R Programming

  1. Statistical Analysis in R
    1. Descriptive Statistics
      1. Measures of Central Tendency
        1. Mean Calculation
          1. `mean()` Function
            1. Trimmed Mean
              1. Weighted Mean
              2. Median Calculation
                1. `median()` Function
                  1. Robust Central Tendency
                  2. Mode Calculation
                    1. Custom Mode Functions
                  3. Measures of Variability
                    1. Variance and Standard Deviation
                      1. `var()` and `sd()` Functions
                        1. Population vs. Sample Statistics
                        2. Range and Interquartile Range
                          1. `range()` Function
                            1. `IQR()` Function
                              1. `quantile()` Function
                              2. Coefficient of Variation
                                1. Mean Absolute Deviation
                                2. Distribution Shape
                                  1. Skewness Measures
                                    1. Kurtosis Measures
                                      1. Distribution Visualization
                                      2. Summary Statistics
                                        1. `summary()` Function
                                          1. `describe()` from psych Package
                                            1. Custom Summary Functions
                                            2. Frequency Analysis
                                              1. `table()` Function
                                                1. Cross-tabulation
                                                  1. Proportions and Percentages
                                                2. Probability Distributions
                                                  1. Distribution Function Naming Convention
                                                    1. Density Functions (`d*`)
                                                      1. Cumulative Distribution Functions (`p*`)
                                                        1. Quantile Functions (`q*`)
                                                          1. Random Number Generation (`r*`)
                                                          2. Continuous Distributions
                                                            1. Normal Distribution
                                                              1. `dnorm()`, `pnorm()`, `qnorm()`, `rnorm()`
                                                                1. Standard Normal Distribution
                                                                  1. Normal Approximations
                                                                  2. Student's t-Distribution
                                                                    1. `dt()`, `pt()`, `qt()`, `rt()`
                                                                      1. Degrees of Freedom
                                                                      2. Chi-squared Distribution
                                                                        1. `dchisq()`, `pchisq()`, `qchisq()`, `rchisq()`
                                                                          1. Applications in Testing
                                                                          2. F-Distribution
                                                                            1. `df()`, `pf()`, `qf()`, `rf()`
                                                                              1. ANOVA Applications
                                                                              2. Uniform Distribution
                                                                                1. `dunif()`, `punif()`, `qunif()`, `runif()`
                                                                                2. Exponential Distribution
                                                                                  1. `dexp()`, `pexp()`, `qexp()`, `rexp()`
                                                                                    1. Rate Parameter
                                                                                  2. Discrete Distributions
                                                                                    1. Binomial Distribution
                                                                                      1. `dbinom()`, `pbinom()`, `qbinom()`, `rbinom()`
                                                                                        1. Success Probability
                                                                                          1. Number of Trials
                                                                                          2. Poisson Distribution
                                                                                            1. `dpois()`, `ppois()`, `qpois()`, `rpois()`
                                                                                              1. Rate Parameter
                                                                                                1. Count Data Applications
                                                                                                2. Geometric Distribution
                                                                                                  1. `dgeom()`, `pgeom()`, `qgeom()`, `rgeom()`
                                                                                                    1. First Success Probability
                                                                                                    2. Negative Binomial Distribution
                                                                                                      1. `dnbinom()`, `pnbinom()`, `qnbinom()`, `rnbinom()`
                                                                                                        1. Overdispersion Modeling
                                                                                                      2. Distribution Fitting
                                                                                                        1. Method of Moments
                                                                                                          1. Maximum Likelihood Estimation
                                                                                                            1. Goodness of Fit Tests
                                                                                                          2. Hypothesis Testing
                                                                                                            1. Hypothesis Testing Framework
                                                                                                              1. Null and Alternative Hypotheses
                                                                                                                1. Type I and Type II Errors
                                                                                                                  1. Significance Levels
                                                                                                                    1. P-values and Interpretation
                                                                                                                      1. Confidence Intervals
                                                                                                                      2. One-sample Tests
                                                                                                                        1. One-sample t-test
                                                                                                                          1. `t.test()` Function
                                                                                                                            1. Assumptions and Diagnostics
                                                                                                                            2. One-sample Proportion Test
                                                                                                                              1. `prop.test()` Function
                                                                                                                              2. Wilcoxon Signed-rank Test
                                                                                                                                1. `wilcox.test()` Function
                                                                                                                                  1. Non-parametric Alternative
                                                                                                                                2. Two-sample Tests
                                                                                                                                  1. Independent Two-sample t-test
                                                                                                                                    1. Equal and Unequal Variances
                                                                                                                                      1. Welch's t-test
                                                                                                                                      2. Paired t-test
                                                                                                                                        1. Dependent Samples
                                                                                                                                          1. Before-after Comparisons
                                                                                                                                          2. Two-sample Proportion Test
                                                                                                                                            1. Mann-Whitney U Test
                                                                                                                                              1. Non-parametric Two-sample Test
                                                                                                                                            2. Tests for Categorical Data
                                                                                                                                              1. Chi-squared Goodness of Fit
                                                                                                                                                1. `chisq.test()` Function
                                                                                                                                                  1. Expected vs. Observed Frequencies
                                                                                                                                                  2. Chi-squared Test of Independence
                                                                                                                                                    1. Contingency Tables
                                                                                                                                                      1. Association Testing
                                                                                                                                                      2. Fisher's Exact Test
                                                                                                                                                        1. `fisher.test()` Function
                                                                                                                                                          1. Small Sample Sizes
                                                                                                                                                        2. Analysis of Variance (ANOVA)
                                                                                                                                                          1. One-way ANOVA
                                                                                                                                                            1. `aov()` Function
                                                                                                                                                              1. Between-group Comparisons
                                                                                                                                                                1. Post-hoc Tests
                                                                                                                                                                2. Two-way ANOVA
                                                                                                                                                                  1. Main Effects and Interactions
                                                                                                                                                                    1. Factorial Designs
                                                                                                                                                                    2. Repeated Measures ANOVA
                                                                                                                                                                      1. ANOVA Assumptions
                                                                                                                                                                        1. Normality Testing
                                                                                                                                                                          1. Homogeneity of Variance
                                                                                                                                                                            1. Independence
                                                                                                                                                                          2. Non-parametric Tests
                                                                                                                                                                            1. Kruskal-Wallis Test
                                                                                                                                                                              1. Non-parametric ANOVA Alternative
                                                                                                                                                                              2. Friedman Test
                                                                                                                                                                                1. Non-parametric Repeated Measures
                                                                                                                                                                            2. Correlation and Association
                                                                                                                                                                              1. Correlation Analysis
                                                                                                                                                                                1. Pearson Correlation
                                                                                                                                                                                  1. `cor()` Function
                                                                                                                                                                                    1. Linear Relationships
                                                                                                                                                                                      1. Assumptions
                                                                                                                                                                                      2. Spearman Rank Correlation
                                                                                                                                                                                        1. Monotonic Relationships
                                                                                                                                                                                          1. Non-parametric Correlation
                                                                                                                                                                                          2. Kendall's Tau
                                                                                                                                                                                            1. Alternative Rank Correlation
                                                                                                                                                                                            2. Partial Correlation
                                                                                                                                                                                              1. Controlling for Other Variables
                                                                                                                                                                                            3. Correlation Testing
                                                                                                                                                                                              1. `cor.test()` Function
                                                                                                                                                                                                1. Significance Testing
                                                                                                                                                                                                  1. Confidence Intervals
                                                                                                                                                                                                  2. Covariance Analysis
                                                                                                                                                                                                    1. `cov()` Function
                                                                                                                                                                                                      1. Covariance Matrices
                                                                                                                                                                                                        1. Relationship to Correlation
                                                                                                                                                                                                        2. Association Measures
                                                                                                                                                                                                          1. Contingency Table Analysis
                                                                                                                                                                                                            1. Cramér's V
                                                                                                                                                                                                              1. Phi Coefficient
                                                                                                                                                                                                            2. Regression Analysis
                                                                                                                                                                                                              1. Simple Linear Regression
                                                                                                                                                                                                                1. `lm()` Function
                                                                                                                                                                                                                  1. Model Formula Syntax
                                                                                                                                                                                                                    1. Least Squares Estimation
                                                                                                                                                                                                                      1. Model Interpretation
                                                                                                                                                                                                                      2. Multiple Linear Regression
                                                                                                                                                                                                                        1. Multiple Predictors
                                                                                                                                                                                                                          1. Model Building Strategies
                                                                                                                                                                                                                            1. Variable Selection
                                                                                                                                                                                                                              1. Multicollinearity
                                                                                                                                                                                                                              2. Model Diagnostics
                                                                                                                                                                                                                                1. Residual Analysis
                                                                                                                                                                                                                                  1. Residual Plots
                                                                                                                                                                                                                                    1. Normality of Residuals
                                                                                                                                                                                                                                      1. Homoscedasticity
                                                                                                                                                                                                                                      2. Influential Observations
                                                                                                                                                                                                                                        1. Cook's Distance
                                                                                                                                                                                                                                          1. Leverage
                                                                                                                                                                                                                                            1. Outlier Detection
                                                                                                                                                                                                                                            2. Model Assumptions
                                                                                                                                                                                                                                              1. Linearity
                                                                                                                                                                                                                                                1. Independence
                                                                                                                                                                                                                                                  1. Normality
                                                                                                                                                                                                                                                    1. Constant Variance
                                                                                                                                                                                                                                                  2. Model Selection
                                                                                                                                                                                                                                                    1. Forward Selection
                                                                                                                                                                                                                                                      1. Backward Elimination
                                                                                                                                                                                                                                                        1. Stepwise Selection
                                                                                                                                                                                                                                                          1. Information Criteria (AIC, BIC)
                                                                                                                                                                                                                                                          2. Generalized Linear Models
                                                                                                                                                                                                                                                            1. `glm()` Function
                                                                                                                                                                                                                                                              1. Exponential Family Distributions
                                                                                                                                                                                                                                                                1. Logistic Regression
                                                                                                                                                                                                                                                                  1. Binary Outcomes
                                                                                                                                                                                                                                                                    1. Odds Ratios
                                                                                                                                                                                                                                                                      1. Model Interpretation
                                                                                                                                                                                                                                                                      2. Poisson Regression
                                                                                                                                                                                                                                                                        1. Count Data
                                                                                                                                                                                                                                                                          1. Rate Models
                                                                                                                                                                                                                                                                            1. Overdispersion
                                                                                                                                                                                                                                                                          2. Model Validation
                                                                                                                                                                                                                                                                            1. Cross-validation
                                                                                                                                                                                                                                                                              1. Train-test Splits
                                                                                                                                                                                                                                                                                1. Performance Metrics
                                                                                                                                                                                                                                                                              2. Time Series Analysis
                                                                                                                                                                                                                                                                                1. Time Series Objects
                                                                                                                                                                                                                                                                                  1. `ts()` Function
                                                                                                                                                                                                                                                                                    1. Time Series Properties
                                                                                                                                                                                                                                                                                      1. Frequency and Seasonality
                                                                                                                                                                                                                                                                                      2. Time Series Decomposition
                                                                                                                                                                                                                                                                                        1. Trend, Seasonal, and Irregular Components
                                                                                                                                                                                                                                                                                          1. `decompose()` Function
                                                                                                                                                                                                                                                                                            1. STL Decomposition
                                                                                                                                                                                                                                                                                            2. Stationarity
                                                                                                                                                                                                                                                                                              1. Stationarity Tests
                                                                                                                                                                                                                                                                                                1. Differencing
                                                                                                                                                                                                                                                                                                  1. Transformation Methods
                                                                                                                                                                                                                                                                                                  2. ARIMA Models
                                                                                                                                                                                                                                                                                                    1. Autoregressive Models
                                                                                                                                                                                                                                                                                                      1. Moving Average Models
                                                                                                                                                                                                                                                                                                        1. ARIMA Model Fitting
                                                                                                                                                                                                                                                                                                          1. Model Selection and Diagnostics

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                                                                                                                                                                                                                                                                                                      10. Data Visualization

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                                                                                                                                                                                                                                                                                                      12. Reproducible Research and Reporting