Univariate analysis is the simplest form of quantitative (statistical) analysis.[1] The analysis is carried out with the description of a single variable and its attributes of the applicable unit of analysis.[1] 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 – the analysis of two variables simultaneously – or multivariate analysis – the analysis of multiple variables simultaneously.[1] Univariate analysis is also used primarily for descriptive purposes, while bivariate and multivariate analysis are geared more towards explanatory purposes.[1] 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.[2][3]
A basic way of presenting univariate data is to create a frequency distribution of the individual cases, which involves presenting the number of attributes of the variable studied for each case observed in the sample.[1] This can be done in a table format, with a bar chart or a similar form of graphical representation.[1] 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 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).[1]
In addition to frequency distribution, univariate analysis commonly involves reporting measures of central tendency (location).[1] This involves describing the way in which quantitative data tend to cluster around some value.[4] In the univariate analysis, the measure of central tendency is an average of a set of measurements, the word average being variously construed as (arithmetic) mean, median, mode or other measure of location, depending on the context.[1]
Another set of measures used in the univariate analysis, complementing the study of the central tendency, involves studying the statistical dispersion.[1] Those measurements look at how the values are distributed around values of central tendency.[1] The dispersion measures most often involve studying the range, interquartile range, and the standard deviation.[1]