In statistics, analysis of variance ( ANOVA ) is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation.

# 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 ).

There are three classes of models used in the analysis of variance, and these are outlined here.

The fixed-effects model of analysis of variance applies to situations in which the experimenter applies one or more treatments to the subjects of the experiment to see if the response variable values change.

The analysis of variance has been studied from several approaches, the most common of which uses a linear model that relates the response to the treatments and blocks.

Even when the statistical model is nonlinear, it can be approximated by a linear model for which an analysis of variance may be appropriate.

" e think of the analysis of variance as a way of understanding and structuring

* Multivariate analysis of variance ( MANOVA ) is used when there is more than one response variable.

means that the usual analysis of variance techniques do not apply.

general case, " The analysis of variance can also be applied to

While the analysis of variance reached fruition in the 20th century,

Sir Ronald Fisher proposed a formal analysis of variance in a 1918 article The Correlation Between Relatives on the Supposition of Mendelian Inheritance.

His first application of the analysis of variance was published in 1921.

* Mixed-design analysis of variance

* Two-way analysis of variance

* One-way analysis of variance

Univariate analysis involves describing the distribution of a single variable, including its central tendency ( including the mean, median, and mode ) and dispersion ( including the range and quantiles of the data-set, and measures of spread such as the variance and standard deviation ).

Analysis of the design of experiments was built on the foundation of the analysis of variance, a collection of models in which the observed variance is partitioned into components due to different factors which are estimated or tested.

Quantitative methods used in I – O psychology include both descriptive statistics and inferential statistics ( e. g., correlation, multiple regression, and analysis of variance ).

More advanced statistical methods employed by some I – O psychologists include logistic regression, multivariate analysis of variance, structural equation modeling, and hierarchical linear modeling ( HLM ; also known as multilevel modeling ).

* In statistics, Wilks's lambda is used in multivariate analysis of variance ( MANOVA analysis ) to compare group means on a combination of dependent variables.

In many of the syllables, intonation can be safely ignored, and much of the tonal analysis can be done without any study of intonation.

The force of the authors' analysis ( if indeed it has any force ) can be felt by the reader, I believe, only after three questions have been successfully answered.

That is why it is so very important that ethical analysis keep clear the problem of decision as to `` permitted '' effects, and not draw back in fright from any conceivable contingency or suffer paralysis of action before possibilities or probabilities unrelated, or not directly morally related, to what we can and may and must do as long as human history endures.

Power analysis can assist in study design by determining what sample size would be required in order to have a reasonable chance of rejecting the null hypothesis when the alternative hypothesis is true.

A matrix can have a considerable effect on the way a chemical analysis is conducted and the quality of its results.

Chemists can use isotope analysis to assist analysts with issues in anthropology, archeology, food chemistry, forensics, geology, and a host of other questions of physical science.

* Principal components analysis – a technique that can be used to simplify a dataset

The focus can be as diverse as the analysis of Homer or Freud.

Run-time efficiency is a topic of great interest in computer science: A program can take seconds, hours or even years to finish executing, depending on which algorithm it implements ( see also performance analysis, which is the analysis of an algorithm's run-time in practice ).

Target acquisition can take many forms, it is usually observation in real time but may be the product of analysis.

In its own right it can be the subject of intense study and analysis, and provides insight into the relationship between God and Man beyond the world of Judaism and for all Monotheism.

Aveni states that one of the strengths of the Brown methodology is that it can explore astronomies invisible to statistical analysis and offers the astronomy of the Incas as another example.

Subsequently spatial measurements can be greatly affected, and careful analysis of the reconstructed volume is needd to ensure the correct results.

Pre-dealt hands also have the advantage that, at the end of the session, diagrams of each deal can be made available to the players for later analysis.

The expression of many genes can be determined by measuring mRNA levels with multiple techniques including microarrays, expressed cDNA sequence tag ( EST ) sequencing, serial analysis of gene expression ( SAGE ) tag sequencing, massively parallel signature sequencing ( MPSS ), RNA-Seq, also known as " Whole Transcriptome Shotgun Sequencing " ( WTSS ), or various applications of multiplexed in-situ hybridization.

From basic functional analysis we know that any ket can be written as

Cost-benefit analysis can inform our decisions opinion piece in 23 April 2012 Wall Street Journal

They can be analyzed using the tools of chemical analysis, e. g. spectroscopy and chromatography.

In addition, the efficiency of an internal combustion engine can be measured in this way, and some states and local municipalities are using combustion analysis to define and rate the efficiency of vehicles on the road today.

Retrosynthetic analysis can be applied to design a complex synthesis reaction.