Tag Archives: chi-square

How to Analyze Frequency Data

How do you analyze frequency data? How will you know that you have obtained frequency data in your research? What statistical test is appropriate for such data usually obtained from surveys?

This article explains answers to these questions. Read on to find out.

Earlier, I discussed the appropriate statistical tools to use based on the type of data a research project gathers. Analyzing the data itself is quite a challenge to students, especially if they do statistical analysis for the first time.

Now, I would like to focus on a single statistical test, i.e., Chi-square. This discussion is not about the computation per se but on the appropriateness of the test for certain questions pursued in a research investigation. Typically, Chi-square is used in analyzing survey data.

When is a Chi-square test employed? What type of data is appropriate for its use? The straightforward answer is that Chi-square is used when dealing with frequency data.

By the way, what is frequency data? I explain that here with an example.

Frequency Data Example

Frequency data is that data usually obtained from categorical or nominal variables (see the different types of variables and how these are measured). It is best used when you have two nominal variables in your study. The two variables with their respective categories can be arranged in column-wise and row-wise manner. Let me illustrate this arrangement by looking into the way two nominal variables are arranged.

A Hypothetical Survey

An electronics merchant might want to know which cellphone brand is popular among male and female students in a university so that he will be able to know the proportion of brands he should offer in the store. He also wants to know whether gender has anything to do with cellphone preference. He commissioned a business researcher to conduct a survey on cellphone preference.

The research question for this study is:

“Is there an association between gender and cellphone preference?”

The two variables in this study, therefore, are 1) the cellphone brand, and 2) gender. For sure, we know that gender has two categories namely, male and female. As for the cellphone brand, that will entirely depend on the businessman who commissioned the study. In his area, the three dominant brands used by students may be used, say, Nokia, Samsung, and Apple’s iPhone.

Organizing the Data Obtained in the Survey

To organize the data obtained in the aforementioned survey, a table may thus be created to see how gender and cellphone preference are related. A hypothetical frequency table based on a study of cellphone preference in a university is given below:

Table 1. Cellphone preference among students in a university by gender.
Brand of Cellphone Preferred









Given the distribution of cellphone preference among students in Table 1, the businessman might be inclined to say that females prefer Nokia over the other brands. But what he is looking into is just data organized in a table. No statistical test has been applied yet.

As both of the variables are nominal or can be classified into categories, the appropriate test to find out if indeed there is an association between gender and cellphone preference is Chi-square.

The formula for Chi-square is:


How should the data be input to the Chi-square formula? What is observed data and what is expected? Details on how to do it is given in another article I wrote in another site using a similar example. I provide a link below:

How to compute for the chi-square value and interpret the results

You may then apply what you have learned in that article to find out whether indeed there is an association between gender and cellphone preference in the example survey given above.

©2015 April 4 P. A. Regoniel