H1

Definition

H1, or the alternative hypothesis, is a statistical hypothesis that proposes a specific relationship or difference between two or more variables. It is the hypothesis that the researcher believes to be true and wants to provide evidence for, in contrast to the null hypothesis (H0).

5 Must Know Facts For Your Next Test

1. The alternative hypothesis (H1) is the hypothesis that the researcher believes to be true and wants to provide evidence for.
2. The alternative hypothesis (H1) is the complement of the null hypothesis (H0), meaning that if the null hypothesis is false, the alternative hypothesis must be true.
3. The alternative hypothesis (H1) can take different forms, such as a difference in means, a relationship between variables, or a specific value for a parameter.
4. The alternative hypothesis (H1) is typically denoted using a symbol that indicates the nature of the relationship, such as ≠, >, or <.
5. The decision to reject or fail to reject the null hypothesis (H0) is based on the p-value, which represents the probability of observing the test statistic or a more extreme value under the assumption that the null hypothesis is true.

Review Questions

• Explain the relationship between the null hypothesis (H0) and the alternative hypothesis (H1) in the context of hypothesis testing.
  • The null hypothesis (H0) and the alternative hypothesis (H1) are complementary statistical hypotheses used in hypothesis testing. The null hypothesis represents the status quo or the assumption that there is no significant difference or relationship between the variables being studied. The alternative hypothesis (H1) is the hypothesis that the researcher believes to be true and wants to provide evidence for, which is the complement of the null hypothesis. The goal of hypothesis testing is to determine whether the evidence from the sample data is strong enough to reject the null hypothesis in favor of the alternative hypothesis.
• Describe how the p-value is used to make a decision about the alternative hypothesis (H1) in the context of hypothesis testing.
  • The p-value is a crucial component in the decision-making process regarding the alternative hypothesis (H1) in hypothesis testing. The p-value represents the probability of observing the test statistic or a more extreme value under the assumption that the null hypothesis (H0) is true. If the p-value is less than the predetermined significance level (e.g., 0.05), the researcher can conclude that the evidence from the sample data is statistically significant and reject the null hypothesis in favor of the alternative hypothesis (H1). Conversely, if the p-value is greater than the significance level, the researcher fails to reject the null hypothesis and does not have sufficient evidence to support the alternative hypothesis (H1).
• Analyze the different forms that the alternative hypothesis (H1) can take and explain how the choice of H1 affects the interpretation of the results in hypothesis testing.
  • The alternative hypothesis (H1) can take various forms, depending on the research question and the nature of the relationship or difference being investigated. For example, H1 can represent a difference in means (e.g., H1: μ1 ≠ μ2), a relationship between variables (e.g., H1: ρ ≠ 0), or a specific value for a parameter (e.g., H1: μ > 50). The choice of H1 directly affects the interpretation of the results in hypothesis testing. If the null hypothesis (H0) is rejected in favor of the alternative hypothesis (H1), the interpretation of the results will depend on the specific form of H1. For instance, if H1 represents a difference in means, the researcher can conclude that there is a statistically significant difference between the two groups. Alternatively, if H1 represents a relationship between variables, the researcher can conclude that there is a statistically significant association between the variables.

Related terms

Null Hypothesis (H0): The null hypothesis is a statistical hypothesis that proposes no significant relationship or difference between variables. It is the hypothesis that the researcher aims to disprove in favor of the alternative hypothesis (H1).

Statistical Significance:

Statistical significance is the likelihood that the observed difference or relationship between variables is due to chance. It is used to determine whether the alternative hypothesis (H1) should be accepted or the null hypothesis (H0) should be retained.

P-value: The p-value is the probability of obtaining the observed test statistic or a more extreme value, given that the null hypothesis (H0) is true. It is used to determine the statistical significance of the results and make a decision about the alternative hypothesis (H1).