What does "One-Sided Hypothesis" mean?
Definition of One-Sided Hypothesis in the context of A/B testing (online controlled experiments).
What is a One-Sided Hypothesis?
A one-sided hypothesis is an alternative hypothesis strictly bounded from above or from below, as opposed to a two-sided hypothesis which is the union of two one-sided hypotheses and is thus unbounded from both above and below. For example, H1: δ > 0 (alt.: H1: θ∈(0,+∞)) is a one-sided hypothesis since the parameter is bounded from below by zero. The corresponding null hypothesis would also be one-sided: H0: δ ≤ 0 (alt.:H0: θ∈(-∞,0])).
A one-sided alternative hypothesis is always used in a superiority test (most A/B tests) as well as in a non-inferiority test. As a statement it corresponds to the claim that the treatment will perform better than the control. While many examples set it to be less than or greater than zero, a one-sided hypothesis can be bounded at any value. For example, if the claim is that effect size is larger than 2% relative lift then H1: δ > 2%.
Consequently, a one-sided null hypothesis is always the complement of a one-sided alternative.
When a one-sided hypothesis is used the respective p-value should also be one-sided (or a one-tailed test as it is sometimes called). If a confidence interval is used to support a one-sided claim it should also be one-sided: one confidence limit is plus or minus infinity, depending on the direction of the hypothesis. If the distribution is symmetric around the mean and you can only calculate a one-sided p-value, a simple way to transform it is to divide it by to. E.g. a two-sided p-value of 0.1 is a one-sided p-value of 0.05. Similarly, a 95% two-sided confidence interval is composed of the intersection of two 97.5% one-sided confidence intervals.
Like this glossary entry? For an in-depth and comprehensive reading on A/B testing stats, check out the book "Statistical Methods in Online A/B Testing" by the author of this glossary, Georgi Georgiev.
Articles on One-Sided Hypothesis
One-tailed vs Two-tailed Tests of Significance in A/B Testing
blog.analytics-toolkit.com
Project OneSided
www.onesided.org
Related A/B Testing terms
Null HypothesisAlternative HypothesisOne-Tailed TestTwo-Tailed TestTwo-Sided HypothesisHypothesis TestingNull Hypothesis Statistical TestAbout the author
Georgi has over twenty years of experience in online marketing, web analytics, statistics, and design of business experiments.
Author of the book "Statistical Methods in Online A/B Testing", white papers on statistical analysis of A/B tests, and a speaker, he has been distinguished as a winner in the Data & Analytics category of the 2024 Experimentation Thought Leadership Awards.
Statistical Methods in Online A/B Testing
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