Statistical Test with one Control Group and Two Test Groups I have the following data:

What can I do to check if there is a significant increase of the ratio of people paying for the product over the total visitings of the website? 
I thought of a Chi-Squared test of Independence, but is it right? Can it be done with A/B testing? Are there any other options?
 A: Confidence intervals. 95% confidence intervals for percent paid are:


*

*$(.0205,.0247)$ for Control, 

*$(.0226,.0297)$ for New 1,

*$(.0235,.0308)$ for New 2 (note overlap with New 1), and 

*$(.0241,.0292)$ for New Combined (narrower on account of larger combined sample size).
The formula for the Wald 95% confidence interval (used above) is $\hat p \pm 1.96\sqrt{\frac{\hat p(1-\hat p)}{n}},$ where $\hat p = X/n.$ (For samples this large, the Agresti-Coull or 'plus=4' correction makes no important difference.)
Tests of binomial proportions. If you do a test comparing Control vs. New Combined as independent proportions or Fisher's Exact test,
you will find a significant difference.
From Minitab statistical software:
Test and CI for Two Proportions 

Sample    X      N  Sample p
1       425  18789  0.022620
2       411  15412  0.026668

Difference = p (1) - p (2)
Estimate for difference:  -0.00404791
95% CI for difference:  (-0.00736298, -0.000732844)
Test for difference = 0 (vs ≠ 0):  Z = -2.39  P-Value = 0.017

Fisher’s exact test: P-Value = 0.017

A: I'd go for a one-sided paired difference test to test whether the difference in ratios is statisticially different from zero. In your case, you would make use of the t-distribution instead of the normal one. However, they are asymptotically the same. Then you could test two differences in ratios ($r$): $r_{new_1} - r_{old} > 0$ and $r_{new_2} - r_{old} > 0$ for both new websites.
