A gas chromatograph is an instrument that measures the amounts of various compounds contained in a sample by separating the various constituents. Because different components are flushed through the system at different rates, chromatographers are able to both measure and distinguish the various constituents of the sample. A counter is placed somewhere along the instrument that records how much material is passing at various times. By looking at the counts at various times, the chemist is able to reconstruct the amounts of various compounds present. The total number of counts is proportional to the amount of the compound present.
An experiment was performed to see whether slowing down the flow rate would increase total counts. A mixture was produced with three different Concentration levels: low, medium, and high. The two Flow Rates used were slow and/art. Each mixture was run 5 times and the total counts recorded each time. Partial box plots for Concentration and Flow Rate show:

A two-way ANOVA with interaction model was run, and the following ANOVA table resulted:

A plot of residuals vs. predicted values showed:

What conclusions about the effect of flow rate do you draw? Do you see any potential problems with the analysis?

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65000 60000 55000 , 50000 - 45000 100000 8 75000 E 50000 25000 Fast Slow Flow Rate High Low Medium Concentration Sum of Mean Source DF Squares Square F-ratio P-value Conc Flow rate 364008E3 364008E3 2965 <0.0001 Interaction 2 203032E3 101516E3 8.27 0.0019 Error Total 2 483655E5 241828E5 1969.44 <0.0001 24 294698E3 122791E3 29 492272E5 4000T 8 あー4000 t -8000 25000 50000 75000 10000 Predicted Values (counts)