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sol4303a1 - 2 A suitable model can be/17(3 where is the...

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2. A suitable model can be: /17 (3) i j ij where : is the overall mean, " is the effect of treatment i , $ is the effect of block j and , are the random errors which are N( 0, F ) - i.e. have a normal distribution with constant variance. 2 We let and . We are also assuming that the observations in the different blocks are independent and that the treatments were randomized to the plots within each block. (2) A plot of the raw data, the ANOVA table and the residual and Cook’s plots are in sol4303a1.doc. The plot of the raw data shows that the treatment with 100 lb nitrogen has a lower phosphorus 2 5 2 5 content while that for 50 lbs nitrogen + 75 lb P O and 100 lbs nitrogen + 75 lb P O have higher phosphorus contents, on average. From this plot we can see also that the profiles for the different blocks are not parallel but cross each other so either there is no difference among blocks - indicating that blocking was not an effective tool - or there is a block by treatment interaction - which will inflate the error term making it harder to detect differences among treatments. The ANOVA indicates that blocks are not significant while treatments are – so probably blocking was not effective. However our analysis must be a RCB since that was how the study was
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