Back To Course

Introduction to Statistics: Help and Review9 chapters | 137 lessons

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Mia Primas*

Mia has taught math and science and has a Master's Degree in Secondary Teaching.

Chi square distributions are a way of mapping the probabilities of values. In this lesson, we'll look at distributions represented in graphs and tables. We'll also look at an example that uses chi square distribution to test the independence of variables.

Sally has a friend, Sarah, that believes certain college majors are more likely to be chosen by students of one gender over another. Sally does not agree with Sarah's claim, so she decided to survey students on her college campus. Once she collected the data, she used a chi square distribution to determine whether her prediction was correct.

**Chi square distribution** is a type of cumulative probability distribution. **Probability distributions** provide the probability of every possible value that may occur. Distributions that are **cumulative** give the probability of a random variable being less than or equal to a particular value. Since the sum of the probabilities of every possible value must equal one, the total area under the curve is equal to one.

To find the probability of a particular value, we find the area under the curve before the value. The area that's after the value is called the ** p-value**, which is important for statistical tests that use chi square. In this figure,

Chi square distributions vary depending on the degrees of freedom. The **degree of freedom** is found by subtracting one from the number of categories in the data. For example, if you gather data about the gender of students enrolled in science, art, and education programs, you have three categories of students: one for each program. My degree of freedom would be 2 (or 3 - 1). In this graph, each curve represents the chi square distribution for a different degree of freedom:

No matter how many degrees of freedom there are, the shape of a chi square distribution is always skewed right. However, as the degree of freedom increases, the shape becomes closer to a normal distribution with a symmetrical bell shape.

Many statistical analyses involve using the *p*-value. However, calculating a portion of the area under the curve can be difficult. This graph can be used to find *p*-values for various degrees of freedom. For example, if the chi square value is 5 for a set of data that has a degree of freedom equal to 4, we can follow the curve to see that the *p*-value is approximately 0.3:

It's often more efficient to use a chi square table. In this table, each row represents a different degree of freedom along with several chi square values. The corresponding *p*-values are listed at the top of each column:

**Chi square** is a calculation used to determine how closely the observed data fit the expected data. In the following chi square calculation formula, *X* represents chi, while *o* and *e* represent the observed and expected values, respectively:

Let's look at an example to see how chi square can be used for a test of independence. In this example, we want to use the data to determine if college students' program choice depends on gender. First, we need to establish a null hypothesis, predicting that students' program of enrollment is independent of their gender. The results of our chi square test will determine whether we should accept or refute the null hypothesis. Statisticians normally accept the null hypothesis if the *p*-value is 0.05 or higher. Here's the data:

Science | Art | Education | |
---|---|---|---|

Female | e: 69, o: 56 |
e: 40, o:43 |
e: 62, o: 74 |

Male | e: 69, o: 82 |
e: 40, o:37 |
e: 62, o: 50 |

Notice that there are two values in each cell of the table: one for the expected value (*e*) and one for the observed value (*o*). The expected values are based on our null hypothesis that program choice does not depend on gender, so there should be an equal number of each gender in the programs. The observed values are from collected data. We can now use our expected and observed values to calculate chi square, like so:

Since there are three categories (science, art, and education), the degree of freedom is 2. Following the row for a degree of freedom of 2 on the chi square table, we look for values nearest to our chi square value of 10. 10 falls between 9.21 and 10.597, so our *p*-value falls between the corresponding *p*-values of 0.01 and 0.005. Since this falls below the *p*-value of 0.05, we would reject the null hypothesis. This tells us that based on our data, the program of choice does depend on gender. Sarah was right!

**Chi square distributions** are used to identify the probability of a value occurring. The probability value can be used to determine how closely observed values fit expected values and whether variables are independent of each other. Once the value of **chi square** is calculated from the chi square equation, the table or graph of the chi square distribution can be used to determine the *p*-value. If the *p*-value is greater than 0.05 for a test of independence, the variables are independent of each other.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
25 in chapter 1 of the course:

Back To Course

Introduction to Statistics: Help and Review9 chapters | 137 lessons

- Descriptive & Inferential Statistics: Definition, Differences & Examples 5:11
- Difference between Populations & Samples in Statistics 3:24
- Defining the Difference between Parameters & Statistics 5:18
- Estimating a Parameter from Sample Data: Process & Examples 7:46
- What is Quantitative Data? - Definition & Examples 4:11
- What is Categorical Data? - Definition & Examples 5:25
- Discrete & Continuous Data: Definition & Examples 3:32
- Nominal, Ordinal, Interval & Ratio Measurements: Definition & Examples 8:29
- The Purpose of Statistical Models 10:20
- Experiments vs Observational Studies: Definition, Differences & Examples 6:21
- Random Selection & Random Allocation: Differences, Benefits & Examples 6:13
- Convenience Sampling in Statistics: Definition & Limitations 6:27
- How Randomized Experiments Are Designed 8:21
- Analyzing & Interpreting the Results of Randomized Experiments 4:46
- Confounding & Bias in Statistics: Definition & Examples 3:59
- Bias in Polls & Surveys: Definition, Common Sources & Examples 4:36
- Misleading Uses of Statistics 8:14
- Causation in Statistics: Definition & Examples 3:28
- Deductive Argument: Definition & Examples
- Dot Plot in Statistics: Definition, Method & Examples 3:57
- Observational Study in Statistics: Definition & Examples 5:55
- Skewness in Statistics: Definition, Formula & Example 6:49
- Uniform Distribution in Statistics: Definition & Examples 4:58
- Confidence Interval: Definition, Formula & Example 7:33
- Chi Square Distribution: Definition & Examples 4:55
- Chi Square: Definition & Analysis 4:04
- How to Calculate a Chi Square: Formula & Example 4:13
- Go to Overview of Statistics: Help and Review

- Computer Science 109: Introduction to Programming
- Introduction to HTML & CSS
- Introduction to JavaScript
- Computer Science 332: Cybersecurity Policies and Management
- Introduction to SQL
- Algorithmic Analysis, Sorting & Searching
- Computer Programming Basics
- Stacks & Queues for Data Structures
- Functions & Modules in Programming
- Built-In Data Types for Programming
- CEOE Test Cost
- PHR Exam Registration Information
- Claiming a Tax Deduction for Your Study.com Teacher Edition
- What is the PHR Exam?
- Anti-Bullying Survey Finds Teachers Lack the Support They Need
- What is the ASCP Exam?
- ASCPI vs ASCP

- Process Synchronization in Operating Systems: Definition & Mechanisms
- Plastic: Types & Uses
- What is a Scotoma? - Definition, Types & Causes
- How to Find the Centroid of a Triangle
- Validating Forms Using JavaScript: Overview & Example
- Past Progressive Lesson Plan
- Practical Application for Programming in R: Using Flow Control Functions
- Quiz & Worksheet - Love in A Midsummer Night's Dream
- Quiz & Worksheet - Washington's Leadership Skills
- Quiz & Worksheet - Memory Partitioning Overview
- Quiz & Worksheet - Formula for Calculating Distance in Math
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- Common Core Worksheets | Printable Math & English Worksheets
- Anti-Bullying Guide | Stop Bullying in Schools

- ACT Reading Section: Prep & Practice
- Excel: Skills Development & Training
- Physics 101 Syllabus Resource & Lesson Plans
- Technical Writing Textbook
- DSST Business Ethics and Society: Study Guide & Test Prep
- Praxis Chemistry: Nomenclature and Chemical Composition
- Application Software
- Quiz & Worksheet - Theory of Social Pathology
- Quiz & Worksheet - History & Components of the Symphony
- Quiz & Worksheet - Properties of Octahedrons
- Quiz & Worksheet - Phineas Gage's Story & Impact on Psychology

- Orthographic Drawing: Definition & Examples
- Infinite Series: Applications, Formula & Examples
- Common Core Standards in Rhode Island (RI)
- How to Pass the NAPLEX
- How to Stop Procrastinating
- Common Core State Standards in New Mexico
- Writing Prompts for Middle School
- Cool Math Puzzles
- Algebra Math Games
- Common Core State Standards in Arkansas
- How to Pass the COMPASS Math Test
- Online Credit Recovery Programs

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject