# One-Way Analysis of Variance (ANOVA)

When the independent variable is two or more categorial variables and the dependent variable is normally distributed. It tests to see if there is a significant difference in the mean of the dependent variable as partitioned by the categorical variable.

## One-Way ANOVA in R

To run the ANOVA test in R first we create a linear model and then call the ANOVA function on it as follows:

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## Discussion

Hypothesis:

H0μ1 = μ2 = μ3 = … = μk

HA: At least two of the group means μ1μ2μ3, …, μk are not equal.

This hypothesis in turn means that if H0 is concluded, any differences in the mean are considered to be noise. If the HA is concluded the differences are more than noise and therefore significant.

The f-test is the ratio of two variances. The ANOVA is an F-test between each regressor, rather than the typical f-test which tests the regression as a whole (t-test??).

## Reference

https://stats.idre.ucla.edu/spss/whatstat/what-statistical-analysis-should-i-usestatistical-analyses-using-spss/

https://courses.lumenlearning.com/introstats1/chapter/one-way-anova/#:~:text=A%20one%2Dway%20ANOVA%20hypothesis,two%20different%20degrees%20of%20freedom.&text=Assumptions%3A-,Each%20population%20from%20which%20a%20sample%20is%20taken%20is%20assumed,standard%20deviations%20(or%20variances).

https://www.pythonfordatascience.org/anova-python/