(dat <- matrix(c(10,40,30,20), nrow = 2, byrow = F))
     [cnt] [int]
[no]   10   30
[yes]  40   20

(dat_0 <- matrix(c(20,30,20,30), nrow = 2, byrow = F))
     [cnt] [int]
[no]   20   20
[yes]  30   30

p1 <- dat[1,1]/sum(dat); p2 <- dat[1,2]/sum(dat);
p3 <- dat[2,1]/sum(dat); p4 <- dat[2,2]/sum(dat);
p1_0 <- dat_0[1,1]/sum(dat_0); p2_0 <- dat_0[1,2]/sum(dat_0);
p3_0 <- dat_0[2,1]/sum(dat_0); p4_0 <- dat_0[2,2]/sum(dat_0);
(w <- sqrt( ((p1_0-p1))^2/(p1_0)
       +((p2_0-p2))^2/(p2_0)
       +((p3_0-p3))^2/(p3_0)
       +((p4_0-p4))^2/(p4_0) ))

[1] 0.4082483

dat_0_better <- matrix(c(40,10,40,10), nrow = 2, byrow = F)
      [cnt] [int]
 [no]   40   40
 [yes]  10   10

p1 <- dat[1,1]/sum(dat); p2 <- dat[1,2]/sum(dat);
p3 <- dat[2,1]/sum(dat); p4 <- dat[2,2]/sum(dat);
p1_0 <- dat_0_better[1,1]/sum(dat_0); p2_0 <- dat_0_better[1,2]/sum(dat_0);
p3_0 <- dat_0_better[2,1]/sum(dat_0); p4_0 <- dat_0_better[2,2]/sum(dat_0);
(w <- sqrt( ((p1_0-p1))^2/(p1_0)
            +((p2_0-p2))^2/(p2_0)
            +((p3_0-p3))^2/(p3_0)
            +((p4_0-p4))^2/(p4_0) ))
[1] 1.118034

library(vcd)
assocstats(dat_0)
assocstats(dat_0_better)