I have two distinct groups made of a different numbers of subjects (111 Millions and 126 Millions). My goal is to evaluate how many subjects in the two groups encounter 10 different diseases. For this purpose, I build a table (reporting here only 4 out of 10 diseases) as follows:

Disease Group A Group B
A 23 M 19 M
B 45 M 18 M
C 19 M 18 M
D 21 M 20 M

In this case there are no means involved: I'm simply counting the number of occurrences (frequency) within each group and for each disease. Is there a way to check whether the the difference is statistically significant for each disease between the two groups? I would proceed with a Chi-squared test isolating each disease, building a contingency table as follows and then run the test.

Disease A Group A Group B Sum
Infected 23 M 19 M 42 M
Not-Infected 88 M 107 M 195 M
Sum 111 M 126 M

Is, in this case the Chi-squared test, the most appropriate test?


1 Answer 1


With such large samples, do you think results of a statistical test adds much value?

Formally, you could used prop.test in R (or essentially equivalently, a chi-squared test on a 2-by-2 table).

prop.test(c(23*10^6,19*10^6), c(111*10^6,126*10^6), cor=F)

        2-sample test for equality of proportions 
        without continuity correction

data:  c(23 * 10^6, 19 * 10^6) out of c(111 * 10^6, 126 * 10^6)
X-squared = 1288000, df = 1, p-value < 2.2e-16
alternative hypothesis: two.sided
95 percent confidence interval:
 0.05631563 0.05651148
sample estimates:
   prop 1    prop 2 
0.2072072 0.1507937 

With millions of subjects is there any doubt that proportions $0.2091$ and $0.1508$ differ? Or does a P-value (predictably) extremely near $0$ somehow seem impressive--or tick someone's supposedly mandatory box?

Note: Output for chisq.test in R follows:

TBL = 10^6*matrix(c(23,19,88,107), byrow=T, nrow=2)
        [,1]     [,2]
[1,] 2.3e+07 1.90e+07
[2,] 8.8e+07 1.07e+08

chisq.test(TBL, cor=F)

         Pearson's Chi-squared test

data:  TBL
X-squared = 1288000, df = 1, p-value < 2.2e-16
  • $\begingroup$ Thanks for your answer. I was only wondering whether other comparisons were possible besides the simple Chi-squared $\endgroup$
    – SavioD
    Apr 7, 2021 at 14:13

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