Statistics
Topics Covered
1. Descriptive Statistics
Data Collection and Sampling
Types of data (qualitative vs. quantitative)
Sampling methods and techniques
Bias and sampling errors
Data Presentation
Graphical representations (histograms, bar charts, pie charts, box plots)
Tables and frequency distributions
Measures of central tendency (mean, median, mode)
Measures of dispersion (range, variance, standard deviation)
Data Summarization
Descriptive measures for different data sets
Comparative analysis of data groups
Exploratory data analysis techniques
2. Probability
Basic Probability Concepts
Definitions and axioms of probability
Conditional probability and independence
Bayes’ theorem
Probability Distributions
Discrete distributions (Binomial, Poisson)
Continuous distributions (Normal, Uniform, Exponential)
Combinatorics
Permutations and combinations
Counting principles and applications
3. Inferential Statistics
Sampling Distributions
Central Limit Theorem
Sampling distribution of the sample mean and proportion
Estimation
Point estimates and interval estimates
Confidence intervals for means, proportions, and variances
Hypothesis Testing
Null and alternative hypotheses
Type I and Type II errors
p-values and significance levels
t-tests, z-tests, chi-square tests
4. Regression and Correlation
Simple Linear Regression
Least squares method
Interpretation of regression coefficients
Assessing model fit (R-squared)
Multiple Linear Regression
Building and interpreting multiple regression models
Multicollinearity and model selection
Correlation Analysis
Pearson and Spearman correlation coefficients
Causation vs. correlation
5. Analysis of Variance (ANOVA)
One-Way ANOVA
Comparing means across multiple groups
Assumptions and applications
Two-Way ANOVA
Factorial designs and interaction effects
Applications in experiments
6. Nonparametric Methods
Chi-Square Tests
Goodness-of-fit tests
Tests for independence
Nonparametric Alternatives to t-tests and ANOVA
Mann-Whitney U test, Kruskal-Wallis test
7. Time Series Analysis
Components of Time Series
Trend, seasonality, cyclicality, and randomness
Forecasting Techniques
Moving averages
Exponential smoothing
ARIMA models
8. Statistical Software and Tools
Using Software for Data Analysis
Introduction to R, Python (with libraries like pandas, NumPy, SciPy, statsmodels)
SPSS, SAS, Excel for statistical analysis
Data Visualization
Creating meaningful visual representations
Using tools like Tableau, matplotlib, ggplot
9. Advanced Topics (Optional Modules)
Multivariate Statistics
Principal Component Analysis (PCA)
Factor Analysis
Survival Analysis
Kaplan-Meier estimator
Cox proportional hazards model
Bayesian Statistics
Bayesian inference
Prior and posterior distributions
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