Modeling and Multivariate Methods - SAS

674 Statistical Details Appendix A
Key Statistical Concepts
Alternative Methods
The statistical literature describes special nonparametric and robust methods, but JMP implements only a
few of them at this time. These methods require fewer distributional assumptions (nonparametric), and
then are more resistant to contamination (robust). However, they are less conducive to a general
methodological approach, and the small sample probabilities on the test statistics can be time consuming to
compute.
If you are interested in linear rank tests and need only normal large sample significance approximations, you
can analyze the ranks of your data to perform the equivalent of a Wilcoxon rank-sum or Kruskal-Wallis
one-way test.
If you are uncertain that a continuous response adequately meets normal assumptions, you can change the
modeling type from continuous to ordinal and then analyze safely, even though this approach sacrifices
some richness in the presentations and some statistical power as well.
Key Statistical Concepts
There are two key concepts that unify classical statistics and encapsulate statistical properties and fitting
principles into forms you can visualize:
• a unifying concept of uncertainty
• two basic fitting machines.
These two ideas help unlock the understanding of statistics with intuitive concepts that are based on the
foundation laid by mathematical statistics.
Statistics is to science what accounting is to business. It is the craft of weighing and balancing observational
evidence. Statistical tests are like credibility audits. But statistical tools can do more than that. They are
instruments of discovery that can show unexpected things about data and lead to interesting new ideas.
Before using these powerful tools, you need to understand a bit about how they work.
Uncertainty, a Unifying Concept
When you do accounting, you total money amounts to get summaries. When you look at scientific
observations in the presence of uncertainty or noise, you need some statistical measurement to summarize
the data. Just as money is additive, uncertainty is additive if you choose the right measure for it.
The best measure is not the direct probability because to get a joint probability you have to assume that the
observations are independent and then multiply probabilities rather than add them. It is easier to take the
log of each probability because then you can sum them and the total is the log of the joint probability.
However, the log of a probability is negative because it is the log of a number between 0 and 1. In order to
keep the numbers positive, JMP uses the negative log of the probability. As the probability becomes smaller,
its negative log becomes larger. This measure is called uncertainty, and it is measured in reverse fashion from
probability.