Unit 2941: Introduction to Applied Statistics

1. Introduction to Statistics

• Definition and scope of statistics
• Types of data: qualitative vs quantitative
• Levels of measurement: nominal, ordinal, interval, ratio
• Importance and applications of statistics in various fields (e.g., business, healthcare, social sciences)

2. Descriptive Statistics

2.1 Measures of Central Tendency

• Mean: calculation and interpretation
• Median: determination and use cases
• Mode: identification and significance

2.2 Measures of Dispersion

• Range: definition and limitations
• Variance: computation and meaning
• Standard deviation: interpretation and use
• Importance of dispersion in data analysis

3. Probability Fundamentals

• Definition and concept of probability
• Calculating probability: classical, relative frequency, and subjective approaches
• Probability rules: addition rule, multiplication rule, complement rule
• Theoretical vs empirical probability: differences and examples

4. Probability Distributions

4.1 Discrete Distributions

• Binomial distribution: assumptions, probability mass function, examples
• Poisson distribution: characteristics and applications

4.2 Continuous Distributions

• Normal distribution: properties, standard normal curve, empirical rule
• Applications of distributions in real-world scenarios

5. Sampling and Sampling Distributions

• Sampling methods: simple random, stratified, systematic, cluster sampling
• Sampling bias and how to avoid it
• Sampling distributions: concept and importance
• Central Limit Theorem: statement and implications

6. Hypothesis Testing

• Formulating hypotheses: null and alternative hypotheses
• Types of errors: Type I and Type II
• Test statistics and significance levels
• Steps in hypothesis testing procedure
• Interpreting p-values and confidence levels

7. Correlation and Regression Analysis

• Correlation analysis: Pearson’s correlation coefficient, interpretation
• Simple linear regression: model, assumptions, estimation of parameters
• Using regression for prediction
• Limitations and diagnostics of regression analysis

8. Inferential Statistics

• Confidence intervals: construction and interpretation
• t-tests: one-sample, independent, and paired samples
• Analysis of Variance (ANOVA): purpose and basic concepts
• Chi-square tests: goodness-of-fit and test of independence

9. Data Visualization

• Importance of visual representation of data
• Common visualization tools: bar charts, histograms, box plots, scatter plots
• Best practices for effective visualization
• Using software tools for creating visualizations (e.g., Excel, R, Python libraries)