o unequal variances...what to do?
  1. transform original Y(it) and proceed as usual,
   redo residual analysis, ANOVA, multiple comparisons
  warning: results hard to interpret
  2. abandon usual ANOVA and follow-ups, check
  other assumptions and apply Satterthwaite

  - TRANSFORMATION (abridged Dean approach, more
  next lecture)
                              __
  1. plot s(i)-squared against Y(i.)
  2. a) if linear use square root of Y(it)
      b) if parabolic use ln(Y(it)) or if zeros
            ln (Y(it)+1)
  3. proceed with usual analysis
  - SATTERTHWAITE
  formula (one contrast):
             ______
(sum of c(i)*Y(i.)  ) +-     t(df*, alpha/2)* 
     sqrt(sum of (c(i)-squared*s(i)-squared/r(i))
              
where df* = 
   square (sum of (c(i)-squared*s(i)-squared/r(i))
----------------------------------------------------------
 sum of 
{[square (c(i)-squared*s(i)-squared/r(i)]/(r(i)-1} 

Example
o checking normality
  1. do a nrmal prob plot and look 
   for a straight line OR
  2. ask if 68% in (-1,1)
     95% in (-2,2) OR
  3. Shapiro-Wilkes (formal test, ignore)

  - to do normal prob plot
  z(it)' vs. ?(q) the z-score for
  Pr(Z<?(q)) = (q-.375)/(n+.25)
  where q is rank of z(it)' among all z(it)
      Blom normal scores
  - what look for:
   * straight line = normal
   * s-shape is heavy tails
   * reverse s is light tails
   * cup is right skew
   * upsided down cup is left skew