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	8	9	14
	12	13	18
System 2	6	13	17
	10	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 Select: less than .005, between .005 and .0125, between .0125 and .025, between .025 and .05, greater than .05
   What is your conclusion with respect to Factor A?
   Select:Factor A is significant, Factor A is not significant
   
3. The p-value for Factor B is Select: less than .005, between .005 and .0125, between .0125 and .025, between .025 and .05, greater than .05
   What is your conclusion with respect to Factor B?
   Select: Factor B is significant, Factor B is not significant
   
4. The p-value for the interaction of factors A and B is Select: less than .005, between .005 and .0125, between .0125 and .025, between .025 and .05, greater than .05
   What is your conclusion with respect to the interaction of Factors A and B?
   Select: The interaction of factors A and B is significant, The interaction of factors A and B is not significant

Answer 1

a)

Anova: Two-Factor With Replication
SUMMARY	Spanish	French	German	Total
System 1
Count	2	2	2	6
Sum	20	22	32	74
Average	10	11	16	12.33333
Variance	8	8	8	13.06667
System 2
Count	2	2	2	6
Sum	16	28	40	84
Average	8	14	20	14
Variance	8	2	18	34.4
Total
Count	4	4	4
Sum	36	50	72
Average	9	12.5	18
Variance	6.666667	6.333333	14
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
factor A	8.333333	1	8.333333	0.961538	0.364669	5.987378
factor B	164.6667	2	82.33333	9.5	0.013824	5.143253
Interaction	20.66667	2	10.33333	1.192308	0.366441	5.143253
Within	52	6	8.666667
Total	245.6667	11

b)

The p-value for Factor A = 0.36467

greater than .05

Factor A is not significant

.........

c)

p value for B= 0.013

between .0125 and .025

: Factor B is significant

...............

d)

p value for interaction : 0.366441

greater than .05

The interaction of factors A and B is not significant

..................

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