Statistics
University — Year 1
Mean, Median and Mode→Standard Deviation→Variance→Normal Distribution→Probability Basics→Bayes' Theorem→Descriptive Statistics: Mean, Median, Mode→Variance and Standard Deviation→Sample Space and Events→Probability Axioms and Rules→Conditional Probability→Independence of Events→Permutations and Combinations→Discrete Random Variables→Continuous Random Variables→Probability Mass Function (PMF)→Probability Density Function (PDF)→Cumulative Distribution Function (CDF)→Expected Value→Binomial Distribution→Poisson Distribution→Uniform Distribution→Exponential Distribution→Standardization and Z-Scores→Central Limit Theorem→Law of Large Numbers→Sampling Distributions→Point Estimation→Interval Estimation and Confidence Intervals→Hypothesis Testing: Fundamentals→Type I and Type II Errors→P-Value and Significance Level→One-Sample t-Test→Two-Sample t-Test→Paired t-Test→Chi-Square Test→Analysis of Variance (ANOVA)→Correlation Coefficient→Pearson Correlation→Linear Regression Model→Least Squares Estimation→Coefficient of Determination (R²)→Residual Analysis→Empirical Rule (68-95-99.7)→Covariance→Joint and Marginal Distributions→Law of Total Probability→Quantile-Quantile Plot (Q-Q Plot)→Skewness and Kurtosis→Outliers: Identification and Treatment→Contingency Tables→
University — Year 2
Hypothesis Testing→Confidence Intervals→Linear Regression→Correlation→Sampling Distribution of the Mean→Sampling Distribution of Proportion→Sampling Distribution of Sample Variance→Method of Moments Estimation→Maximum Likelihood Estimation→Confidence Intervals for Mean (Known Variance)→Confidence Intervals for Mean (Unknown Variance)→Confidence Intervals for Proportion→Confidence Intervals for Variance→Confidence Intervals for Difference of Two Means→Type I and Type II Errors→Power of a Statistical Test→One-Way Analysis of Variance (ANOVA)→Two-Way Analysis of Variance→Post-Hoc Tests (Tukey, Bonferroni)→Chi-Square Goodness of Fit Test→Chi-Square Test of Independence→Simple Linear Regression→Multiple Linear Regression→Regression Diagnostics and Model Validation→Correlation Analysis→Spearman Rank Correlation Coefficient→Mann-Whitney U Test→Wilcoxon Signed-Rank Test→Kruskal-Wallis Test→Logistic Regression→Survival Analysis Basics→Statistical Power and Sample Size Calculation→Bayesian Inference Introduction→Prior and Posterior Distributions→Markov Chain Monte Carlo (MCMC) Basics→Principles of Experimental Design→Factorial Designs→Randomized Block Design→Latin Square Design→Time Series Analysis Basics→Autoregressive (AR) Models→Moving Average (MA) Models→
University — Year 3
Multivariate Analysis→Multiple Regression→Time Series Models→Bayesian Inference→Nonparametric Methods→Experimental Design→Sampling Theory and Methods→Advanced Hypothesis Testing→Distribution Theory→Parameter Estimation Methods→Categorical Data Analysis→Survival Analysis→Mixed Effects Models→Principal Component Analysis→Factor Analysis→Cluster Analysis→Discriminant Analysis→Correspondence Analysis→Generalized Linear Models→Asymptotic Theory→Bootstrap Methods→Cross-Validation Techniques→Model Selection and Comparison→Interaction Effects in Regression→Multicollinearity and Solutions→Heteroscedasticity Detection and Correction→Autocorrelation and Correlograms→Advanced ANOVA Designs→Multivariate Analysis of Variance→Chi-Square Tests and Extensions→Maximum Likelihood Estimation→Method of Moments→Likelihood Ratio Tests→Spline and Smoothing Models→Robust Statistical Methods→Influence Diagnostics→Data Transformations→Missing Data and Imputation Methods→Sensitivity Analysis→Effect Sizes and Practical Significance→Regularization Techniques→