Once measurements are taken, generally need to fit the data to find parameters such as critical exponents, using a multi-parameter fit to data which usually has large errors. This is very difficult!
For example
requires a four parameter fit, and often have so much freedom that a wide
range of values are possible. Usually need to assume 
, and
get 
from other measurements.
Above formula is only true ``asymptotically close'' to 
.
How close is that? Not always clear.
May see ``apparent'' or pseudo-critical exponents,
which change or disappear as the size of the system is increased and
we move closer to 
.
There may also be 
corrections
to the asymptotic formula, which are hard to distinguish from a small
power-law exponent. In this case may need input from theory.