This article on issues related to degrees of freedom is worth a look:

Article Increasing Transparency Through a Multiverse Analysis

Degree of freedom is the highest numbers of source of variation which may vary...For instance, if we would like to conduct an experiment based on nutrient management in rice and allocate 8 treatments, have to be replicated thrice, then degree of freedom for treatment will be 7 and for replication 2... It means, by making 8 blocks, we can allocate 7 treatments as per our choice, but one treatment has to be allocated in that black only which is remaining and last one ..like wise in case of replication... Utility of degree of freedom is calculating mean sum of squares, which are used to calculate F-calculated values whereby one may compare with F-tabulated value and interpret the results based on rejection or acceptance of null hypothesis in question...