Question

A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.

	Language
	Spanish	French	German
System 1	7	8	14
	11	12	18
System 2	5	16	19
	9	18	25

Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use  = .05.

1. Complete the following ANOVA table (to 2 decimals, if necessary). Round p-value to four decimal places.

   Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
   Factor A
   Factor B
   Interaction
   Error
   Total

   
   
2. The p-value for Factor A is Selectless than .005between .005 and .0125between .0125 and .025between .025 and .05greater than .05Item 21
   
   What is your conclusion with respect to Factor A?
   SelectFactor A is significantFactor A is not significantItem 22
   
3. The p-value for Factor B is Selectless than .005between .005 and .0125between .0125 and .025between .025 and .05greater than .05Item 23
   
   What is your conclusion with respect to Factor B?
   SelectFactor B is significantFactor B is not significantItem 24
   
4. The p-value for the interaction of factors A and B is Selectless than .005between .005 and .0125between .0125 and .025between .025 and .05greater than .05Item 25
   
   What is your conclusion with respect to the interaction of Factors A and B?
   SelectThe interaction of factors A and B is significantThe interaction of factors A and B is not significantItem 26

Answer 1

Excel > Data > Data Analysis > Anova: Two-Factor With Replication

Anova: Two-Factor With Replication
SUMMARY	Spanish	French	German	Total
System 1
Count	2	2	2	6
Sum	18	20	32	70
Average	9	10	16	11.66666667
Variance	8	8	8	16.26666667
System 2
Count	2	2	2	6
Sum	14	34	44	92
Average	7	17	22	15.33333333
Variance	8	2	18	52.26666667
Total
Count	4	4	4
Sum	32	54	76
Average	8	13.5	19
Variance	6.666666667	19.66666667	20.66666667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Factor A	40.33333333	1	40.33333333	4.653846154	0.074355681	5.987377607
Factor B	242	2	121	13.96153846	0.005533094	5.14325285
Interaction	48.66666667	2	24.33333333	2.807692308	0.137832923	5.14325285
Within	52	6	8.666666667
Total	383	11

b)

p value for Factor A = 0.0743

P value > 0.05, Do not reject H0

Factor A is not significant

c)

p-value for Factor B = 0.0055

P value between .005 and .0125

Factor B is significant because P value < 0.05

d)

The p-value for the interaction of factors A and B is 0.1378

P value > 0.05

The interaction of factors A and B is not significant