# A Step-by-Step Guide to Chi-square Test Homework-Tips and Example Problem

May 08, 2023 Janet Smithson
United States of America
Chi-square Test
Dr. Janet Smithson has a Ph.D. in Statistics from the University of Chicago and 10+ years of teaching and consulting on statistical analysis, including the Chi-square test.
As a student of statistics, you will learn about many different statistical tests and ideas. The Chi-square test is one of these ideas. It is a statistical test used to see if there is a strong link between two variables.
The Chi-square test is often used in fields such as biology, social sciences, and healthcare. It's an important tool for researchers and analysts in these fields to use to find correlations and trends in data sets.
But many students find it hard to do their Chi-square test homework. You might have trouble with the technical details and formulas needed to do the analysis.
So, we put together this complete guide to help you do your SPSS-related homework easily. In this blog, we'll show you how to correctly set up hypotheses, use technology to do the analysis, and check your work to make sure it's right.
By the end of this guide, you'll know a lot about Chi-square test analysis and have the confidence to do any Chi-square test homework. This guide is for you if you are new to statistics or want to brush up on what you already know. Let's dive in!

## Understanding the Basics of the Chi-square test

Let's get a fundamental understanding of the Chi-square test under our belts before we delve into the specifics of how to go about tackling Chi-square test homework. The chi-square test is a statistical test that is used to determine whether or not there is a significant association between two categorical variables. This can be done by looking at whether or not there is a correlation between the two. The test involves a comparison of the actual data with the data that were anticipated, as well as the computation of the Chi-square test statistic. If the calculated value of the Chi-square test is higher than the critical value, then the null hypothesis is rejected, and it is concluded that there is a significant association between the two variables. The chi-square test is a statistical test that compares two variables to determine whether or not there is a correlation between them.

### Chi-square test Formula

Here is the Chi-square test formula:
χ² = ∑ (O - E)2 / E,
where
χ² is the Chi-square test statistic,
O is the observed frequency,
E is the expected frequency and
is the sum of all the observations.

### Steps to Approach Chi-square Test Homework

Now that you have a basic understanding of the Chi-square test, let's discuss the steps to approach the Chi-square test homework.
Step 1 - Understand the Problem Statement
The first step in tackling Chi-square test homework is to understand the problem statement. Carefully read the problem statement and find the two categorical variables being tested. You should also say how many people were in the sample and how important the results are.
Step 2 - Set Up the Hypotheses
The second step is to set up your hypotheses. The null hypothesis is that there is no significant link between the two variables. The alternative hypothesis is that there is a significant link between the two variables. Based on the problem statement, write down the null and alternative hypotheses.
Step 3 - Calculate the Expected Frequencies
The next step is to calculate the expected frequencies. The expected frequency is calculated using the following formula:
E = (row total x column total) / total
where E is the expected frequency, row total is the total number of observations in the row, column total is the total number of observations in the column, and the total is the total number of observations.
Step 4 - Calculate the Chi-square test Statistic
The next step is to use the formula mentioned earlier to figure out the Chi-square test statistic. Add up the values of each cell's Chi-square test statistic to get the total Chi-square test value.
Step 5 - Compare the Chi-square test Statistic with the Critical Value
The final step is to look at how the Chi-square test statistic compares to the critical value. You can find the critical value in the Chi-square test distribution table, where the degree of freedom equals (number of rows - 1) x (number of columns - 1). If the calculated Chi-square test value is greater than the critical value, then you can reject the null hypothesis and say that there is a significant relationship between the two variables.

## Chi-square test Example

Let's work through a Chi-square test problem as an example of how to use the ideas we've talked about. If you follow the steps we give, you can confidently tackle any Chi-square test problem.
In our example problem, we will look at the connection between gender and political party. We'll use a contingency table to organize the data and then figure out how often each cell is likely to happen. Lastly, we'll use the expected frequencies to figure out the Chi-square test statistic and the p-value.
By working through this example, you'll get a better idea of how to use the Chi-square test to analyze real-world data sets. You'll also be able to use the same method on your own Chi-square test homework. So, let's move on to our first example problem.

### Problem Statement

Suppose you want to determine if there is a significant association between gender and political affiliation among a group of 200 individuals. The data is summarized in the following contingency table:

 Democrat Republicans Independent Total Male 50 40 20 110 Female 60 25 5 90 Total 110 65 25 200
Is there a significant association between gender and political affiliation at a 5% level of significance?

### Solution

Step 1 - Understand the Problem Statement
The problem statement provides us with a contingency table showing the observed frequencies of gender and political affiliation. We need to determine if there is a significant association between the two variables.
Step 2 - Set Up the Hypotheses
The null hypothesis is that there is no significant link between gender and political affiliation, while the alternative hypothesis is that there is a significant link between gender and political affiliation.
H0: There is no significant association between gender and political affiliation.
Ha: There is a significant association between gender and political affiliation.
Step 3 - Calculate the Expected Frequencies
To calculate the expected frequencies, we use the formula:
E = (row total x column total) / grand total
 Democrat Republicans Independent Total Male 60.5 35.75 13.75 110 Female 49.5 29.25 11.25 90 Total 110 65 25 200
Step 4 - Calculate the Chi-square test Statistic
Using the formula:
χ² = ∑ (O - E)² / E
The calculated Chi-square test statistic is 21.81.
Step 5 - Compare the Chi-square test Statistic with the Critical Value
Using a Chi-square test distribution table with one degree of freedom and a 5% level of significance, the critical value is 3.84. Since the calculated Chi-square test statistic (21.81) is more than the critical value (3.84), we can reject the null hypothesis and say that there is a significant link between gender and political affiliation.
Step 6 - Interpretation
In this case, we showed how to solve a Chi-square test problem. We set up the null and alternative hypotheses, figured out the expected frequencies, calculated the Chi-square test statistic, and compared it to the critical value. Based on the results, we rejected the null hypothesis and concluded that there is a significant link between gender and political affiliation.

## Tips for Approaching Chi-square Test Homework

### Tip 1 - Practice

The Chi-Square test is difficult to understand at first, but similar to the vast majority of statistical analyses, it is something that can be learned with a sufficient amount of practice. You should work on improving your understanding of the formula as well as the steps that are involved by solving a variety of problems that involve the Chi-square test. Practice makes perfect, after all. In direct proportion to the amount of Chi-square test homework that you finish, your level of self-assurance will continue to rise.

### Tip 2 - Seek Help

Do not be afraid to ask for assistance if you are having trouble with the Chi-square test homework. You could inquire for assistance from your instructor, teaching assistant, or even other students in the class. You can also access educational resources online, such as digital textbooks, interactive online lessons, and educational websites similar to this one. The act of seeking assistance can provide you with fresh concepts, fresh insights, and new directions, all of which can make it simpler for you to complete your Chi-square test homework.

### Tip 3 - Use Technology

To assist you in performing accurate calculations of Chi-square test statistics on time, a variety of software programs and other tools, from which you can make your selection, are at your disposal. Analyses using the Chi-square statistic can be performed with the assistance of computer programs such as SPSS, SAS, or Excel. With the assistance of these tools, you will be able to analyze complex data sets in a more timely and productive manner, thereby saving you both time and effort in the process.

### Tip 4 - Check Your Work

You have access to a wide range of software and hardware that can assist you in calculating Chi-square test statistics in a timely and accurate manner. This can be done both quickly and accurately. Statistical software programs such as SPSS and SAS, as well as spreadsheet programs like Excel, are all capable of running Chi-square test tests. These tools have the potential to reduce the amount of time and effort that you put in, and they also have the potential to make it simpler for you to examine large and complex data sets.

## Conclusion

The chi-square test is an important statistical tool for figuring out if there is a link between two categorical variables. Before starting your Chi-square test homework, it's important to know what the Chi-square test is and how it works. This includes knowing how to set up the hypotheses correctly, calculate the expected frequencies, and find the Chi-square test statistic. Also, comparing the Chi-square test statistic with the critical value will help you draw meaningful conclusions.
It's important to remember the tips above if you want to do your Chi-square test homework easily. You need to practice solving different kinds of Chi-square test problems, get help when you get stuck, use tools like statistical software to make the process easier, and check your work carefully. These tips will not only help you feel more confident about your Chi-square test homework, but they will also help you understand SPSS statistics better in general. By learning the Chi-square test, you'll be well on your way to becoming a good statistician.