Referring to the steel bar data in Table 9.16 (Example 9.6), construct a formal test of the null hypothesis that TIME does not have any kind of effect (either through a main effect or any type of interaction). Use α = 0:05.
Example 9.6
It is of importance to ascertain how the lengths of steel bars produced by several screw machines are affected by heat treatments and the time of day the bars are produced. A factorial experiment using four machines and two heat treatments was conducted at three different times in one day. This is a three-factor factorial with factors:
Heat treatment, denoted by HEAT, with levels W and L,
• Time of experiment, denoted by TIME, with levels 1, 2, and 3 representing 8:00 A.M., 11:00 A.M., and
3:00 P.M., and
• Machine, denoted by MACHINE with levels A, B, C, and D.
Each factor level combination was run four times. The response is the (code) length of the bars.
The data are given in Table 9.16.