Unit 2959: Statistical Inference and Data Analysis

1. Introduction to Statistical Inference

• Definition and scope of statistical inference
• Population vs. Sample
• Parameters and Statistics
• Parameter estimation techniques
• Hypothesis testing overview
• Difference between descriptive and inferential statistics

2. Sampling Methods

• Importance of sampling in statistics
• Simple Random Sampling
  • Definition and procedure
  • Advantages and limitations
• Stratified Sampling
  • Concept and use cases
  • Advantages and limitations
• Cluster Sampling
  • Methodology and examples
  • Advantages and limitations
• Systematic Sampling
  • Procedure and applications
  • Advantages and limitations

3. Confidence Intervals

• Concept of confidence intervals in inference
• Confidence level and its interpretation
• Calculating confidence intervals for:
  • Population mean (known and unknown variance)
  • Population proportion
• Factors affecting width of confidence intervals
• Practical interpretation and examples

4. Hypothesis Testing

• The hypothesis testing framework
• Formulating null (H0) and alternative (H1) hypotheses
• Choosing appropriate test statistics
• Significance level (alpha) and p-value concepts
• Decision rules and conclusion drawing
• Examples with real data

5. Types of Errors in Hypothesis Testing

• Type I Error (False Positive)
• Type II Error (False Negative)
• Consequences and examples
• Balancing errors: trade-offs and considerations
• Strategies to minimize errors

6. Parametric vs. Nonparametric Tests

• Definition and assumptions of parametric tests
• Definition and use of nonparametric tests
• When to use parametric vs. nonparametric tests
• Examples of common tests:
  • Parametric: t-tests, ANOVA
  • Nonparametric: Mann-Whitney U, Kruskal-Wallis

7. One-Sample and Two-Sample Tests

• One-sample tests
  • One-sample t-test: assumptions, calculation, interpretation
  • One-sample z-test: when to use
• Two-sample tests
  • Independent samples t-test
  • Paired samples t-test
  • Two-sample z-test
• Examples and practical application

8. Analysis of Variance (ANOVA)

• Purpose and rationale of ANOVA
• One-way ANOVA: assumptions and procedure
• Between-group and within-group variability
• F-statistic and interpretation
• Post-hoc tests overview
• Practical examples

9. Chi-Square Tests

• Introduction to Chi-Square tests
• Goodness-of-Fit test
  • Purpose and procedure
  • Calculating expected frequencies
• Test for Independence
  • Contingency tables
  • Interpretation of results
• Assumptions and limitations

10. Power and Sample Size Calculations

• Concept of statistical power
• Factors affecting power: effect size, sample size, alpha, variability
• Calculating power for different tests
• Determining required sample size for studies
• Importance in experimental design
• Practical examples and software tools