I am hoping to compare the sample mean of an experimental group to the sample mean of three control groups.
Here is some context for the study:
The experimental group consists of ~60 persons with a particular criminal record who were afforded various rehabilitative services. For each person, I have a count of their number of rearrests after they began their "treatment."
The control groups are similarly sized (50-70 people) and share similar characteristics to the experimental group. For each person in the control group, I have a count of their number of arrests after the control group began their treatment (i.e. control group is monitored over the same time period). I now want to test if there is a statistically significant difference between the number of rearrests for the experimental group and the control groups.
The distribution of arrests for the experimental group and the control groups is non-normal and skewed to the right. Most people either had zero rearrests or 1 rearrest while fewer and fewer people had >1 rearrest. I did however test for homogeneity of variances, which reflected that the variances are equal.
What test do I use in this case?
Also, what tests do I use under the following assumptions?
Normal Distribution = True and Homogeneity of Variance = True
Normal Distribution = True and Homogeneity of Variance = False
Normal Distribution = False and Homogeneity of Variance = True
Normal Distribution = False and Homogeneity of Variance = False