Basics of Statistical Analysis

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 Observation Data Information Analysis Encode

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.

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

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.

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

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

Numerical Summaries of data Forms of Variation Sum of differences about the mean: Variance: Standard Deviation: Square Root of Variance

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?

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

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.

Example 2: Confidence Intervals for response rates You are the marketing analyst for Online Apparel Company You want to run a promotion for all customers on your database In the past you have run many such promotions Historically you needed a 4.5% response for the promotions to break-even You want to test the viability of the current full-scale promotion by running a small test promotion

Example 2: Confidence Intervals for response rates Test 1,000 names selected at random from the full list. You construct CI based on required rate of 4.5% and n=1000 Confidence Interval= Expected Response ± 1.96*SE The SE=.00655, and CI is (.0322, .0578) 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% © 2007 Prentice Hall

Example 2: Confidence Intervals for response rates 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