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	14	15
	12	18	19
System 2	9	15	15
	13	17	21

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				NA	NA
Total			NA

1. The p-value for Factor A is:
2. What is your conclusion with respect to Factor A?
3. The p-value for Factor B
4. What is your conclusion with respect to Factor B?
5. The p-value for the interaction of factors A and B is
6. What is your conclusion with respect to the interaction of Factors A and B?
   

Answer 1

a)

Anova: Two-Factor With Replication
SUMMARY	Spanish	French	German	Total
System 1
Count	2	2	2	6
Sum	20	32	34	86
Average	10	16	17	14.333333
Variance	8	8	8	16.266667
System 2
Count	2	2	2	6
Sum	22	32	36	90
Average	11	16	18	15
Variance	8	2	18	16
Total
Count	4	4	4
Sum	42	64	70
Average	10.5	16	17.5
Variance	5.6666667	3.3333333	9
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Factor A	1.33	1	1.33	0.15	0.7084	5.9873776
Factor B	108.67	2	54.33	6.27	0.0339	5.1432528
Interaction	0.67	2	0.33	0.04	0.9625	5.1432528
Error	52.00	6	8.67
Total	162.67	11

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

Conclusion with respect to Factor A:

Factor A is not significant.

--

The p-value for Factor B is between .01 and .05

Conclusion with respect to Factor B:

Factor B is significant.

--

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.