compute sample size for chi squared test validation I conduct Chi-squared test for following table:
|______|Feature1|Feature2|              |______|Feature1|Feature2|
|Group1|   70   |   30   |  100 =>      |Group1|   65   |   35   |  100
|Group2|   60   |   40   |  100 =>      |Group2|   65   |   35   |  100
           130  |   70   |

$\chi^2$ = 50/65 + 50/35 = 2.197;
P($\chi^2$  = 2.197) $\approx$ 0.15, so there would be no relation between Groups 1 and 2, if I chosed critical value = 0.20.
However in case critical value is 0.05, I can't make any assumptions.
So the question is I want to compute size of sample (group) that I am to have, if I want to wait till the difference between groups becomes significant ($P(\chi^2) \le0.05$).
There is a size of the effect I would like to be able to detect, but I can't really get the physical meaning of this term. Could you give me an insight on current table?
or 
if I were to observe a larger samples, in which the proportions were exactly the same as in this sample, then how large would this have to be for my result to be significant. And, yes, I'm aware of the case that samples may have different behaviour, if they become larger, but still)
 A: #all code given is in R, using the 'pwr' pachage.

What you are asking falls under power analysis. Power Analysis can help determine the sample size requirements to detect a specific effect size with a specific degree of confidence. If the proportion of observations that fall in each cell is your hypotheses (as seen in the first table), than they are: 0.35, 0.15 for group1 and 0.3, 0.2 for group 2 with (2-1)*(2-1)=1 degrees of freedom. The effect size you chose by these proportions is quite small (in a sense it is the magnitude in the difference between the observed and the expected values):
library(pwr)

> prob <- matrix(c(.35,.15,.3,.2), byrow = TRUE, nrow = 2)
> ES.w2(prob)
[1] 0.1048285

The significance level you want is 0.05 (I guess). The last piece is the  power, which is the 1-P where P is the chance for a type II error (failing to reject a false null hypotheses). This one is tricky, but a good rule of thumb is setting power to 0.9. Given all these:
> pwr.chisq.test(w=0.1048285,df=1,sig.level=0.05,power=0.90)

 Chi squared power calculation 

          w = 0.1048285
          N = 956.1749
         df = 1
  sig.level = 0.05
      power = 0.9

NOTE: N is the number of observations

You need 957 observations.
