16 - Quantitative factors and response functions

Summary

Preliminary examples

(a) A research student was proposing an extensive investigation of the decay of seed germination over time. The change of germination rate over two years was to be examined. Seeds would be treated in various different ways, and seeds from many different sources would be used. The major design questions were how often to test the germination rate during the two years, and how many seeds to use on each test occasion. The student, when questioned about the pattern of decay with time, was adamant that all previous data showed clearly that the relationship of germination rate with time was linear. For each combination of seed source and treatment, about 2000 seeds would be available. How should the 2000 seeds be sampled over the two-year period?

(b) In a rather similar investigation into the decline of strength of weldings used for oil rigs, again looking at the pattern over a long period of stress, the proposed design on which comments were requested was that which was regarded by the engineers concerned as too obvious to require statistical advice. As in the seed germination investigation, it was believed absolutely that the relationship of strength with level of stress was linear. The only analysis which was contemplated was to fit a straight line regression of the variable measuring strength on the length of time for which the stress was applied. The ‘obvious’ design proposed by the engineers was to use equal replication for eight, equally spaced, durations of stress. Can the despised statistician offer any improvement?