Unit 3961: Applied Statistics

1. Introduction to Applied Statistics

• Role of a statistician in diverse fields (healthcare, business, engineering, social sciences)
• Importance of statistics in decision-making processes
• Fundamental concepts: population, sample, variables, data types

2. Descriptive Statistics

• Measures of Central Tendency
  • Mean, median, mode
• Measures of Variability
  • Range, variance, standard deviation, interquartile range
• Graphical Representations
  • Histograms, box plots, bar charts, scatter plots
• Summarizing and describing datasets effectively

3. Inferential Statistics

• Concept of population vs sample
• Sampling distributions
• Hypothesis Testing
  • Null and alternative hypotheses
  • Type I and Type II errors
  • p-values and significance levels
• Confidence Intervals
• Making inferences about populations based on sample data

4. Probability Distributions

• Introduction to probability theory
• Discrete Distributions
  • Binomial distribution: definition, properties, applications
  • Poisson distribution: properties, use cases
• Continuous Distributions
  • Normal distribution: characteristics, standard normal curve
• Applications of probability distributions in statistical analysis

5. Regression Analysis

• Simple Linear Regression
  • Model formulation
  • Least squares estimation
  • Interpretation of coefficients
• Multiple Regression Models
  • Incorporating multiple predictors
  • Assessing model fit (R-squared, adjusted R-squared)
• Checking assumptions (linearity, homoscedasticity, normality)
• Using regression to assess relationships between variables

6. Analysis of Variance (ANOVA)

• Concept and purpose of ANOVA
• One-Way ANOVA
  • Comparing means across more than two groups
  • F-test and interpretation
• Two-Way ANOVA
  • Factorial designs with two independent variables
• Post-hoc Tests
  • Tukey’s HSD, Bonferroni correction
• Assumptions and diagnostics

7. Experimental Design

• Principles of experimental design
  • Randomization, replication, control groups
• Types of experimental designs
  • Completely randomized, randomized block, factorial designs
• Ensuring validity and reliability of conclusions

8. Sampling Techniques

• Importance of proper sampling
• Sampling Methods
  • Simple random sampling
  • Stratified sampling
  • Cluster sampling
• Impact of sampling method on accuracy and bias

9. Statistical Software Applications

• Overview of popular tools
  • R: scripting, packages, visualization
  • Python: libraries such as pandas, numpy, scipy, seaborn
  • SPSS: GUI-based analysis
• Data analysis workflows
• Visualization and interpretation of statistical results

10. Ethical Considerations in Applied Statistics

• Ethical issues in data collection
  • Informed consent, confidentiality
• Data analysis ethics
  • Avoiding data manipulation and bias
• Transparent reporting of statistical findings
• Responsible use of statistics in decision-making