(H0) relative to hypothesis testing, a statement of no difference or independence (e.g., x does not affect Y).
The null hypothesis typically corresponds to a general or default position. For example, the null hypothesis might be that there is no relationship between two measured phenomena or that a potential treatment has no effect. It is important to understand that the null hypothesis can never be proven. A set of data can only reject a null hypothesis or fail to reject it. For example, if comparison of two groups (e.g.: treatment, no treatment) reveals no statistically significant difference between the two, it does not mean that there is no difference in reality. It only means that there is not enough evidence to reject the null hypothesis (in other words, one fails to reject the null hypothesis.
Hypothesis testing works by collecting data and measuring how likely the particular set of data is, assuming the null hypothesis is true. If the data-set is very unlikely, defined as belonging to a set of data that only rarely will be observed (usually in less than either 5% of the time or 1% of the time), the experimenter rejects the null hypothesis concluding it (probably) is false. If the data do not contradict the null hypothesis, then only a weak conclusion can be made; namely that the observed dataset provides no strong evidence against the null hypothesis. As the null hypothesis could be true or false, in this case, in some contexts this is interpreted as meaning that the data give insufficient evidence to make any conclusion, on others it means that there is no evidence to support changing from a currently useful regime to a different one.