outaovii

Identification of outliers in a one-way analysis of variance model II (random effects).

In a one-way analysis of variance random effects model one would expect that the measurements lie close together because the same quantity was measured and states that the class effects stem from a common source and therefore should not difer too much. In the random model some variation is allowed and the decision is assisted by the assumption of the distribution of the random class effects. But one can observe some type of 'outliers', that according to Barnett and Lewis (1994), it is an observation or subset of observations which appears to be inconsistent with the remainder of that set of data. In random effects model can be distinguished three types of outliers:
1. Within the classes
2. Within the random effects
3. Respect to scale (objects occupy the same relative positions in one measurement space as they do in the other).

If the model is satisfied, these outliers are not likely to occur because of the light tails of the normal distribution and homoscedasticity, and it is considered to describe the ideal situation without outliers. Therefore, it is important to set up formal rules that identify these outliers. Wellmann and Gather (2003) provide rules and details of a robust procedure which involves the median-based estimators.

Here, we developed a MATLAB function that deals with such a fundamentals.

**NOTE: For an unbalanced design we are still working on in order to implement the procedure to detect the class scale-outliers. Please, keep on date of the file updatings.**

Inputs:
X - data matrix (column 1= data;column 2=class code).
alpha - significance (default = 0.05).

Outputs:
A complete summary of the identification of outliers:
- within the i-th class.
- within the random effects.
- as a scale-outlier class.