Statistical Analysis

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| Subject classification: this is a mathematics resource.

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## Purpose of Course

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In this course, we will look at the properties behind the basic concepts of probability and statistics and focus on applications of statistical knowledge. We will learn how statistics and probability work together. The subject of statistics involves the study of methods for collecting, summarizing, and interpreting data. Statistics formalizes the process of making decisions—and this course is designed to help you cultivate statistic literacy so that you can use this knowledge to make better decisions. Note that this course has applications in sciences, economics, computer science, finance, psychology, sociology, criminology, and many other fields. Every day, we read articles and reports in print or online. After finishing this course, you should be comfortable asking yourself whether the articles make sense. You will be able to extract information from the articles and display that information effectively. You will also be able to understand the basics of how to draw statistical conclusions. This course will begin with descriptive statistics and the foundation of statistics. You will then learn about probability and random distributions, the latter of which enables us to work with several aspects of random events and their applications. Finally, we will examine a number of ways to investigate the relationships between various characteristics of data. By the end of this course, you should have a grasp on what statistics represent, how to use them to organize and display data, and how to test the data to make effective conclusions.

This course was originally adapted for Wikiversity from the MA121/ECON104 Course Introduction to Statistics at Saylor.org

## Learning Outcomes

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Upon completion of the course, you will be able to:

* Define the meaning of descriptive statistics and statistical inference.
* Distinguish between a population and a sample.
* Explain the purpose of measures of location, variability, and skewness.
* Calculate probabilities.
* Explain the difference between how probabilities are computed for discrete and continuous random variables.
* Recognize and understand discrete probability distribution functions, in general.
* Identify confidence intervals for means and proportions.
* Explain how the central limit theorem applies in inference.
* Calculate and interpret confidence intervals for one population average and one population proportion.
* Differentiate between Type I and Type II errors.
* Conduct and interpret hypothesis tests.
* Compute regression equations for data.
* Use regression equations to make predictions.
* Conduct and interpret ANOVA (Analysis of Variance).

## Content Units

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The links below will direct you to the navigation page for each unit of this course.

### Unit 1: Data And Descriptive Statistics

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* Unit 1 Navigation
* Unit 1 Content

### Unit 2: Probability Topics

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* Unit 2 Navigation
* Unit 2 Content

### Unit 3: Random Variables and Distributions

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* Unit 3 Navigation
* Unit 3 Content

### Unit 4: Central Limit Theorem and Confidence Intervals

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* Unit 4 Navigation
* Unit 4 Content

### Unit 5: Hypothesis Testing

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* Unit 5 Navigation
* Unit 5 Content

### Unit 6: Correlation, Regression, and ANOVA

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* Unit 6 Navigation
* Unit 6 Content

## About the Resources in This Course

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This course project draws upon three main types of resources:

The first are readings and video lectures from Barbara Illowsky and Susan Dean’s Collaborative Statistics, which is available freely under a Creative Commons Attribution 2.0 Generic (CC BY 2.0) license from the following location: http://cnx.org/content/col10522/latest/

The second type of resources in this course are lectures from Khan Academy. These lectures are available under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported (CC BY-NC-SA 3.0) license. Khan Academy has many lectures available from http://www.khanacademy.org/

Finally, the above resources have been woven together and organized into a format analogous to a traditional college-level course by professional consultants that work as experts within the subject area. This process was facilitated by The Saylor Foundation. Additionally, if you have worked through all of the material contained in this project, you may be interested in taking the final exam provided by Saylor.org or completing other courses available there that are not yet on Wikiversity.

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Introduction to Statistical Analysis

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