Statistics for Data Scientists

1. Foundational Knowledge (Beginner Level)

Introduction to Statistics: Descriptive vs. Inferential statistics, Types of data, Population vs. sample.
Data Collection and Sampling: Methods of data collection, Sampling techniques, Sampling errors and bias.
Descriptive Statistics: Measures of central tendency (mean, median, mode), Dispersion (range, variance, std dev), Frequency distributions.
Probability Basics: Definitions of probability, Probability rules, Conditional probability, Probability distributions.
Introductory Probability Distributions: Binomial, Poisson, Normal, and Uniform distributions.

Inferential Statistics: Point estimation, Confidence intervals, Hypothesis testing (z-test, t-test, chi-square).
Correlation and Regression: Pearson/Spearman correlation, Linear regression, Multiple regression.
Analysis of Variance (ANOVA): One-way and two-way ANOVA, Post-hoc tests, Assumptions of ANOVA.
Non-parametric Tests: Mann-Whitney U, Wilcoxon signed-rank, Kruskal-Wallis test.
Advanced Probability Distributions: Exponential, Gamma, Beta, Multinomial distributions.

Advanced Regression Techniques: Polynomial regression, Ridge/Lasso regression, Logistic regression, Generalized Linear Models (GLM).
Time Series Analysis: ARIMA models, Forecasting, Moving averages, Trend analysis, Seasonality detection.
Multivariate Analysis: Principal Component Analysis (PCA), Factor analysis, Discriminant analysis, Cluster analysis.
Bayesian Statistics: Bayes' Theorem, MCMC methods, Bayesian regression, Posterior probability distributions.
Statistical Machine Learning: Decision trees, Random forests, Cross-validation, Overfitting, Dimensionality reduction.

Experimental Design: Completely randomized designs, Randomized block designs, Factorial experiments, DOE techniques.
Survival Analysis: Kaplan-Meier estimator, Cox proportional hazards model, Hazard functions, Time-to-event data.
Big Data Statistics: Sampling from big data, Data mining, Scalable algorithms (MapReduce, Hadoop), Statistical modeling for high-dimensional data.
Multilevel and Mixed Models: Hierarchical models, Fixed/random effects models, Longitudinal analysis.

To effectively apply statistical techniques, mastering various tools and software is essential:

R: Comprehensive tool for data analysis, visualization, and statistical modeling.
Python: Libraries like NumPy, pandas, SciPy, and statsmodels for statistical computing and machine learning.
SPSS: Widely used for social sciences and general statistics.
Excel: Basic analysis and data manipulation.
SAS & MATLAB: Advanced data analysis, predictive modeling, machine learning.

Real-world Projects: Apply knowledge to real-world problems through projects and case studies.
Competitions: Participate in statistical competitions (e.g., Kaggle) to hone your skills and test your knowledge.
Interdisciplinary Collaboration: Collaborate with professionals from different fields to apply statistics in diverse domains.
Continued Learning: Stay updated by reading academic papers, taking advanced courses, and following industry trends.