BIOS 256  --  FALL 1998         Due 26 October 

EXERCISES


A)AVERAGE CORRELATIONS AS FUNCTIONS OF SIGNS

Let
S = i sgn(YY)

be the (centered) sign test statistic for comparing treatments j and j.  Express the average external and internal Spearman and Kendall correlation statistics as functions of the Ss: i.e., give formulas by which these four average correlations can be determined given the Ss, m, n, and (for “external" correlations) the predicted ranks.



B)CONFIDENCE REGIONS FROM RANDOMIZED BLOCKS

In the following randomized blocks experiment assume that, absent experimental error, the two treatments A and B have the effect of reducing the observations by a and b units, respectively, as compared with the control C.

Treatment: A B C
Block 1:132537
Block 2:10 932
Block 3:151431

a)Tabulate the exact distributions for this design (m=n=3) of Friedman's chi-squared statistic and of the
           weighted ranking statistic with linear scores, and hence find the exact P-values for testing the hypothesis
           of  no treatment effects.   (Try  STATXACT --)

b)Draw a confidence chart for (a, b) showing the 50% confidence regions based on the weighted ranking 
test, Friedman's chi-squared, and ordinary two-way analysis of variance.  Note: consider carefully 
whether to use variance or range as the measure of credibility for weighted rankings: one leads to a 
much more complicated chart than the other.