An experimenter is studying the performance of 3 machines. Each machine has two heads that produce the output product. She runs a two-stage nested design in which output from all three machines, both heads on each machine, and 4 observations on each machine-head combination are collected. However, the only computer program she has will only analyze factorial designs, so she (incorrectly) analyzes her experiment as a 2-factor factorial with 4 replicates and obtains the following results:   Factor Sum of Squares Degrees of Freedom Machines 50.00 2 Heads 45.00 1 Machine-head interaction 20.00 2 Error 10.00 18 Total 115.00 23   What is the correct sum of squares for the heads-within-machines nested effect?

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