Question

Four different machines are being considered in an assembly plant. It is decided that 6 different operators are to be used in a randomized block experiment. The machines are assigned in a random order to each operator. The amount of time (in seconds) were recorded.

Machine	1	2	3	4	5	6
1	42.5	39.3	39.6	39.9	42.9	43.6
2	39.8	40.1	40.5	42.3	42.5	43.1
3	40.2	40.5	41.3	43.4	44.2	45.1
4	41.3	422.0	43.5	442.0	45.9	42.3

Yielding the following ANOVA table

	Df	Sum Sq	Mean Sq	F value	Pr (>F)
Factor(machine	3	15.92	5.308	3.339	0.0479
Factor (Operator)	5	42.09	8.417	5.294	0.00533
Residuals	15	23.85	1.59

If operator was ignored and the design of the experiment was treated as a 1-way CRD ANOVA in order to obtain as precise of estimates of differences between two treatment (machine)means as we were able to obtain by using 6 experimental units per treatment in the RBD, approximately how many replicates per treatment would we need? Hint: This a question about how efficient one design is compared to the other.

Answer 1