  Tensor data analysis allows researchers to uncover novel patterns and
relationships that cannot be obtained from matrix data alone. The information
inferred from the patterns provides valuable insights into disease progression,
bioproduction processes, weather fluctuations, and group dynamics. However,
spurious and redundant patterns hamper this process. This work aims at
proposing a statistical frame to assess the probability of patterns in tensor
data to deviate from null expectations, extending well-established principles
for assessing the statistical significance of patterns in matrix data. A
comprehensive discussion on binomial testing for false positive discoveries is
entailed at the light of: variable dependencies, temporal dependencies and
misalignments, and \textit{p}-value corrections under the Benjamini-Hochberg
procedure. Results gathered from the application of state-of-the-art
triclustering algorithms over distinct real-world case studies in biochemical
and biotechnological domains confer validity to the proposed statistical frame
while revealing vulnerabilities of some triclustering searches. The proposed
assessment can be incorporated into existing triclustering algorithms to
mitigate false positive/spurious discoveries and further prune the search
space, reducing their computational complexity.
  Availability: The code is freely available at
https://github.com/JupitersMight/TriSig under the MIT license.
