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Application of variance analysis

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Assignment on
(analysis of variance)
Submitted by:
Vishwajeet srivastav
Roll no. 2009058 submitted to:
Prof. Rahul dalvi

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Analysis of variance
In statistics, analysis of variance (ANOVA) is a collection of statistical models, and their
associated procedures, in which the observed variance is partitioned into components due
to different explanatory variables. In its simplest form ANOVA provides a statistical test of
whether or not the means of several groups are all equal, and therefore generalizes
Student's two sample t-test to more than two groups. ANOVAs are helpful because they
possess a certain advantage over a two-sample t-test. Doing multiple two-sample t-tests
would result in a largely increased chance of committing a type I error. For this reason,
ANOVAs are useful in comparing three or more means.
Overview
There are three conceptual classes of such models:
1. Fixed-effects models assume that the data came from normal populations which may
differ only in their means. (Model 1)
2. Random effects models assume that the data describe a hierarchy of different
populations whose differences are constrained by the hierarchy. (Model 2)
3. Mixed-effect models describe situations where both fixed and random effects are present.
(Model 3)
In practice, there are several types of ANOVA depending on the number of treatments and
the way they are applied to the subjects in the experiment:
One-way ANOVA is used to test for differences among two or more
independent groups. Typically, however, the one-way ANOVA is used to test for differences
among at least three groups, since the two-group case can be covered by a t-test (Gosset,
1908). When there are only two means to compare, the t-test and the F-test are equivalent;
the relation between ANOVA and t is given by F = t2
.
Factorial ANOVA is used when the experimenter wants to study the effects of
two or more treatment variables. The most commonly used type of factorial ANOVA is the
22 (read
"two by two") design, where there are two independent variables and each variable has two
levels or distinct values. However, such use of ANOVA for analysis of 2k factorial designs
and fractional factorial designs is "confusing and makes little sense"; instead it is suggested
to refer the value of the effect divided by its standard error to a t-table.[1] Factorial ANOVA
can also be multi-level such as 33, etc. or higher order such as 2×2×2, etc. but analyses
with higher numbers of factors are rarely done by hand because the calculations are
lengthy. However, since the introduction of data analytic software, the utilization of higher
order designs and analyses has become quite common.
Repeated measures ANOVA is used when the same subjects are used for each treatment

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 Assignment on (analysis of variance) Submitted by: Vishwajeet srivastav Roll no. 2009058 submitted to: Prof. Rahul dalvi Analysis of variance In statistics, analysis of variance (ANOVA) is a collection of statistical models, and their associated procedures, in which the observed variance is partitioned into components due to different explanatory variables. In its simplest form ANOVA provides a statistical test of whether or not the means of several groups are all equal, and therefore generalizes Student's two sample t-test to more than two groups. ANOVAs are helpful because they possess a certain advantage over a two-sample t-test. Doing multiple two-sample t-tests would result in a largely increased chance of committing a type I error. For this reason, ANOVAs are useful in comparing three or more means. Overview There are three conceptual classes of such models: 1. Fixed-effects models assume that the data came from normal populations which may differ only in their means. (Model 1) 2. Random effects models assume that the data describe a hierarchy of different populations whose differences are constrained by the hierarchy. (Model 2) 3. Mixed-effect models describe situations where both fixed and random effects are present. (Model 3) ...
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