Question

In an effort to promote a new product, a marketing firm asks participants to rate the effectiveness of ads that varied by length (short, long) and by type of technology (static, dynamic, interactive). Higher ratings indicated greater effectiveness.

Source of Variation	SS	df	MS	F
Length	10
Technology
Length × Technology	154
Error	570	114
Total	824

(a) Complete the F-table and make a decision to retain or reject the null hypothesis for each hypothesis test. (Assume experimentwise alpha equal to 0.05.)

Source of Variation	SS	df	MS	F
Length	10
Technology
Length × Technology	154
Error	570	114
Total	824

Answer 1

Source of Variation	SS	df	MS	F	P-value
Length	10	1	10	2	0.1600
Technology	90	2	45	9	0.0002
Length × Technology	154	2	77	15.4	0.0000
Error	570	114	5
Total	824	119

Let Factor A = Length,

Factor B = Technology

Calculation for each of the missing value in table is shown below:

SS_Total = SS_A + SS_B + SS_AxB + SS_Error

824 = 10 + SS_B + 154 + 570

SS_B = 824 - (10 + 154 + 570)

SS_B = 90

df_A = a - 1 (Here, a is no. of levels of factor A)

df_A = 2 -1 = 1

df_B = b - 1 (Here, a is no. of levels of factor B)

df_B = 3 -1 = 2

df_AxB = (a - 1)*(b - 1)

df_AxB = 1*2 = 2

df_Total = df_A + df_B + df_AxB + df_Error

df_Total = 1+ 2 + 2 + 114

df_Total = 119

MS_A = SS_A/df_A = 10/1

MS_A = 10

MS_B = SS_B/df_B = 90/2

MS_B = 45

MS_AxB = SS_AxB/df_AxB = 154/2

MS_AxB = 77

MS_Error = SS_Error/df_Error = 570/114

MS_Error = 5

F_statistic (Factor A) = MS_A/MS_Error = 10/5 = 2

F_statistic (Factor B) = MS_A/MS_Error = 45/5 = 9

F_statistic (Factor AxB) = MS_AxB/MS_Error = 77/5 = 15.4

P-value corresponding to F_statistic (Factor A) is 0.1600 (Obtained using online p-value calculator. screenshot attached)

P-value corresponding to F_statistic (Factor B) is 0.0002 (Obtained using online p-value calculator. screenshot attached)

P-value corresponding to F_statistic (Factor AxB) is 0.0000 (Obtained using online p-value calculator. screenshot attached)

Since p-value for Factor A (0.1600) is less than 0.05, there is no statistically significant difference in effectiveness of ads based on length.

Since p-value for Factor B (0.0002) is less than 0.05, there is statistically significant difference in effectiveness of ads based on technology.

Since p-value for Interaction between A and B (<0.0000) is less than 0.05, it shows that interaction effect is statistically significant.