8 A biologist was interested in the effect of different colors of light on the growth of bacteria. She had 40 lights with filters to allocate to various treatments. An equal amount of bacteria was placed on each of 40 Petri dishes and the dishes were randomly allocated using the following treatments: A: "White" or unfiltered light for 30 hours, B: Blue light for 30 hours, C: Green light for 30 hours, D: Blue light for 15 hours and Green light for 15 hours. The contrasts of interest are1 Basics Although the original allocation put 10 dishes in each treatment, when changing the filters in treatment D two dishes were upset. The data are with MS(Within) = 0.725. (a) Explain, in words, the meaning of each contrast. (b) Show that these contrasts are orthogonal but that the estimated contrasts are not uncorrelated under the usual anova model. (c) Show that the following set of contrasts are not orthogonal, but are uncorrelated under the usual anova model. (d) The contrasts in part (c) are constructed to be "close" to the original ones. Estimate both sets of contrasts and their standard errors. (e) Discuss the differences in the estimates in part (d), and decide which set of contrasts you would advise the experimenter to use.