# Advanced Statistics

Taught by Dr. Matthew DeMarinis

Year 1
Univariate Data

1.1 Types of data
1.2 Mean and Median
1.3 Standard Deviation and Variance
1.4 Range, IQR and Finding Outliers
1.5 Graphs and Describing Distributions

Probability
2.1 Counting Techniques, Combinations and Permutations
2.2 Sets and Venn Diagrams
2.3 Basic Probability Models
2.4 General Probability Rules

Discrete Distributions
3.1 Random Variables
3.2 Binomial Distributions
3.3 Geometric Distributions

Continuous Distributions

4.1 Density Curves
4.2 The Normal Distribution
4.3 Standard Normal Calculations
4.4 Sampling Distribution of x and pˆ

Bivariate Data
5.1 Scatter Plots
5.2 Correlation
5.3 The Least Squares Regression Line
5.4 Residuals
5.5 Non-Linear Models
5.6 Relations in Categorical Data

Samples and Experiments
6.1 Sampling
6.2 Designing Experiments
6.3 Simulating Experiments

Year 2
Estimation
7.1 Margins of Error and Estimates
7.2 Confidence Interval for a Proportion
7.3 Confidence Interval for the Difference of Two Proportions
7.4 Confidence Interval for a Mean
7.5 Confidence Interval for the Difference of Two Means

Tests of Significance
8.1 Inference for the Mean of a Population
8.2 Sample Proportions
8.3 Inference for a Population Proportion
8.4 Comparing Two Means
8.5 Comparing Two Proportions
8.6 Goodness of Fit Test
8.7 Two-way Tables

Inference for Regression
9.1 Confidence Intervals
9.2 Test for Slope of Regression Lines