  The security of blockchain systems depends on the distribution of mining
power across participants. If sufficient mining power is controlled by one
entity, they can force their own version of events. This may allow them to
double spend coins, for example. For Proof of Work (PoW) blockchains, however,
the distribution of mining power cannot be read directly from the blockchain
and must instead be inferred from the number of blocks mined in a specific
sample window. We introduce a framework to quantify this statistical
uncertainty for the Nakamoto coefficient, which is a commonly-used measure of
blockchain decentralization. We show that aggregating blocks over a day can
lead to considerable uncertainty, with Bitcoin failing more than half the
hypothesis tests ({\alpha} = 0.05) when using a daily granularity. For these
reasons, we recommend that blocks are aggregated over a sample window of at
least 7 days. Instead of reporting a single value, our approach produces a
range of possible Nakamoto coefficient values that have statistical support at
a particular significance level {\alpha}.
