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Concept# Alternative hypothesis

Summary

In statistical hypothesis testing, the alternative hypothesis is one of the proposed proposition in the hypothesis test. In general the goal of hypothesis test is to demonstrate that in the given condition, there is sufficient evidence supporting the credibility of alternative hypothesis instead of the exclusive proposition in the test (null hypothesis). It is usually consistent with the research hypothesis because it is constructed from literature review, previous studies, etc. However, the research hypothesis is sometimes consistent with the null hypothesis.
In statistics, alternative hypothesis is often denoted as Ha or H1. Hypotheses are formulated to compare in a statistical hypothesis test.
In the domain of inferential statistics two rival hypotheses can be compared by explanatory power and predictive power.
The alternative hypothesis and null hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching conclusions or making judgments on the basis of data. In statistical hypothesis testing, the null hypothesis and alternative hypothesis are two mutually exclusive statements.
"The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength of the evidence against the null hypothesis. Usually, the null hypothesis is a statement of 'no effect' or 'no difference'." Null hypothesis is often denoted as H0.
The statement that is being tested against the null hypothesis is the alternative hypothesis. Alternative hypothesis is often denoted as Ha or H1.
In statistical hypothesis testing, to prove the alternative hypothesis is true, it should be shown that the data is contradictory to the null hypothesis. Namely, there is sufficient evidence against null hypothesis to demonstrate that the alternative hypothesis is true.
One example is where water quality in a stream has been observed over many years, and a test is made of the null hypothesis that "there is no change in quality between the first and second halves of the data", against the alternative hypothesis that "the quality is poorer in the second half of the record".

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