SPSS Statistics

Why do i get Kendall-Tau = 1 despite the rankings are not similar? And why do i get the same standard error for every part worth? Can someone help?

From one of our statisticians:

The design is a completely balanced 2x2x2, analyzed as a main-effects-only model. The reduced full-column-rank design matrix X is:

  1  1  1  1
  1  1  1 -1
  1  1 -1  1
  1  1 -1 -1
  1 -1  1  1
  1 -1  1 -1
  1 -1 -1  1
  1 -1 -1 -1  

Notice that for each pair of columns, the sum of the products of the coefficients across the rows is 0. This is the orthogonality property. This means that the X'X matrix is

  8  0  0  0
  0  8  0  0
  0  0  8  0
  0  0  0  8
 

and the inverse (X'X)^-1 is

   .1250000000   .0000000000   .0000000000   .0000000000
   .0000000000   .1250000000   .0000000000   .0000000000
   .0000000000   .0000000000   .1250000000   .0000000000
   .0000000000   .0000000000   .0000000000   .1250000000
 

Since the estimated covariance matrix of the parameter estimates is (X'X)^-1 times the estimated error variance of the predictions, each parameter estimate will have the same variance and thus standard error estimate. The other estimates shown in the output are just the negatives of the ones computed in the original estimation.

Without the SUBJECT subcommand, CONJOINT averages the data across subjects for each card and calculates a single regression model on the eight resulting cases. While it won't always be this way, it's easy for the rank correlation of the predictions from a regression with only eight cases to be perfect, especially when you're averaging out variation the way you do when averaging the original data across subjects. If you insert the SUBJECT subcommand into these data (or at least the portion visible in this email, which I don't think is all cases, since the results aren't identical to what's shown in the output screen shots), you'll get results for each subject individually in addition to the averaged data results, and for some subjects the rank correlations will be perfect, while for most they won't.

So none of these results are actually weird.