Bivariate analysis : A statistical method to determine the relationship between two continuous variables

The first step in performing an extensive research is to inspect the relationship between the outcome variable, i.e. the element of interest and the potential explanatory variables. However, the number of variable varies and so is the statistical approach used to examine the relationship between the variables.

Depending on the number of variables, data can be classified into univariate, bivariate and multivariate data. When a study is conducted on a single variable, it involves univariate data. For instance, a study is performed on a set of college students to find out their average CAT scores.

Whereas bivariate analysis is when a study is performed on two variables. For e.g., if you wish to study the average CAT scores as well as the age of a group of college students, you will have two pieces of information to determine; CAT score and age.

Multivariate analysis is similar to bivariate, but has more than one dependent variable.

Although all three analysis are of equal importance, since most of the researches involve two variables, bivariate analysis is significantly used in various domains.

This type of analysis delves into the concept of determining the relationship between two variables, the existence of an association, the strength of the association, or differences between two variables and the importance of those differences. Bivariate data need not consist of only independent variables but also could be two sets of factors that are dependent on each other. For e.g., juice sales compared to the temperature of a particular day.

Steps involved in performing bivariate analysis

Bivariate analysis essentially includes four simple steps.

1. Defining the nature of the relationship - This step involves finding a relationship between two variables. For example, if you are examining the relationship between semester exam scores and class size, then the data should report, “ the relationship between the class size and the semester exam scores.”

2. Identifying the type & direction of the relationship - To figure out the type and direction of relationship, determine which type of measurement: nominal, ordinal, and ratio will be used in the data.

3. Determining the statistical significance of the relationship - Statistical significance is utilised to identify if the results are significant to make a connection.

4. Examining the strength of relationship - To inspect whether the bivariate correlation is significant, select a standard formula depending upon the kind of data employed.

Types of bivariate analysis

Bivariate analysis is of three types : (1) numerical & numerical (2) categorical & categorical and (3) numerical & categorical.

1. Numerical & numerical - This category contains scatter plot and linear correlation.

• Scatter plot - A scatter plot, drawn prior to working out a linear correlation or fitting a regression line, is a visual representation of the relationship between two numerical variables. The resulting pattern indicates the strength of the relationship between two variables and the type of variable (linear or nonlinear).

• Linear correlation - This approach assesses the strength of a linear relationship between two variables (numerical). If there isn’t any correlation between two variables, then there is no likelihood for the values of one quantity to decrease or increase with the values of the second quantity.

1. Categorical & categorical - This classification consists of Chi-square test, stacked column chart and combination chart.

• Chi-square test - The chi-square test is based on the difference between the expected frequencies and the observed frequencies. This test is used to examine the association between categorical variables.

• Combination chart - It uses two or more types of charts to highlight that the chart consists of various kinds of information.

• Stacked column chart - Stacked Column chart is a graph that is used to visualize the relationship between two categorical variables. The percentage contribution by each classification from one variable to a total across categories of the second variable.

1. Numerical & categorical - Numerical & categorical division includes line chart with error bars, Z & t-test, and ANOVA test.

• Line chart with error bars - It is a method used to summarise how informations are related to each other and how they differ depending on one another. A line chart with error bar presents information as a series of data points connected via straight line segments.

• Z & t-test - Both the tests evaluates if the average of two groups statistically varies from each other. These analyses are appropriate for correlating the average of a numerical variables for two classification of a categorical variable.

• ANOVA - The ANOVA test evaluates whether the average of two or more groups statistically vary from each other. This method is apt for comparing the average of a numerical variables for more than two divisions of a categorical variable.

Bivariate analysis is one tool in every statistician’s toolbox. It can be used testing simple hypotheses of association. In addition to applications in the academic, bivariate analysis has many practical applications in the real world. That is, it can be used to determine to what extent one can predict a value for one variable if the value of the other variable is known.

Category : Data Collection