[Maths Class Notes] on Chi Square Test Pdf for Exam

Chi Square – Overview

Chi square test is the statistical test that is used to compare the observed results with the results that were expected. Basically, this test is for you to know if the difference between the observed results and expected results is by any chance or if it is due to the relationship between the variables that you are specially studying. Thus this chi-square test is the best test that will help you to understand and interpret the relationship between the two categorical variables.

You need to notice that this test like any other test will illuminate to you that there are relationships Between the variables and these relationships are having some significance IN the static field also. If you run a chi test on variables it is not going to tell you about our casual relationships or any other educational relationships, you are just going to get knowledge about its statistical relationships.

This article will explain to you about the chi-square test, the properties, what it is, and along with this you are going to learn about the formula for the chi-square test, the Chi-Square Method, the formula for chi-square distribution, and further you are provided with examples that help you to understand this topic of chi-square well. At the end, you are provided with the Frequently Asked Questions that will help to clear your inquiries regarding this chi-square test. In total this article provided to you by is the completed package. If you want to have more knowledge of the chi square test you can go look at this topic at the app. As the app has specially designed these articles by experts for the help of students.

What is the Chi Square Test?

I understand that you must be having a lot of questions such as how will you define the chi square test? For this reason we have for you the chi square test explained in a very simple way which is understandable so that next time someone will ask you what chi square test means? You can explain to them the chi square meaning straightforwardly. So let us grab this moment to learn the chi square definition.

In statistics, the Chi Square definition is explained as a test used by researchers for testing the relationships between categorical variables in the same population.

It measures how expectations are compared to actual observed data. The data we usually use to calculate the static must be random, mutually exclusive and raw. It must be drawn from independent variables and requires the sample which must be large enough. 

Chi Square Method

There are basically two types of chi square method.

The test of independence: This test asks you questions based on relationships such as “Does a relationship between gender and SAT scores exist”?

The goodness-of-fit test: This will ask you questions like “if a coin is being tossed 100 times, is there any chance of 50 time here

Table of Chi Square Test

Chi Square Distribution Formula

With the chi square test table given above and the chi square distribution formula, you can find the answers to your questions:

Chi square distribution formula can be written as:

x²c∑(O_i−E1)²/E_i  

Where, c is the chi square test degrees of freedom, O is the observed value(s) and E is the expected value(s).

Chi Square Test Example

Example: Consider a situation where a random poll of 2,000 different voters, both male and female was taken.  The people were classified on the basis of their gender and whether they were democrat, republican, or independent. So the grid will consist of columns labelled as republican, democrat, and independent, whereas two rows labelled as male and female. The data from 2,000 respondents is as follows:

Solution: Our first step to calculate the chi squared statistic will be to find the expected frequencies. The calculation will be made for each “cell” in the grid. Since there are two strata of gender and three categories of political view, we have a total of six expected frequencies. The formula for the expected frequency will be:

E(r,c) =n(r)×c(r)/n

Where, r is the row, c is the column and r is the corresponding total.The expected frequency in this example are: 

E(1,1)=900×800/2000 = 360

E(1,2)=900×800/2000=360

E(1,3)=200×800/2000=80

E(2,1)=900×1200/2000=540

E(1,2)=900×1200/2000=120

E(2,3)=200×1200/2000 = 120

Now, these are the used values to calculate the chi squared statistic using the following chi square distribution formula:

∑[O(r,c)−E(r,c)]²]/E(r,c)

Where, O(r,c) is the observed data for the provided rows and columns.The expression for each observed value in this example are:

O(1,1)= ([400−360])² /360 = 4.44

O(1,2)= ([300−360])² /360=10

O(1,3)= ([100−80])² /80=5

O(2,1)= ([500−540])² /540=2.96

O(2,2)= ([600−540])² /540=6.67

O(2,3)= ([100−120])² /120 = 3.33

So if we equal the sum of these values, it will come upto 32.41. Then we have to look at the chi square test table and find the given chi square test degrees of freedom in our set up to see if the  result is statistically significant or not.

Conclusion

When you use the chi square test you can just determine the fact that there are statically relationships between the two categorical variables that you have. In addition to this, you have to note that this test is basically a statically hypothesis test, that is valid to perform only when the test statistic is chi squared distributed and is under the null hypothesis. You can not calculate the actual relationships between the variables but can find the statically relationships between them. In order to compare the observed value and the actual value or  expected value, this chi square test can be used.