What kind of statistical test could help show this?

I have a log of customer call data, and would like to know what kind of statistical test I could use to test for statistical significance. Customers call with a unique call reason, and fit into either one customer type, young customers or elderly customers.

Call Reason      Young customers      Elderly Customers
Bill Enquiry     5                    28
Product Problem  15                   20


The numbers represent the number of calls for each call reason from each customer type. I want to know how I can test if there is statistically significant difference (with 95% confidence, say) in the type of customers that call for each call reason. For example, looking at the data, it appears that many more elderly customers call with billing enquiries than young customers. How might I rigorously test this?

• What you presented is called a “contingency table”. Among other techniques, you could use a “chi-squared test of independence” to see if both variables (call reason and customer age) are related. The phrases between quotation marks should help you find plenty of relevant material. – Gala Aug 3 '13 at 21:30
• Thanks, I found some material on Fisher's exact test, with a calculator here. So is it valid just to apply this to each row, assuming that the call reasons are independent? – Kevin Paulson Aug 3 '13 at 21:44
• I am not sure how you would do that or what do you mean with “call reasons are independent”. Typically you would apply the test to the whole table. – Gala Aug 3 '13 at 22:15
• I am not sure I understood your problem correctly. Formally you could do that but what this approach would achieve is testing if the proportion of elderly and young customers for each row is 50/50. Imagine that 70% of your customers are elderly but that they are facing exactly the same problems than the younger ones; all these proportions should be significantly different from 50% (I am ignoring some technical issues here) but that's just because you have more elderly customers than young customers. Would that result be of interest to you? – Gala Aug 3 '13 at 22:40
• “Are these proportions statistically significant?” is not really a meaningful question. What do you want to know? If elderly customers are calling more often with a billing enquiry than would be expected based on their number alone or if they represent more than a given proportion (say 50%) of billing enquiries? Those are two different questions. – Gala Aug 3 '13 at 23:01

Do chi-square test of independence to check that is row and column are related or not.

Chi-Square Test: Young customers, Elderly Customers

Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts

       Young    Elderly
customers  Customers  Total
1          5         28     33
14.14      18.86
5.911      4.433

2         15         20     35
15.00      20.00
0.000      0.000

3         25         12     37
15.86      21.14
5.272      3.954


Total 45 60 105

Chi-Sq = 19.569, DF = 2, P-Value = 0.000

Hence, p-value (0.0) < alpha (0.05). reject Ho.

conclusion : Call Reason and Customers age are related .

• It's natural to go right into conducting a test, but consider this. Such tests compare results to what would likely occur if chance alone were at work and if there were no difference in the population between the breakdowns for young and elderly customers. But did chance produce this sample, or is it a convenience sample? If the latter, the findings from the Chi-square test will not apply. In other words, there will be no statement one can make about statistical significance for these data. – rolando2 Aug 12 '13 at 23:19