Looking for relationships between categorical variables
The chi squared independence tests is a widely used technique for looking for a relationship between variables that are categorical. We can use a scatter graph to look for a relationship between GDP and life expectancy, but what about GDP and Continent? We cant put continent on a numerical axis. This tool gives us many new options and is an excellent bit of mathematics.
Key Concepts
In this unit you should learn to…
Understand the nature of the chi squared test of independence as a means of looking for relationships between categorical data
Calculate the chi squared statistic and p number for given data and use them to conclude
Understand and use the language of hypothesis testing and carry out tests from start to finish
Essentials
Slide Gallery
Use these slides to review the material and key points covered in the videos that appear below.
1. What are Chi squared tests of independence?
These two videos explain 1. What the purpose of a Chi squared independence test is and 2. What the fundamental principle behind them is.
2. Understand and calculate expected frequencies
This video lesson takes you through the idea of calculating expected frequencies, from understanding the concept to applying it in context.
3. Calculating the Chi Squared Statistic
This video lesson goes through the process of calculating the chi squared statistic, both so that you can understand it and know how to calculate it.
4. Degrees of freedom and significance levels
These two video lessons cover the key ideas of degrees of freedom and significance levels. Understand them and then how to work with them.
5. Concluding Chi Squared tests
Here are two videos showing how you conclude these tests using 1. The critical value approach and 2. The p-number approach.
Concluding with the critical value
Concluding with the p-number
6. An example test
The following video goes through an example question showing how to get both the calculated statistic and p number from both Casio and TI calculators.
Summary
This section of the page can be used for quick review. The flashcards help you go over key points and the quiz lets you practice answering questions on this subtopic.
Flash Cards
Review these condensed 'key point' flashcards to help you check and keep ideas fresh in your mind.
Test Yourself
Self Checking Quiz
Quiz
Practice your understanding on these quiz questions. Check your answers when you are done and read the hints where you got stuck. If you find there are still some gaps in your understanding then go back to the videos and slides above.
1
A large mount of information is collected about a number of countires. Which of the following would be considered categorical data?
GDP, area, Life expectancy and Infant mortality rates can all be measured with numbers on a scale. The rest can't.
........
2
We start chi squared tests by assuming that.....
The following is a contingency table of results fo a chi squared test to see if wage bracket is dependent the level of education reached. Use it to answer the next 3 questions.
3
What is the value for degrees of freedom for this table?
Degrees of freedom is (rows - 1) x (columns - 1) so (3 - 1) x (3 - 1) = 4
4
What is the expected frequency of people who did not attend university in the low wage bracket?
5
What is the expected frequency of people with a post graduate degree in the high wage bracket?
6
What is the expected frequency of people with a university degree in the medium wage bracket?
7
Calculate the p-number using your GDC (start your answer 0. )
From GDC
8
Calculate the chi squared statistic using your GDC
From GDC
9
Use the p number to test at 10% significance level if these variables are dependent.
Since the p number, 0.835 > 0.10 (10%), the probability of independence is high enough to accept the null hypothesis.
10
To reject the null hypothesis, which of the following conditions should be met?
To reject, the probability of independence must be below the signficance level (10%, 5%, 1%, 0.1, 05, 0.1) and the chi squared statistic (the measure of error) must be bigger the critical value (too big an error)
Exam Style Questions
The following questions are based on IB exam style questions from past exams. You should print these off (from the document at the top) and try to do these questions under exam conditions. Then you can check your work with the video solution.
Question 1
Video solution
Question 2
Video solution
MY PROGRESS
How much of 4.11 Chi Squared Independence tests have you understood?
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Looking for relationships between categorical variables
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