Pitfalls in Statistics - Pharmaceutical Technology

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PharmTech Europe

Pitfalls in Statistics
The hardest errors to spot are the ones that don't look like errors at all.

Pharmaceutical Technology
Volume 35, Issue 4, pp. 40-42

Assay results. Correcting or adjusting one assay result with the result of a second assay that has the same as or larger variance than the first will result in more total variability, not less, because the variances add up. This is known as the "weight to run" problem, in which tablet weight is adjusted using an assay test for potency. This problem can lead to rejecting good lots of materials and products. In most cases, setting the weight equal to the target results in less variation.

Population paremeters. Recognize that the population parameters, such as mu (), the population mean, and sigma (σ), the population standard deviation, are single values, whereas sample estimates of the population mean and sample estimates of the population standard deviation are random results from a distribution. Every additional sample gives slightly different results, so problems arise when sample estimates are treated as if they are population values. This leads to treating other sample estimates such as %RSD and Cpk as if they are without variation. Confidence intervals should be calculated for these statistics to estimate their uncertainty.

Definitions and intervals. Define in exact detail what the phrase "within the variation of the method" means for specific applications because there is no universally accepted definition. Try not to use use confidence intervals to set specification criteria. Instead, use tolerance intervals to get a starting point. Overlapping or non-overlapping confidence intervals are not a significance test.

The most egregious pitfall of all is calculating the sample average plus and minus three times the sample standard deviation without considering the sample size and distribution, and then using it for confidence intervals, setting specification criteria, identifying outliers and all other manner of ad-hoc comparisons. It is not a universal statistical tool. In fact, this equation came about in the 1920s via Dr. Walter Shewhart for defining control charts and is no longer of much use today.

Of course, there are many more potential pitfalls, and when in doubt, contact your local statistician.

Lynn D. Torbeck is a statistician at Torbeck and Assoc., 2000 Dempster Plaza, Evanston, IL 60202, tel. 847.424.1314,
, http://www.torbeck.org/.


1. L. D. Torbeck, "Analytical Validation" supplement to Pharm. Technol. 23, 21-23 (1999).

2. M. Spiegel and L. Stephens, Schaum's Outline of Statistics Fourth Edition (McGraw Hill, NY, NY, 2008).

3. E. R. Tufte, The Visual Display of Quantitative Information (Graphics Press, Cheshire, CT, 1983).


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