Learning Objectives
5 objectives- Understand the foundational concepts of statistical inference including population, sample, and parameter estimation.
- Identify and apply various sampling methods suitable for different research scenarios.
- Calculate and interpret confidence intervals and conduct hypothesis testing with understanding of errors involved.
- Differentiate between parametric and nonparametric tests and perform one-sample and two-sample tests.
- Apply advanced statistical techniques such as ANOVA, Chi-Square tests, and understand the importance of power and sample size calculations.
Content Outline
PreviewUnit 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
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