3 Bivariate data

Bivariate data refers to an instance in which two separate variables are examined and compared. For example, a performance manager may be interested to know how well employees perform their work, that is, to measure the efficiency of the employees. In this example, the performance manager may examine two variables: the number of tasks they complete and the quality of the tasks.

Bivariate data is collected to explore the relationship between two variables and then use this relationship to inform future decisions. One of the main aims of the researcher is to find out whether changes in one variable may be caused by changes in another variable. This type of research involves two basic types of variables: independent variables and dependent variables.

Independent variables: an independent variable is one that stands alone and is not changed by the other variable you are trying to measure. The researcher changes the independent variable to see the effect it will have on the dependent variable.

Dependent variables: a dependent variable is the one that changes because of independent variable manipulation. It is the outcome you are interested in measuring, and it ‘depends’ on your independent variable. In statistics, dependent variables are also called response variables (as they respond to a change in another variable).

For example, say a researcher is interested to know whether mature students’ performance in a maths class changes based on the time of the class. To answer this question, the researcher measures mature students’ performance in a morning class and an evening class. The study finds that mature students perform better in the evening class than in the morning class.

What are the independent and dependent variables in the example above? The independent variable is the time of the class, and the dependent variable is mature students’ performance in maths, as it might change in relation to the independent variable.

In the next activity, you will expand your knowledge of bivariate data.

Activity 8 Bivariate data

Timing: Allow approximately 15 minutes to complete this activity

Watch the following video and make notes on bivariate data in the free response box below.

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Transcript: Video 4

NARRATOR

Hello. In this video, we will discuss what we mean by bivariate data. Well, just by the word bivariate data, we know that we are dealing with some kind of data. But what kind of data is the question. To better understand the word bivariate, we need to break it down in two. The prefix bi means two or twice, and variant means a quantity that can take the value of any member of a particular set, a variable.

So bivariate data are data that have two variables with different values. With bivariate data, we are comparing two different sets of variables. The one variable is the dependent variable, and the other variable is the independent variable. Let's look at an example.

As you can see, this table has three columns. The columns are labeled as days, temperature, and the number of Pepsi cans sold. So this table is showing the data relating to the number of Pepsi cans sold in the different days of a week. The two sets of variant data we have here are the temperature, and the number of Pepsi cans sold.

The temperature on this table is the independent variable, and the number of Pepsi cans is the dependent variable, because the number of Pepsi cans sold depends on the increase or decrease in temperature. As you can see in this table, on the day the temperature was 12 degrees celcius, the number of Pepsi cans sold was 12. When the temperature increased from 12 to 18 degrees celcius, the sale of Pepsi cans also increased.

Now, let's have a look at how these two different sets of data can be compared. We can plot this data into a graph, and the scatter plot is one of the best graphs for representing bivariate data. On this scatter plot here, we have the x-axis, which is the horizontal axis, representing the temperature, which is our independent variable. And on the y-axis, which is the vertical axis, we have the dependent variable, which is the number of Pepsi cans sold.

So from the graph, you can see that with the increase in temperature, we also have an increase in the number of Pepsi cans sold. In other words, this graph shows a positive correlation between the two variables because with the increase in temperature, the sale of Pepsi cans has also increased.

There can be cases where there is no positive correlation, as with the example here, where the increase in temperature has not seen an increase in the number of packets of biscuits sold. This is what we call a negative correlation.

In this video, you learned what bivariate data are, and that they are best graphed in a scatter plot to show either a positive or negative correlation.

End transcript: Video 4

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Bivariate data can be visualised using contingency tables and scatter diagrams. In the next section you will learn about contingency tables.