Alternative hypothesis

Definition

The alternative hypothesis is a statement that proposes a potential outcome or effect that contradicts the null hypothesis. It is the claim that researchers seek to provide evidence for in their studies, and it plays a critical role in hypothesis testing by suggesting that there is a significant difference or effect present. Understanding this concept is essential as it relates to making decisions based on statistical tests, error types, test power, adjustments for multiple comparisons, Bayesian approaches, and determining the necessary sample sizes.

5 Must Know Facts For Your Next Test

1. The alternative hypothesis can be one-tailed, predicting the direction of the effect, or two-tailed, indicating any difference without specifying the direction.
2. In hypothesis testing, evidence supporting the alternative hypothesis leads to rejection of the null hypothesis, suggesting that a significant effect or difference exists.
3. Statistical significance is often determined using p-values; if the p-value is less than a pre-defined threshold (like 0.05), the alternative hypothesis may be accepted.
4. When multiple hypotheses are tested simultaneously, adjustments may be necessary to control for false discoveries related to the alternative hypothesis.
5. In Bayesian statistics, the alternative hypothesis has a different interpretation, focusing on posterior probabilities rather than p-values to assess evidence for competing hypotheses.

Review Questions

• How does the alternative hypothesis interact with the null hypothesis during statistical testing?
  • The alternative hypothesis is directly opposed to the null hypothesis. When conducting statistical tests, researchers use data to assess whether there is enough evidence to reject the null hypothesis in favor of the alternative. If sufficient evidence exists, it suggests that an effect or difference likely exists in reality. This interaction is fundamental for interpreting results and understanding the implications of statistical findings.
• Discuss how Type I and Type II errors relate to the acceptance or rejection of the alternative hypothesis in testing.
  • Type I errors occur when researchers incorrectly reject a true null hypothesis, falsely accepting an alternative hypothesis. Conversely, Type II errors happen when researchers fail to reject a false null hypothesis, meaning they miss supporting the true alternative hypothesis. Both error types highlight the importance of correctly interpreting results and balancing risks when making decisions about accepting or rejecting hypotheses.
• Evaluate the implications of multiple testing on the validity of an alternative hypothesis and how it might affect research conclusions.
  • Multiple testing can increase the likelihood of encountering false positives, leading to incorrect support for an alternative hypothesis. As more tests are conducted, particularly without proper corrections like Bonferroni adjustments, researchers risk inflating Type I error rates. This can mislead conclusions about significant effects or differences and undermine research credibility. Hence, understanding and controlling for these implications is vital for ensuring valid research outcomes.

Related terms

Null Hypothesis: A default statement asserting that there is no effect or difference, which the alternative hypothesis seeks to disprove.

Type I Error:

The error made when the null hypothesis is rejected when it is actually true, often referred to as a 'false positive.'

Power of a Test: The probability that a test correctly rejects the null hypothesis when the alternative hypothesis is true, indicating the test's ability to detect an effect.