This is archived information for Stat 445 Sect 201 (Spring, 2005).
General Advice on Statistical Reports
John Petkau, who taught this course last time it was offered, offers the following advice for writing statistical reports and for doing statistical work in general:
On Plots...
- Use plots, not tables, whenever possible (e.g., for summary statistics).
- Use plots before carrying out the analysis and then to guide your analysis.
On Numbers...
- Citing point estimates without indicating how precisely determined they are is not very useful. One of the "added values" you provide as a statistician is that you are able to provide such information (via standard errors or confidence intervals), thereby allowing a much more meaningful interpretation of the data. Always do this and make sure it is clear which of those descriptions you are providing.
- In general, give standard deviations (SDs), not variances: SDs are on the same scale as the raw data and, more importantly, provide a "quick-and-dirty" description of many sets of data via the "empirical rule": even if the histogram of the data is not terribly well approximated by the normal, about 70% of the data will lie within 1 SD of the average and about 95% will lie within 2 SDs of the average.
- Don't cite meaningless digits in the text of a report. Always round to something sensible, guided by the precision with which the raw data was measured.
- Don't cite a very small p-value as if it is accurate (unless that p-value results from an exact calculation). Keep in mind that in most cases p-values are just approximate, and typically not very accurate if we're looking way out in the tail of the distribution. So, citing as > 0.20, to two digits for values between 0.20 and 0.10, to one digit between 0.09 and 0.001 (or maybe 0.0001?) and then < 0.001 for all smaller p-values might be reasonable.
On Hypothesis Testing and Confidence Intervals...
- Failure to reject Ho is not the same as saying that Ho is true: absence of evidence (in the data to reject Ho) is not the same as evidence of absence (of an effect/difference/etc).
- Hypotheses and confidence intervals are always about population parameters, never about sample statistics.
- Citing actual p-values is much more informative than comparing to an arbitrary value such as 0.05 and then saying "accept" or "reject": why not simply convey the information the p-value provides on the strength of the evidence the data provide against Ho?
- Make sure you understand the correct interpretation of a confidence interval, and that you do not misinterpret it in your reports. Careful wording is usually required.
On Other Matters...
- Initial/exploratory data analysis should have a heavy focus on plots and should include assessment of assumptions before your more formal model-fitting and analysis.
- Assumptions can't actually be "verified". At best, you simply haven't been able to detect departures from the assumptions.
This is archived information for Stat 445 Sect 201 (Spring, 2005).