Alchemer is a powerful online survey and data collection platform that allows you to perform advanced analysis, such as the Chi-Square test. Being able to investigate whether the data from two questions are correlated helps market researchers better understand context in their findings.
What is the Chi-Square Test?
The Chi-Square test is a statistical procedure used by researchers to examine the differences between categorical variables in the same population.
For example, imagine that a research group is interested in whether or not education level and marital status are related for all people in the U.S.
After collecting a simple random sample of 500 U.S. citizens, and administering a survey to this sample, the researchers could first manually observe the frequency distribution of marital status and education category within their sample.
The researchers could then perform a Chi-Square test to validate or provide additional context for these observed frequencies.
Chi-Square calculation formula is as follows:
When is the Chi-Square Test Used in Market Research?
Market researchers use the Chi-Square test when they find themselves in one of the following situations:
- They need to estimate how closely an observed distribution matches an expected distribution. This is referred to as a “goodness-of-fit” test.
- They need to estimate whether two random variables are independent.
When to Use the Chi-Square Test on Survey Results
The Chi-Square test is most useful when analyzing cross tabulations of survey response data.
Because cross tabulations reveal the frequency and percentage of responses to questions by various segments or categories of respondents (gender, profession, education level, etc.), the Chi-Square test informs researchers about whether or not there is a statistically significant difference between how the various segments or categories answered a given question.
Important things to note when considering using the Chi-Square test
First, Chi-Square only tests whether two individual variables are independent in a binary, “yes” or “no” format.
Chi-Square testing does not provide any insight into the degree of difference between the respondent categories, meaning that researchers are not able to tell which statistic (result of the Chi-Square test) is greater or less than the other.
Second, Chi-Square requires researchers to use numerical values, also known as frequency counts, instead of using percentages or ratios. This can limit the flexibility that researchers have in terms of the processes that they use.
What Software is Needed to Run a Chi-Square Test?
Chi-Square tests can be run in either Microsoft Excel or Google Sheets, however, there are more intuitive statistical software packages available to researchers, such as SPSS, Stata, and SAS.
Check out this article on Exporting Your Survey Data with SPSS to learn how to get started today!
Run Chi-Square tests without leaving Alchemer
You don’t need to export your data to a stats package to see whether two questions are related. Build a crosstab report in Alchemer Survey, and the Pearson Chi-Square, degrees of freedom and p-value show up automatically. You can set your significance level to 0.10, 0.05 or 0.01. For small samples, you can switch to Fisher’s Exact Test. That way a hunch about your audience becomes a finding you can share with confidence.
FAQ
What’s the difference between a goodness-of-fit test and a test of independence?
A goodness-of-fit test compares one variable against an expected distribution. For example, it can check whether your respondents’ age mix matches census data. A test of independence uses two variables from the same sample to check whether they’re related, such as education level and preferred contact channel. Most survey analysis uses the test of independence, since it runs on a crosstab.
How do I read a Chi-Square result?
Focus on the p-value. If the p-value falls below your significance level (usually 0.05), the two variables are likely related. If the p-value sits above that threshold, you don’t have enough evidence to say they’re connected. A higher Chi-Square statistic generally points to a bigger gap between what you observed and what you’d expect if the variables were independent.
Does a significant result mean one variable causes the other?
No. Chi-Square tells you two variables move together, not why. A link between location and satisfaction scores might come from staffing, foot traffic or something you haven’t measured yet. Treat a significant result as a question worth digging into, not a final answer.
Does Chi-Square tell me how strong a relationship is?
No. Chi-Square only tells you whether a relationship exists. To measure strength, researchers often follow up with Cramér’s V, which runs from 0 (no association) to 1 (a perfect association).
How big does my sample need to be?
A common rule of thumb is an expected count of at least five in each cell of your crosstab. Very small samples or lots of answer options can push cells below that mark. You have two fixes: group similar answer options together, or use Fisher’s Exact Test, which handles small samples more reliably.
Which survey questions work best with Chi-Square?
Single-select categorical questions work best. These include radio buttons, dropdowns and demographic questions like role or region. Multi-select checkbox questions need extra care, because Chi-Square assumes each respondent lands in exactly one cell.
Can I use percentages instead of counts?
No. Chi-Square needs raw frequency counts. Percentages hide sample size, and sample size drives the result. A 60/40 split from 50 people and a 60/40 split from 5,000 people lead to very different conclusions.
Can I run a Chi-Square test in Alchemer?
Yes. Every crosstab report in Alchemer Survey includes Chi-Square results automatically, along with Fisher’s Exact Test and column proportion testing for deeper analysis.