Is it possible to have 0 p-value when using chi-square test?

[Chen Ma]

Hello,

I am having difficulty interpreting the results I have.

I want to check whether the probability of A and the probability of B are independent or not.

Below is the code and the result I have.


. tab exttot_wo_motor extdur_wo_motor, chi2

exttot_wo_ | extdur_wo_motor
motor | 0 1 | Total
-----------+----------------------+----------
0 | 16,486 7,446 | 23,932
1 | 8,520 16,652 | 25,172
-----------+----------------------+----------
Total | 25,006 24,098 | 49,104

Pearson chi2(1) = 6.0e+03 Pr = 0.000

.
end of do-file


As far as I know, Pr is the p-value so, I thought since the p-value is close to 0 I can reject the null hypothesis and argue that Pr(exttot_wo_motor) and Pr(extdur_wo_motor) are not independent


However, when I also run as below.

. return list

scalars:
r(N) = 49104
r(r) = 2
r(c) = 2
r(chi2) = 6027.114958488087
r(p) = 0

Then, r(p) gives me 0.

I am a bit confused because I have never seen any case with a p-value equal to 0 exactly.

So I was wondering whether I am understanding something wrong.

Thanks in advance.

[Leonardo Guizzetti]

It's not that your p-value is zero, but rather is so small it is below the level of machine precision as to be effectively zero (to a computer). The real value is of course slightly bigger than zero. The below code reproduces the p-value calculation for the chi2 test.

input byte(row col) int(count)
0 0 16486
0 1 7446
1 0 8520
1 1 16652
end

tab row col [fw=count], chi2
di %15.0g chi2tail((`r(r)'-1)*(`r(c)'-1), `r(chi2)')

You can compare this with small cell counts to see the same calculation with a noticeably larger p-value.

[Chen Ma]

Thank you very much.