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An alternative hypothesis often denoted as Ha or H1 is a statement in statistical hypothesis testing that specifies the relationship between two variables. It is usually the hypothesis an experimenter is trying to prove or has already proven.
- An alternative hypothesis proposes a different conclusion than the null hypothesis (H0).
- A hypothesis is a specific, testable statement or prediction about the relationship between variables.
- It suggests that there is a significant effect, relationship, or difference between the variables being studied.
- The hypothesis represents the researcher's theory or belief regarding the population parameters under investigation.
- In hypothesis testing, the goal is to gather evidence to either reject the null hypothesis in favour of the alternative hypothesis or fail to reject the null hypothesis due to insufficient evidence.
- The formulation and testing of alternative hypotheses are fundamental to making informed decisions in various fields such as science, economics, psychology, and medicine.
| Table of Content |
Key Terms: Alternative Hypothesis, Null Hypothesis, Hypothesis, Variables, Types of Alternative Hypothesis, Left-Tailed, Right-Tailed, Two-Tailed
Alternative Hypothesis Definition
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Alternative hypothesis proposes that there is a significant relationship or difference between the variables being studied in statistical inference experiments.
- The statement is true from the researcher's point of view and proves that the null hypothesis should be rejected to replace it with an alternative assumption.
- The alternative hypothesis contradicts the null hypothesis and reflects the researcher's theory or expectation regarding the relationship.
- This means if we assume the null hypothesis to be true then the alternative is false.
- It aids in contributing new knowledge to the field of statistics and making evidence-based conclusions.
- Hypotheses are formulated based on existing knowledge, theories, observations, or intuition, and they guide the research process by providing a clear direction for investigation.
- It serves as a tentative explanation for a phenomenon or a proposed solution to a problem.
Example of Alternative HypothesisExample: We should examine below examples to understand the alternative hypothesis and its interpretation.
Here, two variables are students receiving tutoring and students without any tutoring. The alternative hypothesis states that there is a difference in scores between both groups of students, which seems to be possibly true. Example 2: The new drug treatment reduces symptoms of depression more effectively than the current standard treatment.
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Alternative Hypothesis
Null Hypothesis (H0)
Null hypothesis proposes that there is no significant relationship or difference between the variables being studied. It suggests that any observed effects are due to chance or random variation.
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Types of Alternative Hypothesis
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There are three types of the alternative hypothesis which are as follows:
Left-Tailed
Left-tailed is expected that the sample proportion (π) is less than a specified value, which is denoted by π0, i.e. H1: π < π0
Right-Tailed
Right-tailed represents that the sample proportion (π) is greater than some value, denoted by π0, i.e. H1: π > π0
Two-Tailed
Two-tailed is a type of alternative hypothesis where the sample proportion is not equal to a specific value, which is represented by π0 ie. H1 : π ≠ π0.
Difference between Null and Alternative Hypothesis
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Key differences between the null hypothesis and alternative hypothesis are tabulated below.
| Null Hypothesis | Alternative Hypothesis |
|---|---|
| It states no significant effect, relationship, or difference between variables. | It states that there is a significant effect, relationship, or difference between variables. |
| Typically denoted as H0 | It is denoted as H1 |
| It represents the status quo or the absence of an effect. | It represents the researcher's theory or belief regarding the presence of an effect. |
| The null hypothesis is tested to assess if the evidence supports rejecting it. | Alternative hypothesis is tested to assess if evidence supports rejecting the null hypothesis in favour of it. |
| Often formulated as "no difference," "no effect," or "no association." | Often formulated to reflect a difference, effect, or association between variables. |
Things to Remember
- An alternative hypothesis is a statement saying that a significant difference or relationship exists between two variables.
- It is denoted as H1.
- Alternative hypotheses are formulated to reflect the difference or association of variables.
- It serves as a tentative explanation for a phenomenon or a proposed solution to a problem.
- To determine the alternative hypothesis, we must first draw a sample from an unknown probability distribution
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Sample Questions
Ques. What is the purpose of an alternative hypothesis? (4 marks)
Ans. The purpose of an alternative hypothesis is to propose that there is a significant effect, relationship, or difference between variables being studied.
- It serves as the hypothesis of interest for researchers, reflecting their theory or expectation regarding the relationship between variables.
- In statistical hypothesis testing, the alternative hypothesis is tested to determine if there is enough evidence to reject the null hypothesis in favour of the alternative hypothesis, thus supporting the researcher's theory or expectation.
- Essentially, the alternative hypothesis guides researchers in exploring and making conclusions about the relationships and effects they are investigating.
Ques. What are some common alternative hypotheses in research? (2 marks)
Ans. Alternative hypotheses can vary widely depending on the research question and variables under investigation. Some common examples include hypotheses proposing differences in treatment effectiveness, relationships between variables, the presence of specific effects or associations, or the superiority of one method over another.
Ques. Provide an example of an alternative hypothesis? (3 marks)
Ans. For instance, if a researcher is investigating the effectiveness of a new teaching method on student performance compared to a traditional method, the null hypothesis could be stated as there is no significant difference between the new and traditional teaching method in the students’ performance. While the alternative hypothesis could be formulated as "The new teaching method leads to a higher average test score compared to the traditional teaching method."
Ques. How is the alternative hypothesis tested in statistical hypothesis testing? (5 marks)
Ans. The process of hypothesis testing typically involves the following steps.
- Formulation of Hypotheses: The null hypothesis and the alternative hypothesis are clearly defined based on the research question and the theory or expectation being tested.
- Selection of Statistical Test: Depending on the research design and the type of data collected, an appropriate statistical test is chosen to analyse the data. Common tests include t-tests, chi-square tests, ANOVA, regression analysis, and others.
- Collection of Data: Data relevant to the research question is collected through experiments, surveys, observations, or other methods.
- Calculation of Test Statistic: The collected data are used to calculate a test statistic that quantifies the strength of the evidence against the null hypothesis. This statistic varies depending on the chosen statistical test.
- Determination of Significance Level: A significance level (α) is chosen, representing the threshold for rejecting the null hypothesis. Common values for α include 0.05 and 0.01.
- Comparison with Critical Value or P-value: The calculated test statistic is compared with either a critical value from the appropriate statistical distribution or a p-value. If the test statistic exceeds the critical value or if the p-value is less than the significance level (α), the null hypothesis is rejected in favour of the alternative hypothesis.
- Interpretation of Results: The findings are interpreted in the context of the research question and the alternative hypothesis. If the null hypothesis is rejected, it suggests that there is sufficient evidence to support the alternative hypothesis. If the null hypothesis is not rejected, it indicates that there is insufficient evidence to support the alternative hypothesis.
- Conclusion: A conclusion is drawn based on the results of the statistical test, providing insights into the relationship between variables or the effects being studied.
Ques. How does the alternative hypothesis differ from the null hypothesis? (3 marks)
Ans. The alternative hypothesis and the null hypothesis are two complementary statements in statistical hypothesis testing, differing in their assertions and implications.
- Null Hypothesis assumes no significant effect, relationship, or difference between variables.
- It represents the status quo or the absence of an effect. It is tested to assess if evidence supports rejecting it.
- Alternative Hypothesis assumes a significant effect, relationship, or difference between variables.
- It represents the researcher's theory or belief regarding the presence of an effect and tested to assess if evidence supports rejecting the null hypothesis.
Ques. What is a hypothesis in scientific research, and why is it important? (4 marks)
Ans. In scientific research, a hypothesis is a specific, testable statement or prediction that proposes an explanation for a phenomenon or predicts the outcome of an experiment.
- It serves as a tentative solution to a problem or a starting point for investigation.
- Hypotheses are crucial because they provide a structured framework for research, guiding the formulation of research questions, the design of experiments, the collection and analysis of data, and the interpretation of results.
- By articulating clear hypotheses, researchers can systematically evaluate and refine their theories, contribute new knowledge to their field, and make evidence-based conclusions.
- There are two possible hypotheses in a research i.e. a null hypothesis and an alternative hypothesis.
Ques. How are hypotheses formulated in scientific research? Give the symbolic representation of two types of hypothesis? (3 marks)
Ans. Hypotheses in scientific research are formulated based on existing knowledge, theories, observations, or intuition.
- Researchers often start by identifying a research question or problem they wish to investigate.
- They then review relevant literature, conduct preliminary observations or experiments, and develop a hypothesis that proposes a potential explanation or solution to the research question.
Ques. Can we say an alternative hypothesis is accepted? (2 marks)
Ans. We reject the null hypothesis and accept the alternative if our statistical analysis reveals that the significance level is less than the cut-off value we have chosen (e.g., either 0.05 or 0.01).
Ques. What are the implications of alternative hypothesis? (3 marks)
Ans. A claim that refutes the null hypothesis is part of the alternative hypothesis. A researcher looks into the null hypothesis further in an effort to identify its weaknesses.
- After the study, they may determine if they have sufficient data to reject the null hypothesis by using the alternative hypothesis as a guide.
- They might also decide not to test the alternate hypothesis and go with a different one.
Ques. What are different types of hypotheses? (2 marks)
Ans. There are six different types of hypothesis are as follows:
- Complex hypothesis
- Simple hypothesis
- Null hypothesis
- Directional hypothesis
- Non-directional hypothesis
- Associative and causal hypothesis
Ques. What are the things that researchers must keep in mind while conducting a hypothesis? (3 marks)
Ans. The things that researchers must keep in mind while conducting a hypothesis are as follows:
- When performing research on a theory, testability should come first.
- the production of an endless quantity of entities.
- The hypothesis's apparent applicability to many phenomena conditions.
- The potential for a theory to aid in the eventual explanation of events
- suitability for integration with current knowledge systems.
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