Hₐ

Definition

In the context of testing the significance of the correlation coefficient, Hₐ represents the alternative hypothesis. The alternative hypothesis is a statement that there is a significant relationship or association between the variables being studied, contradicting the null hypothesis.

5 Must Know Facts For Your Next Test

1. The alternative hypothesis, Hₐ, is typically stated as the researcher's prediction or expected outcome of the study.
2. Hₐ is used in conjunction with the null hypothesis, Hₒ, to determine whether the observed correlation coefficient is statistically significant.
3. The test statistic used to evaluate the significance of the correlation coefficient is the t-statistic, which follows a t-distribution.
4. The p-value, or probability value, is compared to the significance level to determine whether to reject or fail to reject the null hypothesis.
5. Rejecting the null hypothesis in favor of the alternative hypothesis indicates that there is sufficient evidence to conclude that a significant relationship exists between the variables.

Review Questions

• Explain the purpose of the alternative hypothesis, Hₐ, in the context of testing the significance of the correlation coefficient.
  • The alternative hypothesis, Hₐ, represents the researcher's prediction or expected outcome of the study. It is used in conjunction with the null hypothesis, Hₒ, to determine whether the observed correlation coefficient is statistically significant. Hₐ is typically stated as the existence of a significant relationship or association between the variables being studied, contradicting the null hypothesis of no significant relationship.
• Describe the relationship between the null hypothesis (Hₒ) and the alternative hypothesis (Hₐ) in the context of testing the significance of the correlation coefficient.
  • The null hypothesis (Hₒ) and the alternative hypothesis (Hₐ) are mutually exclusive and exhaustive statements about the relationship between the variables being studied. Hₒ states that there is no significant relationship between the variables, while Hₐ states that there is a significant relationship. The goal of the statistical test is to determine whether the observed correlation coefficient provides sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.
• Analyze the role of the significance level (α) in the decision to reject or fail to reject the null hypothesis when testing the significance of the correlation coefficient.
  • The significance level (α) represents the maximum probability of rejecting the null hypothesis when it is true, also known as the Type I error rate. When testing the significance of the correlation coefficient, the p-value, or probability value, is compared to the significance level to determine whether to reject or fail to reject the null hypothesis. If the p-value is less than the significance level, the null hypothesis is rejected in favor of the alternative hypothesis, indicating that the observed correlation coefficient is statistically significant. The choice of significance level reflects the researcher's willingness to accept the risk of a Type I error, with lower significance levels (e.g., 0.01 or 0.05) corresponding to a more stringent criterion for rejecting the null hypothesis.

Related terms

Null Hypothesis (Hₒ): The null hypothesis is a statistical hypothesis that states there is no significant relationship or association between the variables being studied.

Correlation Coefficient (r): The correlation coefficient is a statistical measure that quantifies the strength and direction of the linear relationship between two variables.

Significance Level (α): The significance level is the probability of rejecting the null hypothesis when it is true, also known as the Type I error rate.