1. Basics of Statistical Analysis

2. Basics of Analysis The process of data analysis Example 1: –Gift Catalog Marketer –Mails 4 times a year to its customers –Company has I million customers on its file ObservationDataInformation Encode Analysis

3. Example 1 Cataloger would like to know if new customers buy more than old customers? Classify New Customers as anyone who brought within the last twelve months. Analyst takes a sample of 100,000 customers and notices the following.

4. Example 1 5000 orders received in the last month 3000 (60%) were from new customers 2000 (40%) were from old customers So it looks like the new customers are doing better

5. Example 1 Is there any Catch here!!!!! Data at this gross level, has no discrimination between customers within either group. –A customer who bought within the last 11 days is treated exactly similar to a customer who bought within the last 11 months.

6. Example 1 Can we use some other variable to distinguish between old and new Customers? Answer: Actual Dollars spent ! What can we do with this variable? –Find its Mean and Variation. We might find that the average purchase amount for old customers is two or three times larger than the average among new customers

7. Numerical Summaries of data The two basic concepts are the center and the Spread of the data Center of data - Mean, which is given by - Median - Mode

8. Numerical Summaries of data Forms of Variation –Difference about the mean: – Absolute Difference: –Total Sum of Squares: –Variance: –Standard Deviation: SquareRoot[Variance]

9. Confidence Intervals In catalog eg, analyst wants to know average purchase amount of customers He draws two samples of 75 customers each and finds the means to be $68 and $122 Since difference is large, he draws another 38 samples of 75 each The mean of means of the 40 samples turns out to be $ 94.85 How confident should he be of this mean of means?

10. Confidence Intervals Analyst calculates the standard deviation of sample means, called Standard Error (SE) Basic Premise for confidence Intervals –95 percent of the time the true mean purchase amount lies between plus or minus 1.96 standard errors from the mean of the sample means. C.I. = Mean (+or-) (1.96) * Standard Error

11. Confidence Intervals However, if CI is calculated with only one sample then Standard Error of sample mean = Standard deviation of sample Basic Premise for confidence Intervals with one sample –95 percent of the time the true mean lies between plus or minus 1.96 standard errors from the sample means.

12. C.I. For Response Rates Standard error for response rates is S.E.= Where, p = Sample response rate n = sample size

13. Example 2: Test 1,000 names selected at random from a new list. To break-even the list must be expected to have a response rate of 4.5 percent Confidence Interval= Expected Response (+/-) 1.96*SE = p(+/-) 1.96*SE In our case C.I. = 3.22 % to 5.78%. Thus any response between 3.22 and 5.78 % supports hypothesis that true response rate is 4.5%

14. Example 2: The list is mailed and actually pulls in 3.5% Thus, the true response rate maybe 4.5% What if the actual rate pulled in were 5% ? Regression towards mean: Phenomenon of test result being different from true result Give more thought to lists whose cutoff rates lie within confidence interval

15. Determining List Size Let us assume that we expect true p = 0.035 We want to be 95% certain that our test mailing will tell us if true response is between 3.3 % and 3.7% We are saying that Precision = 1.96*SE=.002 (or 0.2%) Hence, –SE=0.002/1.96=0.001020 –0.001020= –0.001020=(0.033775/n)^1/2 –0.00000104=0.033775/n –n=32,437 In general, –n=[p*(1-p)*1.96 2 ]/Precision 2