# Statistics

## Course Overview

Statistics is a comprehensive, Introductory Statistics course designed to cover Data Collection, Data Presentation, Probability, Confidence Intervals, Hypothesis Testing and Correlation with Linear Regression. Because the sheer volume of material is so great, the course is designed to take an entire school year and is intended for students with a proven record of accomplishment and interest in mathematics.

## Course Content

### Unit 1: Introduction to Statistics

This Unit provides students with best practices for collecting data. It identifies types of data and types of data collection practices, with an emphasis on random sampling. The following topics are covered in Unit 1:

- Statistical and Critical Thinking
- Types of Data
- Collecting Sample Data

### Unit 2: Summarizing and Graphing Data

This unit provides students with the skills to take the data they learned to collect in the previous unit and summarize it graphically. It emphasizes presenting data in such a way as to make it easier to understand and do further analysis with. The unit also explores the use of graphs that are used to mislead consumers of the information. The following topics are covered in Unit 2:

- Frequency Distributions
- Histograms
- Graphs that Enlighten and Graphs that Deceive

### Unit 3: Statistics for Describing, Exploring, and Comparing Data

After learning how to collect, organize and present data, the natural next step is to begin the process of numerically analyzing the data. The building blocks for statistical analysis are the measures of center and variation. To that end, this unit covers the following topics:

- Measures of Center
- Measures of Variation
- Measures of Relative Standing and Boxplots

### Unit 4: Probability

Probability is the motor that makes statistical analysis possible. Without a basic understanding of probability, the student will be lost when it comes to more complicated topics. While this unit is meant to only cover rudimentary probability rules, it is still very important to emphasize the importance of probability in statistical analysis. This unit covers the following topics:

- Basic Concepts of Probability
- Addition Rule
- Multiplication Rule: Basics
- Multiplication Rule: Compliments and Conditional Probability
- Counting

### Unit 5: Discrete Probability Distributions

Probability distributions are an integral part of exploring probability of events at a higher level. The binomial distribution, in particular, is the distribution that comes up most often in real world probability problems. This is also an excellent introduction to other probability distributions that are introduced in more advanced classes. This unit covers the following topics:

- Probability Distributions
- Binomial Probability Distributions
- Parameters for Binomial Distributions

### Unit 6: Normal Probability Distributions

This unit is a natural extension from discrete probability distributions to continuous probability distributions. Because the Normal Distribution is the most often used and is foundational to all of statistical analysis, this Unit is perhaps the most important unit in the entire course, particularly since concepts such as the Central Limit Theorem come directly from the Standard Normal Distribution. This unit covers the following topics:

- The Standard Normal Distribution
- Applications of Normal Distributions
- Sampling Distributions and Estimators
- The Central Limit Theorem
- Assessing Normality
- The Normal Approximation to the Binomial

### Unit 7: Estimates and Sample Sizes

This unit is the first time that students begin the process of statistical analysis. They collect data and create confidence intervals, which opens the door to ideas such as inference and hypothesis testing. The following topics are included in the unit:

- Estimating a Population Proportion
- Estimating a Population Mean
- Estimating a Population Standard Deviation or Variance

### Unit 8: Hypothesis Testing

It is in this Unit that students finally get to do formal statistical analysis. They are introduced to the basics of hypothesis testing, why it works, and how it is done with single variate date. The unit covers the following topics:

- Basics of Hypothesis Testing
- Testing a Claim about a Proportion
- Testing a Claim about a Mean

### Unit 9: Inferences from Two Samples

This Unit is the natural extension from comparing a single sample to a parameter to comparing to samples. It is the foundation of Random Controlled Trials and the gold standard of statistical analysis. This unit is the coalescence of everything the students have learned thus far and is easily the most important unit of the entire course. The unit covers the following topics:

- Two Proportions
- Two Means: Independent Samples
- Two Dependent Samples (Matched Pairs)

### Unit 10: Correlation and Regression

This Unit introduces students to the idea of bivariate data, their relationship to each other, and correlation as a means of statistical analysis. Ideas such as correlation, causation, and regression are introduced using technology and graphs. The unit covers the following topics:

- Correlation
- Regression

### Unit 11: Chi-Squared and Analysis of Variance

This is the final unit in the course and can be the most interesting and enjoyable for many students. Students are already well acquainted with writing null and alternative hypothesis, as well as the general idea of using statistical tests. This unit is an extension into more esoteric areas of statistical analysis. The unit covers the following topics:

- Goodness of Fit
- Contingency Tables
- Analysis of Variance (Optional)