Bivariate analysis allows us to study the relationship between two variables. This is very useful in real life. It helps to find out if there is an association between the variables and, if so, what is the strength of the association.

One of the variables will be dependent and the other independent. The variables are named X and Y. Changes are analyzed between the two variables to understand to what extent the change has occurred.

Bivariate analysis helps test the hypothesis of chance and association. Helps predict the value of a dependent variable based on changes in an independent variable.

## What does Bivariate Analysis mean?

Bivariate analysis means analysis of bivariate data. This is a unique statistical analysis used to find out the relationship between two sets of values.

The results obtained from the bivariate analysis are stored in a data table that has two columns. Bivariate analysis should not be confused with two-sample data analysis, in which the variables x and y are not directly related.

Some examples are the length and width of a fossil, the sodium and potassium content of volcanic glass, or the organic matter content throughout a sediment core. When the two variables are measured on the same object, x is often identified as the independent variable, while y is the dependent variable. If both variables are generated in an experiment, the variable manipulated by the experimenter is described as the independent variable. In some cases, both variables are not manipulated and are therefore independent.

Bivariate statistics methods help describe the strength of the relationship between two variables, either by a single parameter, such as Pearson’s correlation coefficient for linear relationships, or by an equation obtained by regression analysis. The equation describing the relationship between x and y can be used to predict the response of y from arbitrary x’s within the range of values of the original data used for the regression. This is especially important if one of the two parameters is difficult to measure. In this case, the relationship between the two variables is first determined by regression analysis on a small training data set. The regression equation is then used to calculate this parameter from the first variable.

Bivariate analysis is not the same as analysis of data from two samples. With two-sample data analysis (such as a two-sample z-test in Excel), the X and Y are not directly related. You can also have a different number of data values in each sample; with bivariate analysis, there is a Y value for each X. Let’s say you have a caloric intake of 3,000 calories a day and weigh 300 pounds. You would write it with the variable x followed by the variable y: (3000,300).

## How a Bivariate Analysis is performed

The following explains how the bivariate analysis is carried out.

Scatter plots – This gives an idea of the patterns that can be formed using the two variables

Regression Analysis – Uses a wide range of tools to determine how the data might be related. The position can follow an exponential curve. Regression analysis provides the equation of a line or curve. It also helps to find the correlation coefficient.

Correlation coefficients – The coefficient allows to know if the data in question are related. When the correlation coefficient is zero, it means that the variables are not related. If the correlation coefficient is a positive or negative 1, it means that the variables are perfectly correlated.

## How many types of Bivariate Correlations are there?

The type of bivariate analysis depends on the type of attributes and variables that are used to analyze the data. Variables can be ordinal, categorical, or numeric. The independent variable is categorical, like the mark of a pen. In this case, probit regression or logit regression is used. If the dependent and independent variables are ordinal, meaning they have a rank or position, the rank correlation coefficient is measured.

If the dependent attribute is ordinal, the ordered probit or ordered logit is used. The dependent attribute may be internal or a relationship such as temperature scale. This is where regression is measured. Below we mention the types of bivariate data correlation.

#### numeric

In this type of variable, both variables of the bivariate data that include the dependent and independent variables have a numerical value.

#### Categorical

When the two variables of bivariate data are in static form, the data is interpreted and statements and predictions are made about it. During the investigation, the analysis will help determine the cause and impact to conclude that the given variable is categorical.

#### numerical and categorical

It is when one of the variables is numerical and the other is categorical.

## Bivariate Data

Data in statistics is sometimes classified according to the number of variables in a particular study. For example, “height” can be one variable and “weight” can be another. Depending on the number of variables being analyzed, the data can be univariate or bivariate.

When a study is conducted that looks at a single variable, that study includes univariate data. For example, a group of college students can be studied to find out their average score on a test, or a group of diabetic patients can be studied to find out their weight.

For example, if you study a group of college students to find out their average test score and their age, you need to find two pieces of the puzzle (the score and the age). Or if you want to find out the weight and height of diabetic patients, then you also have bivariate data. Bivariate data can also be two sets of items that depend on each other. For example:

Ice cream sales compared to the temperature 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 quite useful to be able to predict when a natural event may occur. One of the tools of the statistician is the analysis of bivariate data. Sometimes something as simple as plotting one variable against another on a coordinate plane can give us a clear idea of what the data is trying to tell us.

## Types of Bivariate Analysis

#### descriptive analysis

In descriptive analysis, bivariate analysis can be applied to almost all data visualizations. The types of visualizations such as bar charts, line charts, column charts, etc. can still be used for bivariate analysis.

Using a scatter plot, we can see the pattern of the relationship between the 2 variables. The relationships that are formed can be linear, exponential, seasonal, etc. depending on the data conditions.

Do not forget that the scatter plot is only a tool to detect relationship patterns, not to draw conclusions about the relationship pattern between 2 variables.

#### inferential analysis

Using inferential analysis, valid conclusions can be drawn by testing 2 variables.

Speaking of inferential analysis, there are many types of statistical tests that can be done with 2 variables. Here is a small list of types of test analysis you can do:

###### McNemar’s test

The McNemar test is a bivariate test used to test before and after treatment (Pre-Test and Post-Test) where each individual is used as their own controller. This test is performed for the measurement of nominal and ordinal data. This test is used to test the effectiveness of a particular treatment under the sample conditions. For example, this test is used to determine the effect of moving a person from rural to urban areas on political preference.

###### sign test

The sign test is used to determine if there is a difference between ordinal data obtained from the same sample and pairs. The thing to remember about the sign test is that this test is only able to determine if there is a difference, not the size of the difference. This test is performed by giving a positive or negative sign to the difference between the pairs of data. Sign tests can be used to identify a person’s bias toward two product brands. The data scale used in this test is ordinal

###### Wilcoxon matched pairs test

The Wilcoxon test is a test that is performed to determine whether or not there is a relationship between two variables. The data scale used in this test is ordinal.

###### Paired t test

The paired t-test is a two-variable test that is performed to determine whether or not there is a significant difference in the mean. An example of the use of a paired t-test is to test whether there is a significant difference in the mean between the math and art scores of students in grade A.

###### Fisher’s exact probability test

Fisher’s exact probability test is a test that is performed to determine the significance of a comparative hypothesis in two small samples. independent. This test is used when the data conditions are nominal and ordinal. In the calculations, the data from this test is grouped into 2 independent groups. For example, men and women, and then poor and non-poor. Subsequently, these calculations will be grouped in a 2×2 contingency table.

###### Two-Sample Chi-Square Test

The two-sample Chi-square test is used to determine if there is a relationship between the 2 variables or not. In the two-sample Chi-square test, the data scale used was the nominal scale.

###### Median test

This test is used to test the comparative hypothesis of two independent samples. In this test, the data scales used are nominal and ordinal. This test is based on the median of the random sample. The data scales used in this test are nominal and ordinal.

###### Mann–Whitney U test

The Mann-Whitney U test was used to determine the significance of the differences between the two populations. In this test, the data scale used is ordinal. An example of the Mann-Whitney U test is that of a teacher who wants to find out if the students in her class have a talent for mathematics or if she needs the help of a tutor.

###### Kolmogorov-Smirnov test

The Kolmogorov Smirnov test is a test that is performed to determine if two variables have the same distribution or not. This test is commonly used to test whether the two variables used come from the same distribution before performing further analysis. The data scale used in this test is interval and ratio.

###### Wald–Waldovitz test

The Wald-Waldovitz test is a test that is carried out to check whether the two variables used come from the same population or not. In this test, at least the data used has an ordinal scale.

###### Independent t test

The independent t-test is a test that is carried out to find out if two variables from different groups have the same mean or not. In this test, the data scales used are intervals and ratios. For example, a researcher wants to test whether the mean final exam grade of a favorite school is significantly different from that of a disfavored school.

###### Correlation analysis

Correlation analysis is an analysis used to determine the relationship between two variables. With correlation analysis, we can find out if 2 variables have a positive or negative relationship. It is important to remember that correlation is simply an analysis that explains how strong the relationship is between 2 variables. Correlation analysis cannot be used as a basis for concluding a causal relationship between 2 variables. An example of use of correlation analysis is the relationship between the height and weight of students.

###### Simple linear regression analysis

Simple linear regression analysis is an analysis used to determine the effect of one variable on other variables. Unlike correlation analysis, simple linear regression analysis attempts to explain the causal relationship (causality) between the independent variables and the dependent variable. With this analysis, we can conclude to what extent a variable affects other variables.