Most appropriate test for A/B testing results I looked answers for this question but couldn't find anything clear, everyone says something different.
I wonder what is the most appropriate method for testing the statistical significance of our A/B testing results. Currently, we are using Chi-Sqr but I am not sure if it is good or not for us.
For example:
version A: 90,000 visitors, 50,000 purchases
version B: 45,000 visitors, 25,700 purchases

I want to test if there is a significant difference between the conversion rates of two versions. 
 A: Here is a test of two proportions in Minitab. It uses a normal approximation
which should be accurate for such large numbers of counts. Because
the square of a standard normal distribution is chi-squared with one degree of
freedom, a chi-squared test on a $2 \times 2$ table would be essentially
the same. There are minor differences in how (or whether) various programs
implement 'continuity correction'. 
Test and CI for Two Proportions 

Sample      X      N  Sample p
1       50000  90000  0.555556
2       25700  45000  0.571111

Difference = p (1) - p (2)
Estimate for difference:  -0.0155556
95% CI for difference:  (-0.0211635, -0.00994764)
Test for difference = 0 (vs ≠ 0):  
    Z = -5.44  P-Value = 0.000

The P-value is so small that it is hard to imagine a valid test
would not find a significant difference between A and B proportions.
[Minitab shows P-values to three places, so output 0.000 indicates
a P-value below $0.0005.]$
It would have been easier to know what is puzzling you if you had
shows differences from various tests. Your data seem to be severely
rounded; you should use actual counts in such an analysis.
Note: If all four counts were divided by 100, then proportions would
be the same, but they would not be significantly different. Sample size matters.
Sample    X    N  Sample p
1       500  900  0.555556
2       257  450  0.571111
...
Test for difference = 0 (vs ≠ 0):  
    Z = -0.54  P-Value = 0.587

