11.6 A horticultural experiment conducted in a green house was laid out as a Latin square design, where the blocking factors represent temperature and light inten- sity, respectively. The treatments have a 22 factorial structure, that is, 2 factors A and B each at 2 levels. The layout of the design and the results from the ex- periment (in parentheses) are given below:

(i) Give a linear model for analyzing the data from this experiment and sketch the ANOVA giving sources of variation and d.f. (ii) Obtain the ANOVA table. (iii) Give a numerical expression for the estimate of the interaction A B. (iv) The experiment is to be repeated at different times, so that in the end data from 3 different times, T. T. T3 say, will be available (the experiment above represents T). Even though the temperature and light intensity trends remain, they may be assumed to differ from one time period to the next. It is expected that there is interaction between the time factor and the treatment factors. Give a linear model for data from this experiment and sketch the ANOVA table, giving sources of variation and d.f. (v) For the experiment described in (iv) what is the variance of the estimated main effects, A, B, and interaction, AB?

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Light Intensity Temperature - 1 2 3 4 1 aobo arbi agb a1bo (5) (10) (8) (7) 2 aibi ajbo aobo aob (12) (8) (6) (10) 3 a+bo agb ajb aobo (10) (8) (15) (7) aobi aobo aibo ab (9) (9) (11) (16)