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Univariate analysis is the simplest form of quantitative (statistical) analysis. The analysis is carried out with the description of a single variable in terms of the applicable unit of analysis. For example, if the variable "age" was the subject of the analysis, the researcher would look at how many subjects fall into 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. Univariate analysis is commonly used in the first, descriptive stages of research, before being supplemented by more advanced, inferential bivariate or multivariate analysis.
A basic way of presenting univariate data is to create a frequency distribution of the individual cases, which involves presenting the number of cases in the sample that fall into each category of values of the variable. This can be done in a table format or with a bar chart or a similar form of graphical representation. A sample distribution table is presented below, showing the frequency distribution for a variable "age".
|Age range||Number of cases||Percent|
|Valid cases: 200|
Missing cases: 0
In addition to frequency distribution, univariate analysis commonly involves reporting measures of central tendency (location). This involves describing the way in which quantitative data tend to cluster around some value. In 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 another measure of location, depending on the context. For a categorical variable, such as preferred brand of cereal, only the mode can serve this purpose. For a variable measured on an interval scale, such as temperature on the Celsius scale, or on a ratio scale, such as temperature on the Kelvin scale, the median or mean can also be used.
Another set of measures used in univariate analysis, complementing the study of the central tendency, involves statistical dispersion. These measures look at how the values are distributed around the central tendency. The most common dispersion measures are the range, interquartile range, and the standard deviation.
In the case of time series, which can be ordered along a time scale, univariate analysis can also involve time series analysis such as autoregression, moving average, autoregressive moving average, or autoregressive integrated moving average models. These models describe the relation between the current value of the variable and its various past values.