# Chi-Square Testing

#### Pablo

##### New Member
Hi,i'm new to this forum and I could really use some help. Thanks. I am faced with a business problem where we have set up a banner serving test to a pre-determined set of users. We are looking at the click thorugh based on a number of different attributes, age, income, gender etc to see if these are significant. Each report that we have generated tells us for each attribute how many times the banner was served and how many times it wasd clicked. Example data below:

Age Impressions Unique Visitors Clicks ClickRate
13 - 17 713 71 12 1.68%
18 - 24 4,654 344 71 1.53%
25 - 29 5,461 386 90 1.65%
30 - 34 8,443 379 205 2.43%
35 - 39 4,477 351 62 1.38%
40 - 44 4,066 296 85 2.09%
45 - 49 3,022 303 61 2.02%
50 - 54 3,475 279 61 1.76%

My approach is to use a chi-square test based on the number of clicks against the number of impressions. Example for 13-17 the number of impressions that resulted in a click=12 and the number that did not results in 713-12=701.

Is this the right approach or should I be looking at the unique visitors aswell, as 1 person can generate many impressions and multiple clicks.

Thanks

#### jkotlerman

##### New Member
You can start with a chi-square for the total number of clicks, but I think that single visitor clicks would be able to tell you much better about the type of a person who clicks. You can also use a multivariate logistic regression with clicks as an outcome and all your demographics as independent variables. In this case you should also use just one click per person. The problem with this model is that the same person might come 10 times and click on the 11th time. So to account for this you should use a repeated measures binomial model.

#### Pablo

##### New Member
Thanks for the reply. Thats helpful but the aim of the report is to identify if agegroup is a signifcant contributor to click rate. Would a simple chi-square test of visitors who clicked and did not click be enough data to use? I understand that the problem is a user could click multiple times and at different occassions but will that invaildate the chi-square results?

#### jkotlerman

##### New Member
When dealing with repeated measurements (clicks by the same person more than one time), you have to account for correlation. There are fairly simple methods that you can use to analyze this type of data, but if you are not familiar with repeated measures analysis, then it might be a bit difficult for you to perform this test on your own. I am assuming that you have a way of identifying when the same person comes back again for another click. The first test that I would run is a chi-square for each person, not taking into account how many times they have clicked. So each individual would only be counted once on whether or not they clicked. This is just a start and should give you some idea about the distribution of your data.

Jenny Kotlerman
www.statisticalconsultingnetwork.com