Univariate analysis
Encyclopedia
Univariate analysis is the simplest form of quantitative (statistical) analysis
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

. The analysis is carried out with the description of a single variable and its attributes of the applicable unit of analysis
Unit of analysis
The unit of analysis is the major entity that is being analyzed in the study. It is the 'what' or 'whom' that is being studied. In social science research, typical units of analysis include individuals , groups, social organizations and social artifacts.The literature of International Relations...

. For example, if the variable age was the subject of the analysis, the researcher would look at how many subjects fall into a given age attribute categories.

Univariate analysis contrasts with bivariate analysis
Bivariate analysis
Bivariate analysis is one of the simplest forms of the quantitative analysis. It involves the analysis of two variables , for the purpose of determining the empirical relationship between them...

 – the analysis of two variables simultaneously – or multivariate analysis – the analysis of multiple variables simultaneously. Univariate analysis is also used primarily for descriptive purposes, while bivariate and multivariate analysis are geared more towards explanatory purposes. Univariate analysis is commonly used in the first stages of research, in analyzing the data at hand, before being supplemented by more advance, inferential bivariate or multivariate analysis
Multivariate analysis
Multivariate analysis is based on the statistical principle of multivariate statistics, which involves observation and analysis of more than one statistical variable at a time...

.

A basic way of presenting univariate data is to create a frequency distribution
Frequency distribution
In statistics, a frequency distribution is an arrangement of the values that one or more variables take in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval, and in this way, the table summarizes the distribution of...

 of the individual cases, which involves presenting the number of attributes of the variable studied for each case observed in the sample
Sample (statistics)
In statistics, a sample is a subset of a population. Typically, the population is very large, making a census or a complete enumeration of all the values in the population impractical or impossible. The sample represents a subset of manageable size...

. This can be done in a table format, with a bar chart
Bar chart
A bar chart or bar graph is a chart with rectangular bars with lengths proportional to the values that they represent. The bars can be plotted vertically or horizontally....

 or a similar form of graphical representation. A sample distribution table and a bar chart for an univariate analysis are presented below (the table shows the frequency distribution for a variable "age" and the bar chart, for a variable "incarceration
Incarceration
Incarceration is the detention of a person in prison, typically as punishment for a crime .People are most commonly incarcerated upon suspicion or conviction of committing a crime, and different jurisdictions have differing laws governing the function of incarceration within a larger system of...

 rate"): - this is an edit of the previous as the chart is an example of bivariate, not univariate analysis - as stated above, bivariate analysis is that of two variables and there are 2 variables compared in this graph: incarceration and country.
Age range Frequency Percent
under 18 10 5
18–29 50 25
29–45 40 20
45–65 40 20
over 65 60 30
Valid cases: 200
Missing cases: 0


There are several tools used in univariate analysis; their applicability depends on whether we are dealing with a continuous variable (such as age) or a discrete variable (such as gender).

In addition to frequency distribution, univariate analysis commonly involves reporting measures of central tendency
Central tendency
In statistics, the term central tendency relates to the way in which quantitative data is clustered around some value. A measure of central tendency is a way of specifying - central value...

 (location). This involves describing the way in which quantitative data tend to cluster around some value. In the univariate analysis, the measure of central tendency is an average
Average
In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....

 of a set of measurements, the word average being variously construed as (arithmetic) mean
Mean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....

, median
Median
In probability theory and statistics, a median is described as the numerical value separating the higher half of a sample, a population, or a probability distribution, from the lower half. The median of a finite list of numbers can be found by arranging all the observations from lowest value to...

, mode
Mode (statistics)
In statistics, the mode is the value that occurs most frequently in a data set or a probability distribution. In some fields, notably education, sample data are often called scores, and the sample mode is known as the modal score....

 or other measure of location, depending on the context.

Another set of measures used in the univariate analysis, complementing the study of the central tendency, involves studying the statistical dispersion
Statistical dispersion
In statistics, statistical dispersion is variability or spread in a variable or a probability distribution...

. Those measurements look at how the values are distributed around values of central tendency. The dispersion measures most often involve studying the range
Range (statistics)
In the descriptive statistics, the range is the length of the smallest interval which contains all the data. It is calculated by subtracting the smallest observation from the greatest and provides an indication of statistical dispersion.It is measured in the same units as the data...

, interquartile range
Interquartile range
In descriptive statistics, the interquartile range , also called the midspread or middle fifty, is a measure of statistical dispersion, being equal to the difference between the upper and lower quartiles...

, and the standard deviation
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...

.
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