Two Points, and the Validation That Fails Honestly

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

Two Points, and the Validation That Fails Honestly

A greenhouse deployment calibrates a DHT22 (sensor DHT22_GH_014) with a two-point fit yielding scale 1.0817 and offset -2.38, tuned to a 0.5°C HVAC/greenhouse tolerance. A third, unused validation point then reads 21.45°C against a true reference of 22.5°C. This audit asks the question that validation step invites: does the calibrated sensor actually pass, or does the fit fail the tolerance it was built for?

Companion to the chapter Sensor Calibration Techniques — every number here comes from that chapter.

Ada: The greenhouse example does something braver than most worked examples – it calibrates the DHT22 and then lets the validation step fail. Let me confirm both halves at full precision. Two-point calibration fits corrected = raw x scale + offset from a 0 C low bath (raw 2.20) and a 45 C high bath (raw 43.80):

• Scale: (45.0 - 0.0) / (43.80 - 2.20) = 45.0 / 41.6 = 1.0817308
• Offset: 0.0 - 2.20 x 1.0817308 = -2.379808, i.e. the chapter’s 1.0817 and -2.38

Now the honest part – validation at an unused third point, room reference 22.5 C with raw average 21.45 C:

• Corrected: 21.45 x 1.0817308 + (-2.379808) = 23.203125 - 2.379808 = 20.823 C
• Validation error: 22.5 - 20.823 = 1.677 C, which rounds to the chapter’s 1.68 C

That 1.68 C sits well above the 0.5 C greenhouse tolerance, so the two-point fit is correctly rejected. The design-meaningful lesson is quantitative, not rhetorical: a straight line pinned at 0 C and 45 C still misses the middle by more than three times the allowed error, which is precisely why the validation point must be a third reading the calibration never saw.

Every number above is taken from the chapter’s own material and re-derived step by step.