STATISTICA Blogs

NOTE: Monte Carlo method is available in STATISTICA's Structural Equation Modeling module.

One of the questions that tends to arise in many contexts in statistics is "How big a sample do I need?"

In standard classical testing situations, this is related frequently to the question of statistical power. If you need to reject the null hypothesis to prove a theoretical point, you certainly want to have adequate power to detect a false null hypothesis. Increasing sample size is the most straightforward way of manipulating power.

In covariance structure analysis, the experimenter is frequently in a somewhat different position, i.e., trying to show that a particular model fits the data well. Here, there can be a different reason for worrying about sample size. Specifically, when sample size is insufficient, the iterative procedure may converge to a minimum that is simply impossible, i.e., represents estimates that are way out of line with reality.

A natural question to ask at the outset of a structural modeling study is

"If my model is a good approximation to reality,

and the basic statistical assumptions are met,

and I  gather a sample of size N,
am I likely to obtain results from my analysis that agree with my model?"

Monte Carlo methods can be used to investigate such a question. They can reveal an insufficient sample size, i.e., an N that leaves a high prior probability of a misleading analysis. Such analysis, performed prior to actual gathering of data, can be crucial to the proper design and execution of research involving structural models.

Image Credit: http://www.flickr.com/photos/woodysworld1778/2807986382/