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Analysis of variance
▪ Abstract & history
ANOVA / the analysis of variance is the statistical tool which is used for
segregate the observed data into the various components to apply for more
tests
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So, analysis of variance is used to difference or compare the
means, we commonly used the t-test for differences of the 2- means while
when we have more than 2- kinds of group for comparing then we used
ANOVA
...
As well ANOVA is helpful to check out if you
require to neglect the null hypothesis or accept any other hypothesis
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In 1770, Laplace performed various hypothesis tests while in 1800 Gauss &
the Laplace proposed the least squares technique for joining the different
observations, Laplace understood that how to determine the variance from
the remaining sum of squares
...
After these methods in 1918 Ronald Fischer developed
the name ‘variance’ and also introduce the formal analysis of the variance
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The formula of ANOVA is;
F=

𝑴𝑺𝑻
𝑴𝑺𝑬

In this formula; the ‘F’ is known as the ANOVA coefficient
‘MST’ is equal to the mean sum of squares due to the treatment
‘MSE’ is equal to the mean sum of squares due to the error
Classes of models
There are about three types of models which are used in ANOVA or analysis
of variance
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While the random effects model is useful when the treatment is
not fixed
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The last one is the mixed effects
model possess the experimental variables of the both type of class I and
class ii with various interpretations as well the analysis for 2- types
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of independent variables
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It is used to measure yet
that all the samples are similar
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As well, this type of ANOVA is used for 3 / extra groups of data to detect
about the interaction among the dependent & independent factors
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This type of ANOVA differentiates 3 / more than categorical groups to happen
either may be difference is present among them
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For example, if your group of individuals are divided into the other small groups
& complete various tasks
...
e
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Similar to the above condition, the individuals are divided into the groups on the
basis of attribute that they contain
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e
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o (Limitations)This kind of ANOVA give idea about 2- groups that are various
from each other’s
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➢ Hypothesis of One-way ANOVA
▪ Null hypothesis is that no difference among the groups as well equality
among means
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▪ Ho : 𝜇1 = 𝜇2 = 𝜇3 = ⋯ = 𝜇𝐾
There are no variations in means
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➢ Assumptions of one-way ANOVA
Normality → every sample take from the normally divided population
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As well,
the weigh should be continuous
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The important aim of this
type of ANOVA is to know the relation among the 2- independent factors
on the dependent factors
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So, this type of ANOVA allows to the organization to differentiate
the worker productivity on the basis of 2- independent factors like as the
salary & the skill
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o Example
By using the ANOVA, you can observe that co-relation among the gender &
educational level, on test anxious between the students of university
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The interaction of this type of ANOVA tells you either
the influence of independent factors on the dependent factors is similar to
whole values of the independent factors (& vice versa)
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Their samples should be independent
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As well, the groups possess the similar sample’s size
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The means of the populations are equal to each other for the rows
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The null hypothesis is that no relation among the 2- factors in the population
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The samples should be chosen independently as well randomly
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In the large sample the Linear Model that is used in ANOVA is not
influenced via the minute deviations
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technologynetworks
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investopedia
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asp#:~:text=Analysis
%20of%20variance%2C%20or%20ANOVA,the%20dependent%20and
%20independent%20variables
• https://www-mygreatlearningcom
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ampproject
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mygreatlearning
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google
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mygreatlearning

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