True test for bias

Every scientist and engineer ought to grasp the properties of variances. Those who don’t should not even try to apply a true t-test for bias. And nobody could do it without counting degrees of freedom. It is an irrefutable fact that a true t-test for bias cannot be applied without counting degrees of freedom. That’s why geologists ought to question the validity of geostatistics. The more so since the author of the very first textbook predicted that "…statisticians will find many unqualified statements…” What David didn’t predict was that he would blow a fuse if somebody did. By the way, keep your copy in a safe place. It may well become a collector’s treasure before this millennium is history. Counting degrees of freedom comes to mind as a topic that does not get the respect it so richly deserves. But I’m getting off my train of thought! Here’s a simple but true test for bias applied to an ancient set of paired data.

Observed t-value significant at 99.9% probability

Scientists and engineers ought to apply Student’s t-test in the same way as W S Gosset himself did. All textbooks on applied statistics teach the t-test. It was Volk’s Applied Statistics for Engineers that taught me all about the t-test. Those who want to apply Student’s t-test for bias the proper way should study Chapter Six The t Test. Study not only Section 6.1.4 The Null Hypothesis but even more so Section 6.1.3 Degrees of Freedom. Here’s what Volk wrote, “…we accept a risk of a 5 per cent chance of being in error”. Next, he pointed out, “This error, of falsely rejecting the null hypothesis, is called an error of Type 1”. What I have done in my work is avoid the term “error” without some appropriate adjective. Risk analysis and loss control have played a key role in my work. That’s why I report Type I risk and combined Type I&II risks as intuitive measures for the power of the t-test.

Bias Detection Limits and Probable Bias Ranges

A simple analogy exists between those types of risks and the role of a fire alarm. The Type I statistical risk refers to the event that a fire occurs but the alarm does not sound. The Type II statistical risk refers to the event that the alarm sounds but no fire occurs. The combined Type I and Type II statistical risks refer to the event that a fire occurs and the alarm sounds. Simple comme bonjour! The next step was to define Probable Bias Ranges. It is true that PBRs may sound counterintuitive to those who are not used to working with applied statistics. But surely, PBRs fit the observed bias bon d’un t!

Dr Pierre Gy’s view on accuracy is spelled out on page 17 of his 1979 Sampling of Particulate Materials. Here’s his take, “Accurate: when the absolute value of the bias is not larger than a certain standard of accuracy”. He could have but didn’t mention Standard Reference Materials. SRMs play an important role in calibrating analytical methods and systems. Analytical chemists need SRM’s with confidence intervals for one or more constituents. Gy’s so-called sampling constant is, in fact, a function of a set of four (4) variables. As such, it does have its own variance. What’s more, Gy’s own Student t-Fisher test has raised more eyebrows than interest.

Posted on my website are scores of statistical tests and techniques. I used to attached it as an Appendix to my reports long before Professor Dr Michel David took such a dim view of applied statistics. My son and I in 1992 had to put together Precision and Bias for Mass Measurement Techniques. It was Part 1 of a series on Metrology in Mining and Metallurgy. I hold Canadian copyrights for Metrology in Mining and Metallurgy and for Behind Bre-X, the Whistleblower’s Story. I have scores of blogs to write before I make up my mind what to complete first.