# PART 2 Analysis of Variance

Analysis of variance (ANOVA) is used when we want to test whether there are differences between the means of several populations or groups, based on samples taken from each population.

## Limitations and Assumptions

The test assumes you have collected samples that are truly representative of the population. There are four ways of determining this:

Random sampling: The individuals or individual points in a sample should be selected by some random process in such a way that every individual or point in the population has an equal chance of being selected.

Independent measurements or observations: Each individual in the sample would behave in the same way, regardless of how other members of the sample behave

Normal distributions: The Normal distributions assumption relates to the distribution of the populations being studied, not the samples themselves. We must expect that values will be concentrated symmetrically round some mean value. A frequency distribution curve could be used to test for normality. The curve should not be skewed either to the left or to the right.

Equal variances:  Equal variances is also referred to as homogeneous variance, stable variance, constant variance, or homoscedasticity.  Accurate statistical tests require the “spread” or variance of individual values  to be the same in each of the populations we are comparing