Alternative Hypothesis

Definition

The alternative hypothesis is a statement that contradicts the null hypothesis in a statistical test. It represents the researcher's belief about the relationship or difference between variables, suggesting that the observed effect or relationship is not due to chance.

5 Must Know Facts For Your Next Test

1. The alternative hypothesis is denoted as H1 or Ha, while the null hypothesis is denoted as H0.
2. The alternative hypothesis can be directional (specifying the direction of the effect) or non-directional (only stating that there is a difference).
3. The alternative hypothesis is supported if the test statistic falls in the rejection region, indicating that the observed results are unlikely to have occurred by chance under the null hypothesis.
4. The strength of evidence for the alternative hypothesis is determined by the p-value, which represents the probability of obtaining the observed results or more extreme results if the null hypothesis is true.
5. Failing to reject the null hypothesis does not necessarily mean that the alternative hypothesis is false, as it could be due to insufficient statistical power or a small effect size.

Review Questions

• Explain the relationship between the null hypothesis and the alternative hypothesis in the context of correlation analysis.
  • In the context of correlation analysis, the null hypothesis typically states that there is no significant correlation between two variables, while the alternative hypothesis states that there is a significant correlation. The alternative hypothesis can be directional, specifying the direction of the correlation (positive or negative), or non-directional, simply stating that there is a significant correlation without specifying the direction. The researcher's goal is to gather sufficient evidence to reject the null hypothesis and support the alternative hypothesis, indicating that the observed correlation is unlikely to have occurred by chance.
• Describe how the p-value is used to evaluate the strength of evidence for the alternative hypothesis in correlation analysis.
  • In correlation analysis, the p-value represents the probability of obtaining the observed correlation coefficient (or a more extreme value) if the null hypothesis is true. A lower p-value indicates stronger evidence for the alternative hypothesis, as it suggests that the observed correlation is unlikely to have occurred by chance. The researcher typically sets a significance level (e.g., α = 0.05) as the threshold for rejecting the null hypothesis. If the p-value is less than the significance level, the researcher can conclude that the alternative hypothesis is supported, and the observed correlation is statistically significant. The smaller the p-value, the stronger the evidence for the alternative hypothesis.
• Analyze the implications of failing to reject the null hypothesis in the context of correlation analysis.
  • Failing to reject the null hypothesis in correlation analysis means that the researcher does not have sufficient evidence to conclude that there is a significant correlation between the variables. This does not necessarily mean that the alternative hypothesis is false, as it could be due to a lack of statistical power (i.e., the sample size is too small to detect a significant effect) or a small effect size that is difficult to detect. In this case, the researcher cannot make a definitive conclusion about the relationship between the variables and may need to gather more data or consider other factors that could influence the correlation. Failing to reject the null hypothesis does not imply that the variables are unrelated, but rather that the available evidence is not strong enough to support the alternative hypothesis.

Related terms

Null Hypothesis: The null hypothesis is a statement that there is no significant difference or relationship between the variables being studied.

Statistical Significance: Statistical significance refers to the likelihood that the observed results are due to chance, with a p-value less than the predetermined significance level indicating that the alternative hypothesis is likely true.

Type I Error: A Type I error occurs when the null hypothesis is true, but it is incorrectly rejected, leading to the conclusion that the alternative hypothesis is true.