# Statistics: Analysis of Variance

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3 December 2021

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How would you clarify the analysis of variance, assuming that your audience has not had a statistics class before? When one does a research of information, typically this suggests an analysis of the “mean” or average of that information. .i.e. What is the common time it takes a fifth grader to complete his last math exam?

A take a look at is used to test variations between two means. i.e. the mean of the experiment group vs a management group. An ANOVA take a look at, on the other hand, is indicated when there are three or more means or populations to be examined.

When solely two samples are looked at, the t test and ANOVA check will yield the same outcomes.

Beyond two examples, the t test can be used to evaluate other means using many t checks, however this method becomes unreliable and topic to increased error.

ANOVA or evaluation of variance allows one to make use of statistics to check the differences between two or more means and reduces the likelihood for a kind 1 error, which might happen when taking a glance at multiple two-sample t checks.

This is why use of the ANOVA is indicated for testing hypotheses the place there are multiple means or populations.

ANOVAs basically takes the t take a look at and applies it when testing or evaluating three or more groups, means or variables.

## Example experiment:

Study different types of protein consumption on weight achieve. Is the impact of every kind of protein consumption on weight achieve significantly related or different?

50 males total, 10 males per group, each group fed equal quantity of protein energy but from completely different kind of protein classification.

One method ANOVA – looking at impact of 5 completely different feeding methods to extend weight acquire. (i.e. high pure pink meat protein diet, excessive vegetable protein diet, high protein powder food plan, high fish protein food regimen, etc.). This is a one way ANOVA study as a end result of there is simply one category (protein) that might be examined, because it relates to its impact on weight achieve. It is balanced as there are an equal number of men (10) consuming the identical kind of protein. Simplistically put, the research will give us data as to whether or not each type of protein produces comparable or completely different results (weight gain).

Two means ANOVA, as the name implies, contains the addition of a second variable that may be looked at as affecting weight achieve. i.e. quantity of train.

Three means ANOVA, as the name implies, contains the addition of a third variable. i.e. consumption of “other calories”.

In the end, the experiment might lead one to conclude that several varieties of protein consumption results in weight gain. Unfortunately, experiments are never that reduce and dry, and there are all the time different variables that have to be accounted for. There is what’s called “error” due to “chance” and “beyond human control” or “variation” related to “assignable causes”.

An F take a look at must be used to check these errors and/or variations, to determine if the population variances are the same or different. If the variances are the identical or equal, the F ratio shall be 1. This will allow one to complete their study / experiment and make ultimate conclusions.

## References:

1. https://explorable.com/anova
2. http://onlinestatbook.com/2/analysis_of_variance/intro.html
3. https://people.richland.edu/james/lecture/m170/ch13-f.html

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