Concept:
Analysis of variance (ANOVA) is a collection of statistical models used to analyze the
differences between group means and their associated procedures (such as
"variation" among and between groups). In ANOVA setting, the observed variance in a particular variable is
partitioned into components attributable to different sources of variation. In
its simplest form, ANOVA provides a statistical test of whether or not the means of several groups are
equal, and therefore generalizes t-test to more than two groups.
Doing multiple two-sample t-tests would result in an increased chance of
committing a type I error. For this reason, ANOVAs
are useful in comparing (testing) three or more means (groups or variables) for
statistical significance.
The terminology of ANOVA is
largely from the statistical design of experiments. The experimenter adjusts factors and measures
responses in an attempt to determine an effect. Factors are assigned to
experimental units by a combination of randomization and blocking to ensure the validity of the results. Blinding keeps the weighing
impartial. Responses show a variability that is partially the result of the
effect and is partially random error.
ANOVA is the synthesis of several ideas and it is
used for multiple purposes. As a consequence, it is difficult to define
concisely or precisely.
"Classical ANOVA for
balanced data does three things at once:
1.
As exploratory data analysis, an ANOVA is an organization of an additive
data decomposition, and its sums of squares indicate the variance of each
component of the decomposition (or, equivalently, each set of terms of a linear
model).
2.
Comparisons of mean squares, along with F-tests ... allow testing
of a nested sequence of models.
3.
Closely related to the ANOVA is a linear model fit with coefficient
estimates and standard errors."[1]
In short, ANOVA is a statistical tool used in
several ways to develop and confirm an explanation for the observed data.
Additionally:
4.
It is computationally elegant and relatively robust against violations
of its assumptions.
5.
ANOVA provides industrial strength (multiple sample comparison)
statistical analysis.
6.
It has been adapted to the analysis of a variety of experimental
designs.
As a result: ANOVA
"has long enjoyed the status of being the most used (some
would say abused) statistical technique in psychological
research." ANOVA "is probably the most useful technique
in the field of statistical inference."
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