Statistics Course Outline
Unit 1: Foundations of Vocabulary and Basic Statistical Calculations
A. Understanding Statistics
1. Descriptive and Inferential Statistics
2. Variables and Types of Data
3. Data Collection and Sampling Techniques
4. Observational and Experimental Studies
5. Uses and Misuses of Statistics
B. Frequency Distributions and Graphs
1. Organizing Data
2. Histograms, Frequency Polygons, and Ogives
3. Other Types of Graphs
C. Data Description
1. Measures of Central Tendency
2. Measures of Variation
3. Measures of Position
4. Measures of Position
5. Exploratory Data Analysis
D. Planning a Study
1. Methods of Data Collection
2. Planning and Conducting Surveys
3. Planning and Conducting Experiments
Unit 2: Probability and Probability Distributions
A. Probability and Counting Rules
1. Sample Spaces and Probability
2. The Addition Rules for Probability
3. The Multiplication Rules and Conditional Probability
4. Counting Rules
5. Probability and Counting Rules
B. Discrete Probability Distributions
1. Discrete Probability Distributions
2. Mean, Variance, Standard Deviation, and Expectation
3. The Binomial Distribution
4. Multinomial Distribution
5. Poisson Distribution
6. Hypergeometric Distribution
C. The Normal Distribution
1. Properties of the Normal Distribution
2. The Standard Normal Distribution
3. Applications of the Normal Distribution
4. The Central Limit Theorem
5. The Normal Approximation to the Binomial Distribution
Unit 3: Inferential Statistics
A. Confidence Intervals and Sample Size
1. Confidence Intervals for the Mean (s Known or n ≥ 30) and Sample Size
2. Confidence Intervals for the Mean (s Unknown or n < 30)
3. Confidence Intervals and Sample Size for Proportions
4. Confidence Intervals for Variances and Standard Deviations
B. Hypothesis Testing
1. Steps in Hypothesis Testing - Traditional Method
2. Z - Test for a Mean
3. t - Test for a Mean
4. Z - Test for a Proportion
5. Chi Square test for a Variance or Standard Deviation
6. P – Value Approach
7. Confidence Interval Approach
C. Testing the Difference Between Two Means, Variances, or Proportions
1. Testing the Difference Between Two Means: Large Samples
2. Testing the Difference Between Two Variances
3. Testing the Difference Between Two Means: Small Independent Samples
4. Testing the Difference Between Two Means: Small Dependent Samples
5. Testing the Difference Between Proportions
D. Correlation and Regression
1. Scatter Plots
2. Correlation
3. Regression
4. Coefficient of Determination and Standard Error of the Estimate
5. Variables and The Power of Prediction
E. Chi-Square Tests
1. Test for Goodness of Fit
2. Tests Using Contingency Tables
F. Analysis of Variance (Anova) Testing
1. One-Way Analysis of Variance
2. The Scheffé Test and the Tukey Test
3. Two-Way Analysis of Variance
Unit 4: Nonparametric Statistics
A. Advantages and Disadvantages of Nonparametric Methods
B. Types of Tests
1. The Sign Test
2. The Wilcoxon Rank Sum Test
3. The Wilcoxon Signed-Rank Test
4. The Kruskal-Wallis Test
5. The Spearman Rank Correlation Coefficient and the Runs Test