The calculation of degrees of freedom (d.f.) is related to the number of free parameters in the parameter space of the model. The d.f. is the difference between the number of free parameters in parameter spaces of alternative and null hypothesis. These free parameters depend on the cross-covariance matrix of the two data sets. For instance, if there are d signals correlated in m and n-dimensional complex-valued data sets (m

Tanuj, thank you so much for answering my query. However, I am still finding it a little difficult to comprehend the same with regards to the values obtained by me. The sample size of my study is 250. I have eight independent variables and three dependent variables that I have entered into the canonical correlation analysis. I'm attaching the screenshot of the results that I have obtained in the tests of significance. Basically, I have been able to work out the Wilk's Lambda statistic but I am unable to follow the f-statictic value obtained here.

See here:

https://onlinecourses.science.psu.edu/stat505/node/163

The symbols are explained on the previoous chapters:

N = sample size,

g = number of groups (IVs),

p = number of dimensions (DVs)

However, for the number of groups you report I get different results. It matches when the number of groups was g = 9 (not 8), I get

df1 = 24.0000

df2 = 693.7739

Thank you very much!