Null Hypothesis
A Null Hypothesis is a statistical hypothesis that represents the default assumption or status quo belief to be tested in a statistical hypothesis testing task, typically asserting no effect, no difference, or no relationship between variables.
- AKA: H₀, H0, Default Hypothesis, Status Quo Hypothesis, Baseline Hypothesis, Test Hypothesis.
- Context:
- It can typically state that any observed difference or effect results purely from random chance or sampling variation.
- It can typically be formulated to be falsifiable through empirical observation and statistical evidence.
- It can typically serve as the starting point for statistical inference until sufficient evidence suggests otherwise.
- It can typically be rejected but never definitively proven true through hypothesis testing.
- It can often specify exact parameter values (e.g., μ = 0) in parametric tests.
- It can often represent "no treatment effect" in controlled experiments and clinical trials.
- It can often be tested using various test statistics that follow known probability distributions.
- It can often determine the null distribution used to calculate p-values.
- It can range from being a Simple Null Hypothesis to being a Composite Null Hypothesis, depending on its parameter specification completeness.
- It can range from being a Point Null Hypothesis to being an Interval Null Hypothesis, depending on its parameter value constraint.
- It can range from being a Rejected Null Hypothesis to being a Not-Rejected Null Hypothesis, depending on its test outcome.
- It can range from being a One-Tailed Null Hypothesis to being a Two-Tailed Null Hypothesis, depending on its directional specification.
- It can range from being a Strong Null Hypothesis to being a Weak Null Hypothesis, depending on its assumption stringency.
- It can range from being a Exact Null Hypothesis to being an Approximate Null Hypothesis, depending on its parameter precision.
- ...
- Example(s):
- Statistical Null Hypotheses, such as:
- Mean Comparison Null Hypothesis: H₀: μ₁ = μ₂ (two population means are equal).
- Correlation Null Hypothesis: H₀: ρ = 0 (no correlation between variables).
- Regression Null Hypothesis: H₀: β = 0 (no regression relationship).
- Proportion Null Hypothesis: H₀: p = 0.5 (probability equals 50%).
- Distribution Null Hypotheses, such as:
- Normality Null Hypothesis: H₀: Data follows normal distribution.
- Independence Null Hypothesis: H₀: Variables are independent.
- Homogeneity Null Hypothesis: H₀: Variances are equal across groups.
- Medical Null Hypotheses, such as:
- Treatment Efficacy Null Hypothesis: H₀: Drug has no effect on disease.
- Diagnostic Test Null Hypothesis: H₀: Test accuracy equals chance.
- Legal Null Hypotheses, such as:
- Presumption of Innocence: H₀: Defendant is innocent until proven guilty.
- No Discrimination Hypothesis: H₀: No systematic bias in hiring practices.
- ...
- Statistical Null Hypotheses, such as:
- Counter-Example(s):
- Alternative Hypothesis, which proposes an effect, difference, or relationship exists.
- Research Hypothesis, which is a conceptual prediction rather than statistical formulation.
- Working Hypothesis, which guides investigation rather than statistical testing.
- Scientific Theory, which is broader than a testable statistical statement.
- See: Alternative Hypothesis, Statistical Hypothesis Testing Task, Type I Error, Type II Error, Test Statistic, P-Value, Statistical Significance Level, Null Distribution, Neyman-Pearson Framework, Fisher's Significance Testing, Composite Hypothesis, Simple Hypothesis, Statistical Power.
References
2011
- (Wikipedia, 2011) ⇒ http://en.wikipedia.org/wiki/Null-hypothesis
- QUOTE: The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. 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).
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Much of the terminology used in connection with null hypotheses derives from the immediate relation to statistical hypothesis testing; part of this terminology is outlined here, but see this list of definitions for a more complete set. Simple hypothesis: Any hypothesis which specifies the population distribution completely. Composite hypothesis: Any hypothesis which does not specify the population distribution completely.
A point hypothesis is more complicated to describe. The term arises in contexts where the set of all possible population distributions is put in parametric form. A point hypothesis is one where exact values are specified for either all the parameters or for a subset of the parameters. Formally, the case where only a subset of parameters is defined is still a composite hypothesis; nonetheless, the term point hypothesis is often applied in such cases, particularly where the hypothesis test can be structured in such a way that the distribution of the test statistic (the distribution under the null hypothesis) does not depend on the parameters whose values have not been specified under the point null hypothesis. Careful treatments of point hypotheses for subsets of parameters do consider them as composite hypotheses and study how the p-value for a fixed critical value of the test statistic varies with the parameters that are not specified by the null hypothesis.
A one-tailed hypothesis is a hypothesis in which the value of a parameter is specified as being either: above a certain value, or below a certain value. An example of a one-tailed null hypothesis would be that, in a medical context, an existing treatment, A, is no worse than a new treatment, B. The corresponding alternative hypothesis would be that B is better than A. Here if the null hypothesis were accepted (i.e. there is no reason to reject the hypothesis that A is at least as good as B), the conclusion would be that treatment A should continue to be used. If the null hypothesis were rejected, the result would be that treatment B would used in future, given that there is evidence that it is better than A. A hypothesis test would look for evidence that B is better than A, not for evidence that the outcomes of treatments A and B are different. Formulating the hypothesis as a "better than" comparison is said to give the hypothesis directionality.
- QUOTE: The practice of science involves formulating and testing hypotheses, assertions that are capable of being proven false using a test of observed data. 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.
2008
- (Lehmann & Romano, 2008) ⇒ E.L. Lehmann and Joseph P. Romano. (2008). "Testing Statistical Hypotheses." Springer.
- NOTE: The null hypothesis H₀ represents a hypothesis of no change or no effect. In the Neyman-Pearson framework, it is treated symmetrically with the alternative hypothesis, while in Fisher's approach, only the null hypothesis is explicitly formulated and tested.
1935
- (Fisher, 1935) ⇒ Ronald A. Fisher. (1935). "The Design of Experiments." Oliver and Boyd.
- NOTE: The null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation. Every experiment may be said to exist only in order to give the facts a chance of disproving the null hypothesis.