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 α = 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 .

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 α = 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 .

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 α = 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 .

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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