In a previous blog I suggested that many readers in many applied areas are reading statistics texts under duress for a course or project, and are in truth somewhere between disinterested and terrified. In my new SAS Press book Business Statistics Made Easy in SAS® I make use of various
Part 1 of this topic presented a simple Sudoku solver. By treating Sudoku as an exact cover problem, the algorithm efficiently found solutions to simple Sudoku problems using basic logic. Unfortunately, the simple solver fails when presented with more difficult Sudoku problems. The puzzle on the right was obtained from
Sudoku solvers have been written in SAS using a variety of methods (e.g., the DATA step, PROC SQL, and PROC CLP). Surprisingly, SAS/IML appears to have been overlooked for this purpose. On a challenge from a coworker, I wrote this blog post to demonstrate the flexibility of SAS/IML in the
When teaching statistics, it is often useful to produce a normal density plot with shading under the curve. For example, consider a one-sided hypothesis test. An alpha value of .05 would correspond to a Z-score cutoff of 1.645. This means that 95% of a standard normal curve falls below a
I recently received this interesting question regarding Multilevel Models after one of my last blog posts: Question: Can you tell me when a multilevel-model is not appropriate? I have data that by design is clustered but the random intercept in the null model is not significant. I have seen advice
Multilevel models (also called hierarchical linear models) are used to analyze clustered or grouped data, as well as longitudinal or repeated measures data. Consider the simple scenario shown below, where Y is continuous and is shown as a function of a continuous predictor variable, X (which has been standardized). If
If you have data where the observations are not independent due to nesting or clustering, you may need a multilevel model. Another scenario that would require a multilevel model is if you have data where observations have been gathered multiple times on the same subject (a.k.a., longitudinal data or repeated
FINALLY…the simplest ESTIMATE statements to write are for continuous variables not involved in interactions or higher order terms. Consider a data set containing the 2004 SAT scores for each of the 50 states. The file includes the combined math and verbal SAT scores (TOTAL), the state (STATE) and the percent
My previous blog demonstrated the most difficult type of ESTIMATE statement to write—a two-way (or higher) ANOVA with interactions. An "easy button" for ESTIMATE statement comes by having a simpler model. Models with only main effects and no interactions make writing ESTIMATE statements straightforward. Consider first a one-way ANOVA. A
When asked to select the best (or worst) of something in a business setting, do you wish you had "magic glasses" to see the answer? PROC GLM and other statistical modeling procedures have their own versions of such an item with their ESTIMATE (and CONTRAST) statements. They allow you to
