# Univariate, Bivariate, and Multivariate Data Analysis from ROP

Research Optimus (ROP) is one of the world’s leading research agencies that offers white-label research services like univariate, bivariate, and multivariate data analysis to businesses and research firms.

We use data analysis as a methodical approach of applying statistical measures to describe, analyze, and evaluate data. Our expert researchers analyze patterns and relationships among variables.

Our core team is based out of Bangalore in India. We work with large MNCs, SMEs, and research agencies as their offshore partner for research. Our customers include several Fortune 5000 companies from across America, Europe, and Australia, who outsource their research projects to us to reap the cost advantage.

## Univariate Analysis

Univariate analysis is the easiest method of quantitative data analysis. As the name suggests, “Uni,” meaning “one,” in univariate analysis, there is only one dependable variable. It is used to test the hypothesis and draw inferences. The objective is to derive data, describe and summarize it, and analyze the pattern in it.

• Height
in cm
• 164
• 167.3
• 170
• 174
• 178
• 180
• 186

In a set of data, the univariate analysis explores each variable separately. It analyzes the range and central tendency of the values, describes the pattern of responses towards the variable.

A variable is a condition or a category that the data falls under. For instance, the analysis may be looking into the variable of “age” or “weight” of demography. It takes one variable into concern at a time, i.e., either “age” or “weight.”

In a set of data, the univariate analysis explores each variable separately. It analyzes the range and central tendency of the values, describes the pattern of responses towards the variable.

A variable is a condition or a category that the data falls under. For instance, the analysis may be looking into the variable of “age” or “weight” of demography. It takes one variable into concern at a time, i.e., either “age” or “weight.”

Age Group Frequency
26
26 - 35
36 - 45
46 - 55
56 - 65
66+

This Data can then be inputted into a graph that is easily readable, as opposed to one that shows mass of different ages,

N.B. Its is important to note that not all univariate analysis will require grouping of categories e. g. location

The univariate method is commonly used in analyzing data for cases where there is a single variable for each element in a data sample or when there are multiple variables on each data set.

The patterns that are identified from the univariate analysis can be described in the following ways:

• #### Central Tendency

(Mean, Mode and Median)

• #### Dispersion

(Range, Variance)

• #### Quartiles

(Interquartile Range)

• #### Standard deviation

Univariate data can be described through graphs:

###### Bar Charts

A bar graph is very useful while making comparisons between categories of data or different groups of data. It helps to track changes over time.

###### Pie Charts

A pie chart gives an overview of the group of data broken into smaller pieces that reflects in each slice of the pie. The whole pie represents 100 percent, and the slices represent the relative size of that group or category.

###### Histograms

Similar to bar charts, histograms display the same categorical variables against the category of data. The height of the bars signifies the number of components in that category. The bin indicates the number of data points in a range.

###### Frequency Distribution Tables

As the name suggests, the frequency distribution reflects the frequency of an occurrence in the data.

###### Frequency Polygons

Akin to the histogram, a frequency polygon is used to compare data sets or reflects the cumulative frequency distribution.

#### Case Study

Sports organizations from the Southeastern United States wanted to research their fan satisfaction, document satisfied customers, and retain them. Univariate analysis of variance (ANOVA) was done where usage signified the group variable and satisfaction level, and the six components represented the dependent variable. It helped to determine if satisfaction differs across various levels of usage. It also helped the organization understand areas of high and low satisfaction among their fans.

## Bivariate Analysis

In Bivariate Analysis, there are two variables wherein the analysis is related to cause and the relationship between the two variables. For example, points scored by the winning team in the Super Bowl from 1960 to 2010.

Multivariate analytical techniques represent a variety of mathematical models used to measure and quantify outcomes, taking into account the important factors that can influence this relationship. There are several multivariate analytical techniques that one can use to examine the relationship among variables. The most popular is multiple regression analysis, which helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. Other techniques include factor analysis, path analysis, and multiple analyses of variance (MANOVA).

Types of Bivariate Analysis

01
###### Scatter Plots

It shows the measure of the influence of one variable on the other.

02
###### Regression Analysis

It is used to analyze how the data is related to each other.

03
###### Correlation Coefficients

It analyzes if the variables are related. “0” suggests that the variables are not related to each other, and
“1” reveals a positive or a negative correlation.

#### Case Study

An Indian FMCG company took up the bivariate test to examine the relationship between sales and advertising within a period of 2014-2015 to 2017-2018. They employed various tools like regression, mean, standard deviation, correlation, coefficient of variation, kurtosis, and more to get an insight into the data. The inference was the dependency of the advertising expenses of the period on the sales of the previous year was more than the dependency of the sales revenue on the advertising expenses.

## Multivariate Analysis

Multivariate data involves three or more variables. For example, when a web developer wants to examine the click and conversion rates of four different web pages among men and women, the relationship between the variables can be measured through multivariate variables. In a pharmaceutical experiment on drugs, multivariate analysis is used to analyze the multiple responses of a patient on a drug.

Any company that wants to succeed in this global marketplace will focus on obtaining and analyzing market research surveys using the statistical methods of bivariate and multivariate analysis to gain a competitive advantage over its peers.

Few ways to perform the analysis are:

01
###### Regression Analysis

It is used to find out the pattern in a set of data.

02
###### MANOVA

MANOVA is ANOVA for the various dependent variables. It is done to check if the response variable changes when the independent variable is manipulated.

02
###### Factor Analysis

It is a way to shrink large sets of data into manageable ones. It brings out the hidden patterns and how they overlap and traits in multiple patterns.

02
###### Path Analysis

It is used to examine the causal models by determining the relationships between the dependable variable and multiple independent variables.

#### Case Study

A premium hotel and resort from Florida employed a multivariate study to analyze the best combination of the “call to action” button and form title on their website. The objective was to invite more visitors to their website to check their rates and room availability. They monitored the clicks on the CTA button and came up with 12 combinations to compare. The final combination showed an improved conversion rate up to 9.1%.