Hi, everyone. What's the different, if any, between calculating the coefficient of variation of a group of data disposed in a experimental design with different treatments (for ANOVA) and a "free" group of data. I supose, there might be a difference in case of ANOVA, ´cause the treatments may affect the evaluated variable between groups of replications of the same treatment.
The coefficient of variation for a model can be calculated with the differences between predicted and actual values from the model, following a similar procedure as for CV for a "free" group which uses the differences between the values and the mean.
You can compare these by creating a model that has one predictor equal to the mean of measurement variable. Note that if you use a definition of CV as standard deviation / mean, if the formula for sample standard deviation is used, the model method and free group method will be slightly different. If you use the population standard deviation, they should be the same.
An example in R follows.
A = c(1,2,3,4,5,6,7,8,9,10)
sd_pop = sqrt(mean((A - mean(A))^2))
cv_free = sd_pop / mean(A)
cv_free
### [1] 0.522233
sd(A) / mean(A)
### [1] 0.5504819
### Note: this cv using the sample standard deviaton
B = rep(mean(A), length(A))
model = lm(A ~ B)
actual = A
predy = predict(model)
mse = mean((actual - predy)^2)
rmse = sqrt(mse)
cv_model = rmse/mean(actual)
cv_model
# [1] 0.522233
The coefficient of variation is the percent of the average deviation (in the form of SD) from the mean to the mean. The ANOVA on the other hand is a model that compares the with in variation (variation among the replications) with the among variation (variation between the different levels of the treatment, a statistic usually called the F-ratio.
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