Most of the students may struggle with the analysis of variance (ANOVA). Here in this presentation you can clear all your doubts in analysis of variance with suitable examples.

1. Analysis of Variance
(ANOVA): Everything You
Need to Know
PRESENTED BY STATANALYTICA TEAM
Stat Analytica

2. Presentation Outline
DISCUSSION POINTS
What is Analysis of Variance (ANOVA)?
The Formula for ANOVA
What Does the Analysis of Variance Reveal?
Example of How to Use ANOVA
Types of ANOVA
One-way ANOVA
Two-way ANOVA
ANOVA Table
Analysis of Variance Repeated Measures
Conclusion

3. Analysis of variance (ANOVA) is a collection of
statistical models. It is one of the significant
aspects of statistics. The statistics students
should be aware of the analysis of variance. But
most of the statistics students find it
challenging to understand analysis of variance.
But it is not that difficult. In this blog, we are
going to share with you everything you need to
know about analysis of variance.
Overview

4. Analysis of variance (ANOVA) is the most powerful analytic tool available in statistics. It
splits an observed aggregate variability that is found inside the data set. Then separate the
data into systematic factors and random factors. In the systematic factor, that data set has
statistical influence. On the other hand, random factors don’t have this feature. The analyst
uses the ANOVA to determine the influence that the independent variable has on the
dependent variable. With the use of Analysis of Variance (ANOVA), we test the differences
between two or more means. Most of the statisticians have an opinion that it should be
known as “Analysis of Means.” We use it to it test the general rather than to find the
difference among means. With the help of this tool, the researchers can able to conduct
many tests simultaneously.
What is Analysis of Variance (ANOVA)?

5. The Formula for ANOVA
F=ANOVA coefficient
MST=Mean sum of squares due to
treatment
MSE=Mean sum of squares due to
error
WHERE
F= MSE/MST

6. What Does the Analysis of
Variance Reveal?
In the initial stage of the ANOVA test, analyze factors that
affect a given data set. When the initial stage finishes, then
the analyst performs additional testing on the methodical
factors. It helps them to contribute to the data set with
consistency measurably. Then the analyst performs the f-test
that helps to generate the additional data that align with the
proper regression model. The analysis of methods also allows
you to compare more than two groups at the same time to
test that the relationship exists between them or not. You can
determine the variability of the samples and within samples
with the results of ANOVA. If the tested group doesn’t have any
difference, then it is called the null hypothesis, and the result
of F-ratio statistics will also be close to 1.

7. Example of How to Use ANOVA
There are different types of ANOVA test. And these tests
depend on the number of factors. You can apply ANOVA when
the data needs to be experimental. It is also an alternative to
the statistics software. But you should use it for small samples.
And if you want to perform ANOVA for a large number of
experimental designs, then you should use the same sample
size with various factors.
The researcher might use the ANOVA for various purposes. But
here are a few examples of analysis of variance. The test
students from multiple schools to see if the students from one
school from the other schools. In the field of business
application, the marketing experts can test the two different
marketing strategies of the business to see that one strategy is
better than the other one in terms of cost efficiency and time
efficiency.

8. Types of
ANOVA
ONE-WAY ANOVA
One way ANOVA is the unidirectional ANOVA. In this ANOVA,
there are sole response variables as compared with the two-
way ANOVA. It evaluates the impact of a sole factor. And this
factor is determined that the samples are the same or not.
Besides, it is also used to determine that there is any
statistically significant difference between the mean of three
or more independent groups.
TWO-WAY ANOVA
A two-way ANOVA is the extended version of the one-way
ANOVA. In two-way ANOVA, you will have two independents. It
utilizes the interaction between the two factors. And these
tests have the effect of two factors at the same time. In this
ANOVA, the statistical test is used to determine the effect of
two nominal predictor variables on a continuous outcome
variable.

9. ANOVA Table
In the Analysis of Variance (ANOVA), we use the statistical analysis to test the degree of differences
between two or more groups in an experiment. besides, we use the ANOVA table to display the
results in tabular form. And this data is used to test the test hypotheses about the population mean.
There are one or two ways to show the ANOVA table, depending on the various factors.

10. The significant columns
in the ANOVA table are
as follows:
“Source” – It means the source
which is responsible for the
variation in the data.
“DF” – degree of freedom of the
data.
“SS”- the sum of the squares of
the data.
“MS”- mean sum of the squares
of the data.
“F” – F-statistic.
“P” – P-value.

11. The significant columns
in the ANOVA table are
as follows:
1. “Factor” – It indicates the
variability that results from
the factor of interest.
“Error” – It means the
unexplained random error or
the variability within the
groups.
“Total” – It is the total
deviation of the data from
the grand mean.

12. In the ANOVA table, If the obtained P-value is less than or equivalent to
the significance level, then the null hypothesis gets automatically
rejected and concluded that all the means are not equal to the given
population.
INTERPRETATION OF THE ANOVA
TABLE IS AS FOLLOWS:

13. Analysis of
Variance
Repeated
Measures
Analysis of repeated measures ANOVA is the equivalent of the
one-way ANOVA. It is also referred to as a within-subjects
ANOVA with correlated samples. It is used to detect the
difference between the related means. The procedure to
perform the analysis of variance designs are using the general
linear models approach. It includes the three between-subject
terms. The Repeated measures designs are quite popular. The
reason is it allows the subject to serve as their own control.
Besides, it also improves the precision of the experiment with
the help of reducing the size of the error variance of the F-
tests. It uses the general linear model framework to perform
the calculations.

14. Conclusion
Analysis of variance is widely used by the
researchers. As statistics experts, we have
provided enough details here about the
analysis of variance. Now you may be well
aware of the analysis of variance. If you want
to get good command over it, then you should
try to implement it in real life. But if you still
find it difficult to understand the analysis in
ANOVA, then you can take help from us.

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