Hypothesis testing assesses whether data are inconsistent with a given hypothesis (usually a null hypothesis of no effect).
Statistical hypothesis testing assesses whether data are inconsistent with a given hypothesis (usually a null hypothesis of no effect). In practice, this is often associated with the Null Hypothesis Statistical Testing framework, based on ideas from Fisher as well as Neyman & Pearson. However, other approaches exist, such as Bayesian hypothesis testing.
Note that testing a statistical hypothesis is only one component of testing a research hypothesis. Careful experimental or study design is needed for the statistical hypothesis to lead to insight regarding the research hypothesis.
