# 'Low Level' Error Terms in Expected Mean Square Calculation

1. Apr 5, 2012

### 3.141592654

I'm currently studying experiments where one or more factors are random, i.e. random effects models. In this model a professor explained that the Expected Mean Square calculations for any factor are:

Expected Mean Square (factor) = (lower level error terms) + (term relating to factor)

For example, if A and B are both random, then

Expected Mean Square (A) = (Error variance) + n*(AB Interaction variance) + n*b*(A variance)

My question is why does the AB interaction variance get classified as a 'lower level' error in relation to A and as a result get included in the Expected Mean Square calculation for factor A?

Thanks.

2. Apr 5, 2012

### chiro

Hey 3.141592654.

In terms of statistical purposes, classifying interaction effects separately is useful because if there is a significant interaction then in the context of experimental design, we will want to redesign the experiment so that this interaction is removed (or in practice minimized) so that it does not effect the statistical analysis and the accuracy of its interpretation.

If there is serious confounding going on then we will not be able to distinctly know what effects are going on and this is the reason why assessing interactions statistically is important because without taking this into account, we would have processes that are essentially are creating some kind of hidden behaviour that would jeopardize the accuracy of a statistical assessment.

In terms of your actual question I looked up mean square here through this website:

http://en.wikipedia.org/wiki/Mean_squared_error

Intuitively in terms of how interaction effects contribute to larger errors for an accurate estimator, the above gives a little insight into this. Remember that if interactions are significant this will have a huge affect on the applicability of the model.

In terms of the 'lower level terms', maybe you could post a definition of what is meant by this as I have not come across this before myself.