# Two-sample test of proportions

In my research, I aim to compare websites and need to identify if the websites differ significantly from each other. I have divided the website into two categories. I have sampled 45 websites in the first category and 30 websites in the the other category. I need to identify if the first set of websites differ significantly from the second set. My data is largely nominal, as I just count the presence or absence of certain elements on the webpages.

So, during my data collection stage, I counted the Presence or Absence of certain elements on these website, and calculated the the percentage of occurrence of these elements, for the two sets of websites.

When I had the percentage of each elements for both the sets, I applied the Two Sample Test of Proportions, and tested my hypotheses (Is one set different from the other in terms of element A, B, C...etc). I had 60 elements, and I applied the test separately 60 times for each element.

My results do make sense, but I am just not sure if the test is a valid measure for my research. Can someone please help.

• Why are you not sure if the test is a valid measure for my research? Commented Jul 18, 2012 at 13:44
• well, mainly because its the first time i am applying it and when i read about it, it says that the test assumes Normal Distribution. I am not sure if I can assume this.
– MaO
Commented Jul 18, 2012 at 16:59

• To elaborate on @Michael Chernick's point, suppose you are testing at 5% level of significance, then, even if all of the 60 null hypotheses are true, the expected number of incorrect rejection is 3, and this number increases with increasing number of tests. To control this issue that arises with multiplicity, we can apply Bonferroni correction (reducing $\alpha$ to $\alpha/n$), Sidak correction (reducing $\alpha$ to $1-(1-\alpha)^{\frac{1}{n}}$) or control quantities like FWER or FDR. A brilliant reference is Bradley Efron's IMS monograph titled 'Large scale Inference'. Commented Jul 18, 2012 at 15:50