So you want to test if the mean of a numeric outcome differs among more than two groups. Question: Are the distributions for all groups normal?
A normal distribution is the classic bell curve. It is symmetric, with most cases falling near the mean and fewer cases falling away from the mean in either tail.
Example:
For more information: Assessing normality
ONE OR MORE GROUPS ARE NOT NORMAL
If the variable’s distribution is skewed, has more than one mode (peak), or contains outliers, then it will fail the normality assumption of many parametric statistical methods.
Example:
