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Univariate analysis involves examining each explanatory variable
in the dataset separately. Most traditional methods of analysing
data can be used for univariate analysis, including analysis of
variance (ANOVA), tests for goodness-of-fit, and correlation and
regression. In contrast, the aim of multivariate analyses is to
find patterns of relationships in a dataset between two or more
variables simultaneously. Some of the tests listed below can be
described as univariate or multivariate, depending on the number
of variables being examined. The patterns identified using univariate
or multivariate statistics can then be used to generate additional
hypotheses, which may be tested with further experimental or field
survey work.
Learning materials for Design & Analysis of Biological Studies
SBI209 provides an overview of the techniques mentioned in this
section. You can refer to these at (http://www.cdu.edu.au/faculties/science/sbes/resources
/SBI209/S209L3-Topics8-11/index.htm).
Goodness-of-fit tests
Goodness-of-fit tests are used to compare observed frequency distributions
of data with theoretical or expected distributions. Frequency distributions
analysed using these tests include the distribution of population
age classes, the distribution of phenotypes within a population,
or the distribution of individuals in space within or between habitats.
You may have heard of two widely used goodness-of-fit tests; the
Chi-squared test and the Komolgrov-Smirnov tests.
In most cases, to conduct a goodness-of-fit test the data must
be expressed in counts or frequencies (not percentage
data).
Analysis of variance (ANOVA)
ANOVA is used to test hypotheses about differences in the mean
among different groups. One- or mulit-factor ANOVA allows differences
in mean values of response variables (e.g. animal abundance or species
richness) to be compared for different factors (e.g. vegetation
type, season or site). For example, mean species richness (the response
or dependent variable) could be compared among different vegetation
types (the explanatory or independent variable), e.g. 'woodland',
'grassland' and 'rainforest'. These different vegetation categories
are known as 'treatments' in the ANOVA. In comparing the means between
treatments, the amount of variation in the distribution of
the data about the mean is taken into account. In addition to the
relatively straightforward ANOVA described above, more complex ANOVA
designs also exist. For example, 'Repeated measures' ANOVA can be
used to analyse data where samples have been drawn from the same
plot on more than one occasion (e.g. monitoring change in a variable
over time).
To conduct an ANOVA, the response variable data must be continuous,
and the explanatory variable data must be categorical.
NB. the t-test is calculated as for ANOVA, however it can
only test for differences between between two means.
Correlation
Correlation is a measure of the strength and direction of a linear
association between two or more continuous variables. For
example, it can be used to explore relationships between species
abundance and an environmental attribute such as rainfall.
Regression
Regression analysis also explores the relation between two or more
continuous variables. However, regression also provides a
mathematical description of the relationship between those variables
(in the form of a regression equation). This allows predictions
to be made about the response variable.
Regression analysis is related to correlation analysis, but allows
for a measure of the extent to which the value of an explanatory
variable explains the value of another (response) variable.
back to "Types of statistical analysis"
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