re #15, as this note on the Wolfram website says, "The Bonferroni correction is a multiple-comparison correction used when several dependent or independent statistical tests are being performed simultaneously" (emphasis added).

Cheers,
Bruce

[David Speed]

Thanks a lot Bruce!

[Wang Weiping]

I fully agree with the risks of post hoc testing, particularly without coping with familywise error.

Among users of other statistical packages (such as SPSS), I gather chi-square residuals is in much more common parlance, so to speak.

As far as I'm concerned, though, it seems Stata doesn't provide automatically the residuals issued from a chi-square test.

However, the user-written SSC tabchi (by Nick Cox) can precisely do that, as Nick pointed out in #2.

Below, a toy example:

. sysuse auto
(1978 Automobile Data)

. gen myrep = rep78
(5 missing values generated)

. replace myrep = 1 if myrep <3
(8 real changes made)

. tab myrep

myrep | Freq. Percent Cum.
------------+-----------------------------------
1 | 10 14.49 14.49
3 | 30 43.48 57.97
4 | 18 26.09 84.06
5 | 11 15.94 100.00
------------+-----------------------------------
Total | 69 100.00

. tab myrep foreign, exp chi2

+--------------------+
| Key |
|--------------------|
| frequency |
| expected frequency |
+--------------------+

| Car type
myrep | Domestic Foreign | Total
-----------+----------------------+----------
1 | 10 0 | 10
| 7.0 3.0 | 10.0
-----------+----------------------+----------
3 | 27 3 | 30
| 20.9 9.1 | 30.0
-----------+----------------------+----------
4 | 9 9 | 18
| 12.5 5.5 | 18.0
-----------+----------------------+----------
5 | 2 9 | 11
| 7.7 3.3 | 11.0
-----------+----------------------+----------
Total | 48 21 | 69
| 48.0 21.0 | 69.0

Pearson chi2(3) = 27.2640 Pr = 0.000

. tabchi myrep foreign, a

observed frequency
expected frequency
adjusted residual

------------------------------
| Car type
myrep | Domestic Foreign
----------+-------------------
1 | 10 0
| 6.957 3.043
| 2.262 -2.262
|
3 | 27 3
| 20.870 9.130
| 3.236 -3.236
|
4 | 9 9
| 12.522 5.478
| -2.098 2.098
|
5 | 2 9
| 7.652 3.348
| -4.040 4.040
------------------------------


2 cells with expected frequency < 5

Pearson chi2(3) = 27.2640 Pr = 0.000
likelihood-ratio chi2(3) = 29.9121 Pr = 0.000

In general, absolute residuals beyond 3 are considered somewhat "implicated" in the statistical difference. Depending on the data, even beyond 2.

Hopefully that helps

Dear Prof. Marcos Almeida ,

You said that "In general, absolute residuals beyond 3 are considered somewhat "implicated" in the statistical difference. " Do you mean that , for the variable myrep, if myrep=5 , there is a statistics difference between domestic and foreign car. Because you mentioned that absolute residuals > 3.

Looking forward to your reply.


Best regard !

[Marcos Almeida]

Wang Weiping In the example provided in #5, we observe that myrep 3 and myrep 5 present absolute residuals beyond 3, hence both are strongly "implicated" with regards to the statistical difference.