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	6	12	11
	10	16	15
System 2	9	13	17
	13	15	23

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 significant

Answer 1

Output using excel:

a)

SUMMARY	Spanish	French	German	Total
System 1
Count	2	2	2	6
Sum	16	28	26	70
Average	8	14	13	11.66667
Variance	8	8	8	13.06667
System 2
Count	2	2	2	6
Sum	22	28	40	90
Average	11	14	20	15
Variance	8	2	18	22.4
Total
Count	4	4	4
Sum	38	56	66
Average	9.5	14	16.5
Variance	8.333333	3.333333	25
ANOVA
Source of Variation	SS	df	MS	F	P-value
Factor A	33.33	1	33.33	3.85	0.0975
Factor B	100.67	2	50.33	5.81	0.0395
Interaction	24.67	2	12.33	1.42	0.3120
Error	52.00	6	8.67
Total	210.67	11

b) For Factor A:

The p-value for Factor A is greater than .05

Conclusion with respect to Factor A:

Factor A is not significant.

-----------------

c) For Factor B:

The p-value for Factor B is between .025 and .05.

Conclusion with respect to Factor B:

Factor B is significant.

-----------------

d) For interaction:

The p-value for the interaction of factors A and B is greater than .05

Conclusion with respect to the interaction of Factors A and B:

The interaction of factors A and B is not significant.