Beginner Level
1. Introduction to Statistics
- What is Statistics?
- Importance of statistics in data science
- Types of statistics (descriptive vs. inferential)
2. Descriptive Statistics
- Measures of Central Tendency
- Mean, median, and mode
- Measures of Dispersion
- Range, variance, and standard deviation
- Data Visualization
- Histograms, bar charts, and box plots
- Introduction to data distribution
3. Probability Basics
- Understanding Probability
- Definitions and rules of probability
- Conditional probability and independence
- Probability Distributions
- Discrete distributions (Binomial, Poisson)
- Continuous distributions (Normal distribution)
4. Sampling and Sampling Distributions
- Basics of Sampling
- Population vs. sample
- Types of sampling methods (random, stratified, systematic)
- Central Limit Theorem
- Importance of the Central Limit Theorem in statistics
Intermediate Level
1. Inferential Statistics
- Hypothesis Testing
- Null and alternative hypotheses
- Type I and Type II errors
- p-Values and Significance Levels
- Understanding p-values and their interpretation
- Setting significance levels (α)
2. Confidence Intervals
- Constructing Confidence Intervals
- Confidence intervals for means and proportions
- Interpreting confidence intervals
3. Advanced Probability Distributions
- Common Distributions
- Normal, t-distribution, chi-square distribution, F-distribution
- Application of distributions in hypothesis testing
4. Correlation and Regression
- Understanding Correlation
- Pearson correlation coefficient
- Spearman’s rank correlation
- Simple Linear Regression
- Model formulation and interpretation
- Assumptions of linear regression
Advanced Level
1. Multiple Regression Analysis
- Extending Simple Linear Regression
- Multiple regression concepts and interpretation
- Checking for multicollinearity
- Model Diagnostics
- Residual analysis and goodness-of-fit measures
2. ANOVA (Analysis of Variance)
- Understanding ANOVA
- One-way and two-way ANOVA
- Post-hoc tests (Tukey’s HSD, Bonferroni)
3. Non-Parametric Statistics
- Non-Parametric Tests
- When to use non-parametric tests
- Wilcoxon signed-rank test, Kruskal-Wallis test, Chi-square test
4. Time Series Analysis
- Analyzing Time Series Data
- Components of time series (trend, seasonality, cyclicity)
- Forecasting methods (moving averages, ARIMA)
5. Statistical Software and Tools
- Using Statistical Software
- Introduction to R or Python for statistical analysis
- Performing statistical tests and creating visualizations using software
