Hypothesis testing.pptx)_a lecture to master's students
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Hypothesis Testing, a lecture to Master's students. By Mangasini Katundu Visiting Professor, UNILAK, 2024/2025
Hypothesis testing.pptx)_a lecture to master's students
- 1. HYPOTHESIS TESTING PROF. MANGASINI KATUNDU VISITING PROFESSOR, UNILAK, RWANDA 2024/2025
- 2. HYPOTHESIS DEFINED • A hypothesis is a proposed explanation or intelligent guess about a phenomenon, made on a basis of limited evidence, that can be tested through experimentation or observation. • It’s typically used as a starting point for scientific research and is structured to be testable and falsifiable, meaning it can be supported or disproven through data collection and analysis.
- 3. TYPES OF HYPOTHESES There are several types of hypotheses, each serving a different purpose. Two types are common in statistical testing: 1. Null Hypothesis (H or ₀ HN):The null hypothesis posits that there is no effect or relationship between the variables being studied. It suggests that any observed differences or effects are due to chance or random variation. • Example: There is no difference in plant growth between those exposed to more sunlight and those exposed to less sunlight.
- 4. TYPES OF HYPOTHESES CONT… 2.Alternative Hypothesis (H or H ₁ a): The alternative hypothesis contradicts the null hypothesis. • It suggests that there is a significant effect or relationship between the variables. • Example: "Plants exposed to more sunlight will grow taller than those exposed to less sunlight."
- 5. DIFFERENCES BETWEEN H₀ AND H₁ HYPOTHESES • The null hypothesis (H ) and alternative hypothesis (H or Ha) ₀ ₁ are fundamental to statistical testing, and they differ in their purpose and what they suggest about the relationship between variables.
- 6. DIFFERENCES BETWEEN H₀ AND H₁ HYPOTHESES 1. Purpose: • Null Hypothesis (H ) ₀ : It assumes that there is no effect, no relationship, or no difference between the variables being studied. • It’s the starting point for statistical testing, and the goal is often to test whether there is enough evidence to reject it. • Alternative Hypothesis (H or Ha) ₁ : It proposes that there is an effect, a relationship, or a difference between the variables. • The alternative hypothesis is what researchers generally hope to support through their experiment or data analysis.
- 7. DIFFERENCES BETWEEN H₀ AND H₁ HYPOTHESES • 2. Nature: • Null Hypothesis (H ) ₀ : It is a statement of no effect or no relationship (Statement of equality). • It assumes that any observed effects or differences in data are due to random chance or sampling error. • Alternative Hypothesis (H or Ha) ₁ : It is a statement of existence of an effect or relationship. • It suggests that there is a true effect or difference (Statement of inequality).
- 8. DIFFERENCES BETWEEN H₀ AND H₁ HYPOTHESES 3.Testing: • Null Hypothesis (H ) ₀ : It is usually tested first, and you either fail to reject or reject it based on the data. Rejecting the null hypothesis means you have enough evidence to support the alternative hypothesis. • Alternative Hypothesis (H or Ha) ₁ : If the null hypothesis is rejected, the alternative hypothesis is considered supported by the data. It represents what the researcher is testing for.
- 9. DIFFERENCES BETWEEN H₀ AND H₁ HYPOTHESES 4. Statistical Significance: • Null Hypothesis (H ) ₀ : If data shows no statistically significant effect (i.e., the p-value is greater than a chosen significance level, like 0.05), you fail to reject the null hypothesis. • Alternative Hypothesis (H or Ha) ₁ : If data shows a statistically significant effect (i.e., the p-value is less than 0.05), you reject the null hypothesis and accept the alternative hypothesis.
- 10. DIFFERENCES BETWEEN H₀ AND H₁ HYPOTHESES 5. Direction: • Null Hypothesis (H ) ₀ :The null hypothesis typically suggests no difference or no change. It doesn’t specify a direction (positive or negative) of any relationship. • Alternative Hypothesis (H or Ha) ₁ : The alternative hypothesis can either be directional (predicting a specific direction of change or effect) or non-directional (just predicting a difference without specifying direction).
- 11. DIFFERENCES BETWEEN H₀ AND H₁ HYPOTHESES • Example: • Null Hypothesis (H ) ₀ : "There is no difference in plant growth between those exposed to more sunlight and those exposed to less sunlight." • Alternative Hypothesis (H ) ₁ : "There is a difference in plant growth between those exposed to more sunlight and those exposed to less sunlight."
- 12. STEPSTO FOLLOW IN HYPOTHESES TESTING • 1. Formulate Hypotheses: • The null (H ) and alternative (H or Ha) hypotheses should be clearly defined. Ensure ₀ ₁ they are specific, testable, and based on existing theory or prior evidence. • 2. Decide on the Significance Level ( ): α • Choosing α: The significance level (commonly set at 0.05) determines the threshold for rejecting the null hypothesis. It represents the probability of making a Type I error (incorrectly rejecting the null hypothesis when it's true). • Type I Error:The risk of concluding there’s an effect when there is none.The significance level controls this risk.
- 13. STEPSTO FOLLOW IN HYPOTHESES TESTING 3. Select the Appropriate StatisticalTest • The choice of statistical test depends on factors like the type of data, the number of groups being compared, and the nature of the hypothesis. Common tests include: • t-test (for comparing means between two groups) • ANOVA (for comparing means across three or more groups) • Chi-square test (for categorical data) • Correlation or regression analysis (for testing relationships between continuous variables)
- 14. MEASURES OF CORRELATION Correlation refers to the relationship between two or more variables.The most commonly used measures of correlation include: 1. Pearson Correlation Coefficient (r):This is the most widely used measure of linear correlation. It is suitable for interval or ratio data and assumes that the relationship between the variables is linear and that the variables are normally distributed. 2. Spearman's Rank Correlation Coefficient ( or rs) ρ : This measures the strength and direction of the monotonic relationship between two variables. It's a non-parametric test and doesn’t require the assumption of normality. It is especially useful for ordinal data or when the data is not linearly related.
- 15. MEASURES OF CORRELATION 3. Kendall'sTau ( ) τ : Like Spearman's, Kendall’s Tau is a non-parametric measure of the strength of association between two variables, based on the ranks of the data. It’s typically used when data has many tied ranks. It can give a more reliable measure when the sample size is small. 4. Point-Biserial Correlation: This is used when one variable is continuous (interval or ratio) and the other is binary (dichotomous), such as when comparing the average scores of two groups. 5. Phi Coefficient: This is used when both variables are binary (dichotomous), measuring the degree of association between two binary variables.
- 16. MEASURES OF CORRELATION Interpretation: • Correlation ranges from -1 to +1: • +1 indicates a perfect positive linear relationship. • -1 indicates a perfect negative linear relationship. • 0 indicates no linear relationship. • Above 0 but less than +-0.5 indicates a weak positive/negative relationship. • Above or equal to +-0.5 but less than +- 1 indicates Strong relationship.
- 17. STEPSTO FOLLOW IN HYPOTHESESTESTING • 4. Collect and Analyze Data • Gather data from your sample. Make sure your sample is representative of the population to ensure the results are valid. • Perform the chosen statistical test using software like SPSS, R, Python, Excel, etc., to calculate the test statistic (e.g., t-value, F-statistic) and the corresponding p-value.
- 18. STEPSTO FOLLOW IN HYPOTHESES TESTING 5. Compute theTest Statistic and P-value • The test statistic is a value calculated from your sample data that helps you decide whether to reject the null hypothesis. • The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.
- 19. STEPSTO FOLLOW IN HYPOTHESESTESTING 6. Compare the P-value with the Significance Level ( ) α • If the p-value is less than or equal to the significance level ( ) α i.e. 0.05, reject the null hypothesis (H ). ₀ This means there is enough evidence to support the alternative hypothesis. • If the p-value is greater than , i.e. 0.05, fail to reject the null hypothesis α .This means there is insufficient evidence to support the alternative hypothesis.
- 20. STEPSTO FOLLOW IN HYPOTHESESTESTING 7. Draw a Conclusion • Based on the comparison of the p-value and : α • If you reject H , you conclude that there is significant evidence to ₀ support the alternative hypothesis. • If you fail to reject H , you conclude that there is not enough evidence ₀ to support the alternative hypothesis, and the null hypothesis stands.
- 21. STEPSTO FOLLOW IN HYPOTHESES TESTING Example: 1. If the p-value is 0.03 and = 0.05, reject H and conclude that there is a α ₀ significant difference in plant growth based on sunlight exposure. 2. If the p-value is 0.08 and = 0.05, fail to reject H and conclude that α ₀ there is no significant difference.
- 22. STEPSTO FOLLOW IN HYPOTHESES TESTING 8. Report the Results • Clearly report the findings, including the test statistic, p-value, confidence intervals (if relevant), and your conclusion. • Also, mention any limitations or considerations, such as sample size, assumptions of the test, or external factors that could influence the results. • It’s important to evaluate the practical significance or effect size of the results. Statistical significance does not always imply that the difference or relationship has real-world importance.
- 23. GROUP ASSIGNMENT 2 1. Using data by Abebe, test the following hypotheses, and write the report: H₀: There is no association between household income and age of respondents in years. H : ₀ There is no relationship between years with current employer and job satisfaction. 2. Using data by Bekele test the following hypotheses, and write the report: H : ₀ There is no correlation between marital status and level of education of respondents. H : ₀ There is no association between number of people in the household and price of primary vehicle.
- 24. THANKYOU! MURAKOZE! ASANTE! MERCI! NGIYABONGA! SHKRAN!