Unit 3963: Applied Statistics

1. Introduction to Applied Statistics

• Role and responsibilities of applied statisticians
• Importance of statistics in science, business, healthcare, social sciences, and engineering
• Basic concepts: population vs. sample, variables, data types
• Principles of statistical thinking

2. Descriptive Statistics

• Summarizing data: frequency distributions and tables
• Measures of central tendency: mean, median, mode
• Measures of dispersion: range, variance, standard deviation, interquartile range
• Graphical representations: histograms, bar charts, pie charts, box plots, scatterplots

3. Probability Theory

• Basic probability concepts: experiments, outcomes, events
• Probability rules and laws: addition, multiplication, complement
• Random variables: discrete and continuous
• Probability distributions: binomial, normal, Poisson distributions

4. Sampling Techniques

• Importance of sampling in statistics
• Types of sampling methods:
  • Simple random sampling
  • Stratified sampling
  • Cluster sampling
  • Systematic sampling
• Sampling bias and sampling error

5. Inferential Statistics

• Concept of population inference from sample data
• Hypothesis testing: null and alternative hypotheses, type I and II errors
• Confidence intervals and their interpretation
• Introduction to regression analysis (detailed in section 8)

6. Experimental Design

• Principles of experimental design: control groups, randomization, replication
• Types of experimental designs: completely randomized, randomized block, factorial designs
• Validity and reliability in experiments
• Ethical considerations in experimental research

7. Statistical Software Applications

• Overview of popular statistical software: R, SAS, SPSS
• Data input and management
• Performing basic analyses and generating descriptive statistics
• Creating visualizations
• Interpreting output and reporting results

8. Regression Analysis

• Introduction to regression models
• Simple linear regression: assumptions, fitting, interpretation
• Multiple regression: model building, multicollinearity
• Logistic regression: modeling categorical outcomes
• Model diagnostics and validation

9. Data Visualization

• Principles of effective data visualization
• Common chart types and their appropriate uses
• Advanced visualization techniques: heatmaps, interactive dashboards
• Communicating findings clearly through visuals

10. Time Series Analysis

• Characteristics of time series data
• Trend analysis and seasonal decomposition
• Moving averages and smoothing techniques
• Forecasting methods: ARIMA models, exponential smoothing
• Applications and case studies