# Univariate analysis

Univariate analysis is perhaps the simplest form of statistical analysis. Like other forms of statistics, it can be inferential or descriptive. The key fact is that only one variable is involved.

Univariate analysis can yield misleading results in cases in which multivariate analysis is more appropriate.

## Descriptive methods

Descriptive statistics describe a sample or population. They can be part of exploratory data analysis.

The appropriate statistic depends on the level of measurement. For nominal variables, a frequency table and a listing of the mode(s) is sufficient. For ordinal variables the median can be calculated as a measure of central tendency and the range (and variations of it) as a measure of dispersion. For interval level variables, the arithmetic mean (average) and standard deviation are added to the toolbox and, for ratio level variables, we add the geometric mean and harmonic mean as measures of central tendency and the coefficient of variation as a measure of dispersion.

For interval and ratio level data, further descriptors include the variable's skewness and kurtosis.

## Inferential methods

Inferential methods allow us to infer from a sample to a population. For a nominal variable a one-way chi-square (goodness of fit) test can help determine if our sample matches that of some population. For interval and ratio level data, a one-sample t-test can let us infer whether the mean in our sample matches some proposed number (typically 0). Other available tests of location include the one-sample sign test and Wilcoxon signed rank test.