Alternative hypothesis

Definition

The alternative hypothesis is a statement that proposes a potential outcome or effect that differs from the null hypothesis. It is often what researchers aim to support through statistical testing, suggesting that there is a significant effect or difference present in the data being studied. This hypothesis plays a crucial role in various statistical methodologies, serving as a foundation for testing and model comparison.

5 Must Know Facts For Your Next Test

1. In hypothesis testing, the alternative hypothesis can be one-sided or two-sided, depending on whether it specifies a direction of the effect or not.
2. The strength of evidence against the null hypothesis is often evaluated using likelihood ratios or p-values in relation to the alternative hypothesis.
3. In Bayesian approaches, the alternative hypothesis is compared to the null hypothesis by evaluating posterior probabilities rather than relying solely on p-values.
4. Establishing an alternative hypothesis allows researchers to define their research question clearly and set specific expectations for their analysis.
5. The alternative hypothesis can guide model selection, as seen in methods like the Bayesian Information Criterion, which compares different models based on how well they fit the data relative to their complexity.

Review Questions

• How does the alternative hypothesis differ from the null hypothesis in terms of statistical testing?
  • The alternative hypothesis proposes that there is a significant effect or difference present in the data being analyzed, while the null hypothesis asserts that no such effect exists. Researchers typically seek to provide evidence supporting the alternative hypothesis through various statistical tests. This creates a framework where findings can either reject the null in favor of the alternative or fail to provide sufficient evidence to do so.
• Discuss the implications of choosing one-sided versus two-sided alternative hypotheses in research design.
  • Choosing between a one-sided and two-sided alternative hypothesis can significantly impact the conclusions drawn from research. A one-sided alternative focuses on detecting an effect in one direction, which can increase statistical power for that specific test but may miss effects in the opposite direction. In contrast, a two-sided alternative allows for detection of effects in both directions but requires stronger evidence to reject the null hypothesis. The choice depends on research goals and hypotheses about expected outcomes.
• Evaluate how Bayesian methods incorporate the alternative hypothesis differently than traditional frequentist approaches.
  • Bayesian methods offer a different framework by treating hypotheses probabilistically rather than relying solely on p-values and fixed significance levels. In this approach, researchers assign prior probabilities to both the null and alternative hypotheses, updating these beliefs based on observed data to derive posterior probabilities. This allows for a more nuanced understanding of evidence supporting an alternative hypothesis and enables direct comparisons between hypotheses, contrasting with frequentist methods that focus more on rejecting or failing to reject the null.

Related terms

null hypothesis: The null hypothesis is a statement asserting that there is no effect or difference, serving as the default position in hypothesis testing.

p-value: The p-value is the probability of obtaining test results at least as extreme as the observed results, under the assumption that the null hypothesis is true.

Type I error: A Type I error occurs when the null hypothesis is incorrectly rejected when it is actually true, leading to a false positive conclusion.