Fundamentals of Statistics

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2. What Is Hypothesis?

2.1. Null and Alternative Hypothesis

Setting up and testing hypotheses is an essential part of statistical inference. In each problem considered, the question of interest is simplified into two competing claims or hypotheses, the null hypothesis (H0) and the alternative hypothesis (H1).

The null hypothesis (H0) is formulated to capture our current understanding (the ‘established facts’). The word ‘null’ can be thought of as ‘no change’. A null hypothesis is typically the standard assumption and is defined as the prediction that there is no interaction between variables (a statement that proposes there is no causal relationship, for example, between an investigational medicine and a reduction in symptoms and that outcome measures [even if indicative of a symptom reduction] are due to chance).

The alternative hypothesis (H1) is formulated to capture what we want to show by doing the study. An alternative hypothesis in a clinical trial might be that the new medicine is better than the current standard of treatment against which it is tested.

These two hypotheses should be stated in such a way that they become mutually exclusive. That is, if one is true, the other must be false.

Taking the example from above the hypotheses might be formulated as follows:

  • The null hypothesis (H0): there is no difference between the existing standard of care treatment ‘A’ and the new treatment ‘B’ and any observed differences in outcome measures are due to chance.
  • The alternative hypothesis (H1): the new treatment ‘B' is better than the existing standard of care treatment ‘A’.