{"id":14028,"date":"2026-03-23T15:42:08","date_gmt":"2026-03-23T15:42:08","guid":{"rendered":"https:\/\/www.blopig.com\/blog\/?p=14028"},"modified":"2026-03-25T10:23:38","modified_gmt":"2026-03-25T10:23:38","slug":"misconduct-bias-or-benign-a-case-of-missing-angstroms","status":"publish","type":"post","link":"https:\/\/www.blopig.com\/blog\/2026\/03\/misconduct-bias-or-benign-a-case-of-missing-angstroms\/","title":{"rendered":"Misconduct, Bias or Benign? A Case of Missing \u00c5ngstr\u00f6ms"},"content":{"rendered":"\n

An \u00c5ngstr\u00f6m<\/strong><\/p>\n\n\n\n

An \u00c5ngstr\u00f6m (\u00c5) is a unit of length equal to 10\u221210 <\/sup>metres; one ten-billionth of a metre. It sits at a comfortable scale for the atomic world, with the diameter of a hydrogen atom, the length of a chemical bond, all measured in \u00c5ngstr\u00f6m.<\/p>\n\n\n\n

It is not an International System of Units (Syst\u00e8me International d’Unit\u00e9s) “SI” unit. In fact, it has been formally deprecated in favour of the nanometre (1 \u00c5 = 0.1 nm), and standards bodies such as NIST and the BIPM discourage its use. Yet, in structural biology and chemistry, crystallography, and materials science, the \u00c5ngstr\u00f6m persists. I would say, partly out of stubbornness, but mostly out of convenience. Saying a protein structure was solved at 2.1 \u00c5 feels natural in a way that 0.21 nm does not.<\/p>\n\n\n\n

So we keep using it. And because we keep using it, we inherit its quirks and history.<\/p>\n\n\n\n\n\n\n\n

Preamble: Missing Z-values in Medical Research<\/strong><\/p>\n\n\n\n

Before I share with you the particular quirk I wrote this blog about, let us discuss a different but hopefully apparently similar anomaly.<\/p>\n\n\n\n

In medical statistics, Barnett & Wren (2019) examined decades of Medline papers and noticed something odd: missing Z-values. More precisely, there was a suspicious scarcity of results just shy of conventional significance thresholds.<\/p>\n\n\n\n

\"\"<\/a><\/figure>\n\n\n\n

This is the statistical analogue of a cliff edge: results pile up just beyond p < 0.05, and vanish tangentially at p \u2265<\/mo>\\geq<\/annotation><\/semantics><\/math> 0.05 (corresponding to z-values of +\/- 1.96). You have probably seen this before, a critical value of 0.05 is by and large the default of statistical thresholds, in pretty much every major scientific field.<\/p>\n\n\n\n

Two well known mechanisms explain this:<\/p>\n\n\n\n

    \n
  1. Publication bias:<\/strong> non-significant results are less likely to be published<\/li>\n\n\n\n
  2. P-hacking \/ “researcher degrees of freedom”: <\/strong>analyses are nudged until they cross significance thresholds<\/li>\n<\/ol>\n\n\n\n

    van Zwet & Cator (2021) describe this as the “significance filter” where only results that pass a threshold survive to be seen. The consequence is a distorted distribution: not a smooth continuum, but one with suspicious gaps and spikes. This raises the broader questions:<\/p>\n\n\n\n

    When humans report numbers, do we see the underlying truth? Or just the thresholds we (and what we believe others) care about? Regardless, it does not help the overwhelming nature of scientific discovery being abundant with true positives, and very few negatives (at least in terms of significance).<\/p>\n\n\n\n

    The RCSB-PDB<\/strong><\/p>\n\n\n\n

    With that question in mind, let us turn to structural biology.<\/p>\n\n\n\n

    Using the RCSB Protein Data Bank API<\/a>, I retrieved 199,761 protein structures solved by X-ray diffraction. For each, I extracted the reported refined resolution, the canonical measure of structural quality for the model, as reported by the authors who deposited the structural model.<\/p>\n\n\n\n

    At first glance, everything looks reassuringly normal.<\/p>\n\n\n\n

    \"\"<\/a><\/figure>\n\n\n\n