9. Factorial experiment

"Permission-based e-mail marketing" describes the tactic of marketing one's products and services through e-mail, but with the recipient's permission. This is in contrast to spamming, which is done without regard for the recipient's wishes.

An industry expert offered the following advice to permission-based e-mail marketers: "The first key is to make your efforts more subscriber-centric and permission verified....The second key is to test, test, test. E-mail is so cost-effective, measurable, and immediate, that it is the perfect medium to improve through testing." (Source: Whitney M. Keyes, "Exact Target Shares Tip on E-mail Marketing," Seattle Post-Intelligencer, June 25, 2008)

Heeding this advice, an e-mail marketer conducted a factorial experiment to test the effectiveness of two factors in generating sales. The first factor, called Factor A, consists of three different subject lines for the e-mail message. The second factor, called Factor B, is whether the e-mail message includes an Amazon.com voucher that the recipient can redeem if a purchase is made.

The experimental units are batches of 20,000 e-mail addresses obtained from the marketer's database. E-mail messages, adjusted according to the factor levels, are sent to all the addresses in each batch, and the total sales amount for each batch is recorded as a measure of response.

If the number of replications is 10, the number of observations is ______ .

The results of the study are summarized by the corresponding sample means below. All figures are in dollars.

Data Summary

	Factor B:	Data Summary
Voucher	No Voucher	Factor A Sample Means
Factor A:	Subject Line 1	232.10	152.50	192.30
	Subject Line 2	154.00	148.20	151.10
	Subject Line 3	131.20	143.10	137.15
	Factor B Sample Means	172.43	147.93

Use the information in the table above to answer the following question. The total sales amount for the sample assigned e-mail messages with Subject Line 1 and no voucher is ____ . The average sales amount for units assigned e-mail messages with Subject Line 1 is____ . The average sales amount for units assigned e-mail messages with no voucher is ____ . The overall sample mean response for the experiment is _____ .

The investigator performed an analysis of variance (ANOVA) to test the hypothesis that the populations defined by the treatment combinations are equal. We would like to determine the presence of main effects due to Factors A and B, respectively, and the interaction effect of both. Some of the results are presented in the table below.

ANOVA Table
Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Factor A	______	_______	16,445.20	4.924	0.0109
Factor B	_______	_______	9,003.90	2.696	0.1064
Interaction	23,553.20	_______	______	_____	0.0364
Error	______	_____	_______
Total	245,786.84	59

Please go through the following steps to complete the ANOVA table above.

1. The sum of squared deviations of the Factor A sample means from the overall sample mean is 1,644.52. The sum of squared deviations of the Factor B sample means from the overall sample mean is 300.13. Select the appropriate value for the sums of squares for Factors A and B in the ANOVA table.

2. Select the appropriate value for the sum of squares due to error in the ANOVA table.

3. Select the appropriate degrees of freedom for all the sums of squares in the ANOVA table.

4. Select the appropriate values for the mean square due to interaction, the mean square due to error, and the F statistic for the interaction effect.

Use the results from the completed ANOVA table to make the following conclusions.

At the significance level of = 0.05, the main effect due to Factor A is ____ ; the main effect due to Factor B is____ ; and the interaction effect of the two factors is ____ .