• Attitude toward assumptions. As software engineers are aware, a major difference between statistics and mathematics is that for the latter, it matters only that assumptions be correctly stated, whereas for the former, it is essential that the prevailing assumptions be supported by the data. This distinction is important, but unfortunately it is often taken too literally by many who use statistical techniques. Tukey has long argued that what is important is not so much that assumptions are violated but rather that their effect on conclusions is well understood. Thus for a linear model, where the standard assumptions include normality, homoscedasticity, and independence, their importance to statements of inference is exactly in the opposite order. Statistics textbooks, courses, and consulting activities should convey the statistician's level of understanding of and perspective on the importance of assumptions for statistical inference methods.

  • Visualization. The importance of plotting data in all aspects of statistical work cannot be overemphasized. Graphics is important in exploratory stages to ascertain how complex a model the data can support; in the analysis stage for display of residuals to examine what a currently entertained model has failed to account for; and in the presentation stage where graphics can provide succinct and convincing summaries of the statistical analysis and associated uncertainty. Visualization can also help software engineers cope with, and understand, the huge quantities of data collected in the software development process.

  • Tools. Software engineers tend to think of statisticians as people who know how to run a regression software package. Although statisticians prefer to think of themselves more as problem solvers, it is still important that they point out good statistical computing tools-for instance, S, SAS, GLIM, RS1, and so on-to software engineers. A CATS report (NRC, 1991) attempts to provide an overview of statistical computing languages, systems, and packages, but for such material to be useful to software engineers, a more focused overview will be required.

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