The statistics used on this site are rather opaque. To allow users (and myself) to get some feeling on how the relevant programs perform, this test page has been added. Internaly, it fills a 5 by 5 table with random data. The cells are numbered from 0-24 and each cell I is filled with pairs of uniformly random numbers with the first number in the range [I-1, I+1]. The value of the second number depends on the first number and the requested correlation. The mean value of the first number in each cell I is therefore, I. The Standard Deviation of the numbers is the that of uniform distributed numbers between [-1, 1] or SD([-1, 1]) = SQRT(1/3) = 0.577350269189626..... The requested Stadard Deviation can be chosen. The range is then scaled to [-target_SD / SQRT(1/3) , target_SD / SQRT(1/3)].
When using the WITHIN option for calculation of the variance, the variances of the marginal cells (i.e., row and column Totals), are calculated after reducing the cell mean to zero. The variances of the row and column totals are then independent from the between cell differences in the means. For the statistics, one degree of freedom per cell (-mean) is subtracted. Correlation coefficients calculated using WITHIN variances should also be independent from cell mean differences. Again, one degree of freedom is removed for every cell (-mean).
The Normalized Correlations are calculated from normalized cell values. In this case, the values in each cell are transformed to a standard normal distribution N{0,1}, i.e., scaled as r' = (r - MEAN(r))/SD(r), which results in mean = 0 and sd = 1. TWO degrees of freedom are subtracted for every cell (i.e., for mean and sd).
Often, calculations should be done accounting for variation in a third, unwanted, dimension.
An example would be SUBJECT variation. These so called NUISANCE factors should be
corrected for in the calculations, but should NOT show up in the final display. For the CORRECTED
MEANS function, nuisance factors are necessary.
The NUISANCE factor option constructs a 3D table, where a separate 6 value dimension of
unwanted factors is introduced. This implies the WITHIN variance option or the CORRECTED MEANS
function. Displayed are the Total values for the third, unwanted, dimension. For example, if a
display of Speaking style versus Stress is wanted, the Subject could be made the nuisance
factor. Correlations or Corrected Means would be calculated for all subjects combined, for
each of the speaking styles X Stress values. The Subjects would not show up in the display.
The NUISANCE factor introduces 6 hidden cells for each "visible" cell in the table. A nuisance factor is added to each value in a hidden cell (from 'U'-'Z'). The factor is (in order) 0, -0.5, 1.0, -1.5, 2.0, -2.5. So, for each nuisance factor, the averages are displaced by the same amount.
For the calculation of correlations, the desired correlation coefficient R can be entered. If the pairs in cell I are labeled (r, s), then
Finaly, you can upload a plain ASCII text file with your own data. These will be processed according to the settings
of the form. The format of the data-lines in the file is:
Where values in []-brackets are optional. Labels should contain only plain characters and NO white-space, i.e., [a-zA-Z0-9;:.,-]. Empty lines and lines starting with # are ignored. If the file is too large, it will be silently discarded.