I collaborated in a study about cognitive training which had 2 groups of participants. First of all, I would need to compare if the personal variables (age, years education...) and neuropsychological variables of participants in one group do not differ significantly from participants in the other group before I carry on. I want to do this to ensure that differences in the outcome of the experiment following the cognitive training are, indeed, due to the different cognitive training and not preexisting variables. How could I do this preanalysis checking? (which statistical test to use in spss?)
you can use a t-test. t-tests are used to see if there are significant differences in means between groups. Or you can use a Chi-squared test to see if the distribution of age, years of education etc. is the same in both groups.
Otherwise, if you work with linear regression, you should keep those features constant by including them as variables in your linear regression.