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Additional resources for A Bayesian Alternative to Parametric Hypothesis Testing
Moreover, after doing a few of the calculations, the procedure becomes fairly transparent and the actual calculations can go quite smoothly.
Compare the conclusions from analyses (a), (b) and (c). (d) Write out an anova table (Source and df) for an experiment with the same number of crates, but with six shipments. Do the same for an experiment with three shipments and half the number of crates. Comment on these designs. 22, assume that the experiment was done according to the ﬁrst ﬁeld layout, that is, a completely randomized design (the data are in dataset DataLayout). (a) Reproduce the anova table in the example and carry out the F -tests.
So the contrasts are uncorrelated if Cov(Y¯i , Y¯i ) = 0 and i i i The former occurs if the means are uncorrelated, and the latter can occur if a b /ri = 0, which is the case in the oneway anova. 4 Suppose we have a full set of p orthogonal vectors a1 , a2 , . . , ap where ai = (ai1 , ai2 , . . , aip ) and ai ai = 1 and ai ai = 0 for all i and i . Deﬁne the matrix A = i ai ai , the sum of the outer products of the vectors ai . Then direct matrix multiplication will verify that 2 2 A = ai ai i = ai ai ai ai = i i ai ai = A i because ai ai = 1 if i = i and 0 if i = i .
A Bayesian Alternative to Parametric Hypothesis Testing by Rueda R.