  The ubiquity of power-law relations in empirical data displays physicists'
love of simple laws and uncovering common causes among seemingly unrelated
phenomena. However, many reported power laws lack statistical support and
mechanistic backings, not to mention discrepancies with real data are often
explained away as corrections due to finite size or other variables. We propose
a simple experiment and rigorous statistical procedures to look into these
issues. Making use of the fact that the occurrence rate and pulse intensity of
crumple sound obey power law with an exponent that varies with material, we
simulate a complex system with two driving mechanisms by crumpling two
different sheets together. The probability function of crumple sound is found
to transit from two power-law terms to a {\it bona fide} power law as
compaction increases. In addition to showing the vicinity of these two
distributions in the phase space, this observation nicely demonstrates the
effect of interactions to bring about a subtle change in macroscopic behavior
and more information may be retrieved if the data are subject to sorting. Our
analyses are based on the Akaike information criterion that is a direct
measurement of information loss and emphasizes the need to strike a balance
between model simplicity and goodness of fit. As a show of force, the Akaike
information criterion also found the Gutenberg-Richter law for earthquakes and
the scale-free model for brain functional network, 2-dimensional sand pile, and
solar flare intensity to suffer excessive loss of information. They resemble
more the crumpled-together ball at low compactions in that there appear to be
two driving mechanisms that take turns occurring.
