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The aim of the present paper is to estimate and control the Type I and TypeII errors of a simple hypothesis testing problem of the drift/viscositycoefficient for stochastic fractional heat equation driven by additive noise.Assuming that one path of the first $N$ Fourier modes of the solution isobserved continuously over a finite time interval $[0,T]$, we propose a newclass of rejection regions and provide computable thresholds for $T$, and $N$,that guarantee that the statistical errors are smaller than a given upperbound. The considered tests are of likelihood ratio type. The main ideas, andthe proofs, are based on sharp large deviation bounds. Finally, we illustratethe theoretical results by numerical simulations.

A note on error estimation for hypothesis testing problems for some linear SPDEs