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Univariate & Bivariate Methods
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Comparing samples
Univariate methods include tests that compare samples from different groups. Typically univariate methods are designed to evaluate 1 variable at a time, although a second variable used to group or sort the variables may be implied. For example, a single variable, such as number of eutrophic diatoms, may be grouped by a second variable, such as presence or absence of agriculture in the watershed. The means, distributions, or variances from the 2 samples could be compared. A simpler case involves just the variable of interest and a specified value of interest, for example, testing whether the observed mean differs from zero, rather than the mean calculated for another group.
Analysis of variance (ANOVA)
When a 3rd or 4th variable is included, you need a multiple comparison framework, for example, ANOVA. With ANOVA you may also include additional variables for crossed or nested designs. Although typically used to test for statistical differences in groups, ANOVA is also a powerful tool for evaluating and comparing the precision of measurements or the relative contribution of different factors to the total variance.
Correlation and regression
Correlation and regression are more accurately called bivariate methods because they involve the full range of both variables rather than just using 1 variable to categorize another. Regression is used to predict the values of 1 variable from another while correlation is used to test the strength of association between 2 variables. Both methods are used somewhat interchangeably to test whether variables increase or decrease together (or go in opposite directions).
Nonparametric alternative tests
For most of the tests described here you have a choice of whether to use parametric or nonparametric models. If you are unsure whether the underlying distribution is normally distributed, a nonparametric test may be a better choice.