Bivariate Analysis

Bivariate Analysis Definition

Bivariate data helps you in studying two variables. For example, you are studying a group of college students. To find out their average SAT score and their age, you have two pieces of the puzzle to find (SAT score and age). Both SAT and age are variables. Now suppose you need to find a relation between the weights and heights of college students, then also you have bivariate data. Bi means two, variate means variables. Analysis of the changes in the two variables is called bivariate analysis. Out of the two variables, one is dependent and the other is independent. 

Data in statistics are sometimes classified according to how many variables are in a particular study. For example, “height” and “weight” might be two different variables. Depending on the number of variables being looked at, the data might be univariate, or it might be bivariate.

When you conduct a study that looks at a single variable, that study involves univariate data. Bivariate data could also be two sets of items that are dependent on each other. For example:

  • Sale of Ice cream compared to the temperature of that day.

  • Traffic accidents along with the weather on a particular day.

Bivariate data has many practical uses in real life. For example, it is pretty helpful to be able to predict when a natural event might occur. One tool in the statistician’s toolbox is bivariate data analysis. Sometimes, something as simple as plotting one variable against another on a Cartesian plane can give you a clear picture of what the data is trying to tell you. For example, the scatterplot below shows the relationship between the time between eruptions at Old Faithful vs. the duration of the eruption.

What is Bivariate Analysis?

Bivariate analysis is an analysis of two variables to determine the relationships between them. They are often reported in quality of life research. It is one of the simplest forms of quantitative (statistical) analysis. It involves the analysis of two variables (it is often denoted as X, Y), for the purpose of determining the empirical relationship between them.

Bivariate analysis is extremely helpful in testing simple hypotheses of association. It is very helpful in determining to what extent it becomes easier to know and predicts a value for one variable (possibly a dependent variable) if the value of the other variable (possibly the independent variable) is known (see also correlation and simple linear regression). There can be a contrast between bivariate analysis and univariate analysis in which only one variable is analysed. Both univariate analysis and bivariate analysis can be descriptive or inferential. We can say, it is the analysis of the relationship between the two variables. Bivariate analysis is a simple (two-variable) and special case of multivariate analysis (where  simultaneously multiple relations between multiple variables are examined)

Bivariate analysis can be defined as the analysis of bivariate data. It is one of the simplest forms of statistical analysis, which is used to find out if there is a relationship between two sets of values. Usually, it involves the variables X and Y.

  • The univariate analysis involves an analysis of one (“uni”) variable.

  • The bivariate analysis involves the analysis of exactly two variables.

  • The multivariate analysis involves the analysis of more than two variables.

The results we get from the bivariate analysis can be stored in a two-column data table. For example, you might be eager to find out the relationship between the caloric intake and the weight (of course, the two are related very strongly) Caloric intake will be your independent variable, X, and weight will be your dependent variable, Y.


bivariate analysis

Bivariate analysis and two sample data analysis are not the same. With two sample data analysis (like a two-sample is a test in Excel), X and Y are not directly related and there will also be a different number of data values in each sample. With bivariate analysis, there is a Y value for each X. For example, suppose you had a caloric intake of 3,000 calories per day and a weight of 300lbs. You will have to write that with the x-variable followed by the y-variable: (3000,300).

Here are Two sample data analysis

Sample 1: 100,45,88,99

Sample 2: 44,33,101

Bivariate analysis

(X,Y)=(100,56),(23,84),(398,63),(56,42)


Types of Bivariate Analysis

Some of the common types of bivariate analysis include:

1. Scatter Plots: Scatterplot provides you with a visual idea of the pattern that your variables follow.

Graph-A simple scatterplot

2. Regression Analysis: Regression analysis is a catch-all term for a wide variety of tools that can be used to determine how your data points might be related. The points in the image above seem like they could follow an exponential curve (as opposed to a straight line). Regression analysis not only provides you an equation for that curve or line but also gives you the correlation coefficient.

3. Correlation Coefficients: Calculation of values for correlation coefficients are performed using a computer, although here, you can find the steps to find the correlation coefficient by hand. This coefficient acknowledges you if the variables are related. Basically, by ‘0’ means they aren't correlated (i.e. related in some way), while a ‘1’ (either positive or negative) means that the variables are perfectly correlated (i.e. they are perfectly in sync with each other).

FAQ (Frequently Asked Questions)

Question 1: What is the Importance of Doing Uni-variable Analysis of Variables before doing Multivariate Analysis Given the Fact that Outcomes of Multivariate Analyses are More Accurate?

Solution: There is no need to do both. In fact, for a given research question, only one of the two is appropriate. 

Analyzing the data in various different ways is quite understandable, especially when doing “hypothesis-generating” research without having a clear hypothesis in mind. However, there lies a risk of p-hacking: if you analyze the data in 10 different ways.

A multivariable analysis is never more accurate than a simple t-test. In fact, the more simple the test would be more powerful. The main reason multivariable analysis is done is that you get to identify causal effects.