Alternative Hypothesis

An alternative hypothesis in statistics refers to a proposed statement or argument in the hypothesis test. It indicates the existence of the statistical relationship between variables and usually aligns with the research hypothesis.  

It is one of the two mutually exclusive statements in statistical hypothesis testing. In other words, it is the hypothesis opposing the null hypothesis. In simple terms, it points to the hypothesis that gets proved if there is enough evidence to defy the null hypothesis.

• The alternative hypothesis definition in research points to one of the stated statements in the hypothesis test. The symbols H_a or H₁ denotes it.
• It contradicts the null hypothesis based on the current phase, and successful verification of the alternative statement disproves the null hypothesis.
• It favors and proposes the presence of a statistical relationship between variables and usually aligns with the research hypothesis.  The main types used in the statistical hypothesis testing are point, one-tailed directional, two-tailed directional, and non-directional.
• Instead of favoring the null hypothesis, researchers are more likely to try hard to prove the alternative so that researchers can explore new avenues with its interpretation.

The alternative hypothesis in research indicates a connection between the two variables in the study, that is, the dependent and independent variables. On the other hand, the null hypothesis asserts that there is no connection between them. An experimental hypothesis predicts what corresponding change(s) will occur in the dependent variable when the independent variable is changed. Either null or alternative hypotheses get accepted during the process. If the alternative is proved, then the rejection of null occurs. In other words, if the null hypothesis is disproved, then the other opposing statement gets accepted. 

It plays a significant role in contemporary statistical hypothesis testing. Famous statisticians Jerzy Neyman and Egon Pearson developed the idea of an alternative hypothesis in testing. It is employed in the Neyman-Pearson lemma technique, introduced by Jerzy Neyman and Egon Pearson, to determine whether the hypothesis test has the greatest statistical power. The main types are point, one-tailed directional, two-tailed directional, and non-directional.

The correct formation of it is important in research. It is widely applied in research in statistics, medicine, psychology, science, mathematics, etc. Explanations for how something delivers a benefit are sometimes basic and vague when it is viewed in a positive light. It may be possible to summarize an alternative theory by addressing issues or important matters.

In decisions made in the presence of ambiguity, alternative theories or suggestions are typically disregarded or given little consideration. It also depends on how things are portrayed or represented. When a particular depiction was used, the alternative frequently fell by the wayside or was given less consideration. However, a representation that prompts further research exudes hope and enthusiasm or makes assessments resulting in the acceptance of alternatives.

The symbols H_a or H₁ denotes it. Let’s look into some of the representations interpreting different scenarios:

• Left tailed: The sample proportion (π) is less than the specified value (π0), (H₁ = π < π0)
• Two-tailed: The sample proportion (π) is not equal to a specific value (π0), (H₁ = π ≠ π0)
• Right-tailed: The sample proportion (π) is greater than some value (π0), (H₁ = π > π0)

Let’s look into the following null and alternative hypothesis examples for a better understanding of the concept:

Research question: Does food C increases the risk of a heart attack?

• H_a: Consumption of food C increases the risk of heart attack (Alternative: align with the research question or hypothesis)
• H₀: Consumption of food C does not increase the risk of heart attack (Null hypothesis)

Here, H_a and H₀ are contradictory statements. Therefore, the null hypothesis is initially presumed to be true, and if it is proven wrong, then the null hypothesis is rejected, and the alternative hypothesis is accepted.

Let's look into some of the significant interpretations:

• First, it is important when researchers are trying to prove a statement.
• Its interpretation depends on the determination of hypothesis testing, ensuring that the change is not by chance and essentially based on the data sample and population undertaken for the experiment.
• It defines that a random cause can influence the data sample distracting it from the expected outcome.
• Researchers are more inclined toward an alternative theory than a null one.
• Its interpretation help researchers explore new possibilities and define a situation more accurately than the null hypothesis.
• Its interpretation defines new results and the potential of claims.

This has been a guide to What is Alternative Hypothesis & its definition. Here, we explain its interpretation, symbol, and example. You may learn more from the following articles –

• Null vs. Alternative Hypothesis
• Statistical Analysis
• Bonferroni Test