Statistical Analysis with Categorical Data

Video Lesson on Statistical Analysis with Categorical Data

Statistical Analysis with Categorical Data

Learn why percentages are so important when analyzing categorical data in this video lesson. Watch as the data is turned into a data table and a visual bar graph as ways to analyze the data.

What Is Categorical Data?

When you take a survey or fill out application forms at various places, you come across categorical data. So, what exactly is categorical data? It is the kind of information that can be categorized. For example, your race, gender, and occupation are all different types of categorical data. Your answer for race can be categorized into groups such as Asian, Caucasian, etc. For occupation, your answer can be categorized into groups such as teacher, student, artist, etc.

Data as Percentage

With this type of data, part of the analysis process involves changing your data into percentages. Let's work through an example scenario to see how the analysis process works. Our scenario is that we have just surveyed a group of 100 people about their natural hair color. After going through all the data, we found that 30 people had brown hair, 20 people had blonde hair, 40 people had black hair, and 10 people had red hair. Notice how we were able to group the people in our survey into just a few groups. For each person that answered a certain way, we added a 1 for that group. Now that we have this information, we need to analyze it and present it in such a way that makes it easy to understand and use. Having just our numbers doesn't do much for us. But, if we change the numbers to percentages, we can gain a better understanding of what's going on.

To change our numbers to percentages, we take the number from each group and divide it by the total number of data, and then we convert this decimal into a percent by multiplying by 100. For our brown hair, we divide 30 by 100 to get 0.3. 0.3 multiplied by 100 is 30%. For blonde hair, we get 20%. For black hair, we have 40%, and for red hair we have 10%.

Data Table

Now that we have our percentages, we need a way to present it to others for it to make more sense. One way we can present it is with a data table, which is a way to organize the information into rows and columns. We will present it with a title row and our information in two columns. The title row will state what each column is for. The first column is for 'Hair Color,' and the second column is for the 'Result.' We write our groups in the column for Hair Color, and we write our respective percentages in the next column.

Hair Color Result

Brown 30%

Blonde 20%

Black 40%

Red 10%

We can glance at our finished table and quickly gain the information we need. We can look at it and easily see that 40% of our population has black hair. We can use this information for business purposes if we wanted to market hair accessories for people. If we know that the majority of our population has black hair, then we will produce more accessories that match with black hair.

Bar Graph

Another way we can present our information, which will make it easy to analyze, is with the use of a bar graph, a graph that shows our data using bars. The way we create a bar graph is by writing our various groups on the x-axis, and then we draw bars of various heights to correspond with the number of people in each group. Our first group we write down is Brown, and our bar has a height of 30 because that's how many people are in this group. We do likewise with the rest of the groups. Blonde has a bar height of 20, Black has a bar height of 40, and Red has a bar height of 10. We can easily look at this bar graph below and see which group is more popular and which group is the minority.

Example of a bar graph with hair color data

In my bar graph, I decided to keep the numbers instead of using percentages. Why? Because in a bar graph, it is easy to see which bar is taller than another. In table form, though, it is easier to understand the information if it is presented using percentages. You could also use the percentages for your bar heights in your bar graph. You can use whichever one you feel will convey the information in the best manner. You can graph both to compare, and then choose the one that is easiest to read.

Lesson Summary

In review, categorical data is data that can be categorized into groups. Examples include gender, occupation, and race. The two ways to analyze this information is with the use of either a data table, information presented in rows and columns, or a bar graph, a graph with bars of various heights. For a data table, while you can report your data using the numbers for each group, most times it makes more sense to report the groups using their percentages. For the bar graph, you can graph it using either the percentages or the numbers for each group. You choose the one that makes more sense for your situation. Graph both to see which one is easier to read and understand.

Learning Outcomes

Complete this lesson so that you can:

  • Provide examples of categorical data
  • Analyze categorical data using both a data table and a bar graph
  • Know when to use percentages and when to use numbers when evaluating categorical data
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