Adjusted R2 is a modification of R2 that adjusts for the number of explanatory terms in a model. Unlike R2, the adjusted R2 increases only if the new term improves the model more than would be expected by chance. The adjusted R2 can be negative, and will always be less than or equal to R2.

However, I've been reading Discovering Statistics Using SPSS by Andy Field and he explains that adjusted R squared is the amount of variance in the outcome that the model explains in the population (instead of just the sample).

This seem like very different interpretations. Are both correct? Thanks,