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?
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)