Question 9.16: A 2^5 factorial experiment was conducted to estimate the eff...
A 2^5 factorial experiment was conducted to estimate the effects of five factors on the quality of lightbulbs manufactured by a certain process. The factors were A: plant (1 or 2), B: machine type (low or high speed), C: shift (day or evening), D: lead wire material (standard or new), and E: method of loading materials into the assembler (manual or automatic). One replicate was obtained for each treatment. Table 9.9 presents the results. Compute estimates of the main effects and interactions, and their sums of squares. Assume that the third-, fourth-, and fifth-order interactions are negligible, and add their sums of squares to use as a substitute for an error sum of squares. Use this substitute to test hypotheses concerning the main effects and second-order interactions.
TABLE 9.9 | |||||||
Treatment | Outcome | Treatment | Outcome | Treatment | Outcome | Treatment | Outcome |
1 | 32.07 | d | 35.64 | e | 25.1 | de | 40.6 |
a | 39.27 | ad | 35.91 | ae | 39.25 | ade | 37.57 |
b | 34.81 | bd | 47.75 | be | 37.77 | bde | 47.22 |
ab | 43.07 | abd | 51.47 | abe | 46.69 | abde | 56.87 |
c | 31 .55 | cd | 33. 16 | ce | 32.55 | cde | 34.51 |
ac | 36.51 | acd | 35.32 | ace | 32.56 | acde | 36.67 |
bc | 28.8 | bcd | 48.26 | bce | 28.99 | bcde | 45.15 |
abc | 43.05 | abcd | 53.28 | abce | 48.92 | abcde | 48.72 |
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