A factorial experiment was designed to test for any significant differences in t

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. Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use alpha = .05. a. Complete the following ANOVA table (to 2 decimals, if necessary). b. The p-value for Factor A is What is your conclusion with respect to Factor A? c. The p-value for Factor B is What is your conclusion with respect to Factor B? d. The p-value for the interaction of factors A and B is What is your conclusion with respect to the interaction of Factors A and B?

Explanation / Answer

a) The ANOVA table for the given data is as follows

b) The p-value for Facor A is 0.17 which is greater than the significance level i.e., 0.17 > 0.05

Hence the conclusion with respect to factor A is there is no significant difference due to language translator system

c) The p-value for Facor B is 0.04 which is smaller than the significance level i.e., 0.04 < 0.05

Hence the conclusion with respect to factor B is there is a significant difference due to type of language

d)

The p-value for interaction for facors A and B is 0.77 which is greater than the significance level i.e., 0.77 > 0.05

Hence the conclusion with respect to interaction for facors A and B is there is no significant difference due to the interaction of facors A and B

ANOVA Source of Variation SS df MS F P-value F crit Factor A 21.33 1 21.33 2.46 0.17 5.99 Factor B 100.67 2 50.33 5.81 0.04 5.14 Interaction 4.67 2 2.33 0.27 0.77 5.14 Within 52 6 8.67 Total 178.67 11

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