The Monte Carlo simulations reported in the paper were performed as follows.

- Data were simulated in MLn, with a pre-specified variance-covariance matrix. The variance and covariance quantities in this matrix determine whether the matrix is spherical, and whether the data have homogeneous variance. For a particular variance-covariance matrix, 100 data sets were simulated. Each data set was simulated to have n=24 trials, k=3 conditions, and j=24 participants (1728 observations). Condition means were simulated to be {-0.2, 0, +0.2}. Total variance was simulated to be unity.

For each data set, the fixed effect was tested (using chi square, with df=2, alpha=.05, critical value is 5.99) and the result was logged (example log).

The 100 data sets were written as a large transposed matrix (100x1728, row-by-row) to a text file (example). Simulations were controlled by macro files for MLn (example macro). - The transposed matrix was re-transposed to a conventional data layout, with rows representing observations and column representing data sets (1728x100, column-by-column, example). This was done in S-Plus 2000 using this script.
- Data were then read into SPSS 11.0 in multivariate layout, with 72 observations (columns) per participant and 100 (data sets) x 24 (participants) = 2400 rows.

Data were re-partitioned into chunks corresponding to separate data sets, and fed into a repeated-measures ANOVA using the GLM command for repeated measures. This was done in SPSS 11.0 using this example syntax script and output mode set to "draft". - The resulting output (LARGE example) was copied into a plain-text editor, and sorted. The 100 test statistics for the 100 data sets thus were grouped together. These 100 (text lines reporting) statistics were re-sorted and classified by their significance value. Finally, the number of significant test statistics (at alpha=.05) was noted down.
- These numbers were edited into an S-Plus script that constructs the corresponding figure in the paper. The figure was saved in native S-Plus format, in Windows Metafile format and in Encapsulated PostScript, for further text processing.

2003.10.08 HQ