Homework SourseA factorial experiment was designed to test for any signific
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 = .05.
Complete the following ANOVA table (to 2 decimals, if necessary).
| Spanish | French | German | |
| System 1 | 10 | 12 | 11 |
| 14 | 16 | 15 | |
| System 2 | 8 | 17 | 19 |
| 12 | 19 | 25 |
Solution
We use excel to complete the table
Anova: Two-Factor With Replication
| We use excel to complete the table Anova: Two-Factor With Replication | ||||||
| SUMMARY | Total | |||||
| Count | 2 | 2 | 2 | 6 | ||
| Sum | 26 | 27 | 26 | 79 | ||
| Average | 13 | 13.5 | 13 | 13.16667 | ||
| Variance | 18 | 4.5 | 0 | 4.566667 | ||
| Count | 2 | 2 | 2 | 6 | ||
| Sum | 26 | 36 | 44 | 106 | ||
| Average | 13 | 18 | 22 | 17.66667 | ||
| Variance | 2 | 2 | 18 | 20.66667 | ||
| Total | ||||||
| Count | 4 | 4 | 4 | |||
| Sum | 52 | 63 | 70 | |||
| Average | 13 | 15.75 | 17.5 | |||
| Variance | 6.666667 | 8.916667 | 33 | |||
| ANOVA | ||||||
| Source of Variation | SS | df | MS | F | P-value | F crit |
| Sample | 60.75 | 1 | 60.75 | 8.191011 | 0.028727 | 5.987378 |
| Columns | 41.16667 | 2 | 20.58333 | 2.775281 | 0.140167 | 5.143253 |
| Interaction | 40.5 | 2 | 20.25 | 2.730337 | 0.143491 | 5.143253 |
| Within | 44.5 | 6 | 7.416667 | |||
| Total | 186.9167 | 11 |
