Two Points, and the Validation That Fails Honestly
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.
See the relationship before changing it
The figure reads from left to right. The blue card is validation raw reading. The middle card applies this page's rule. The green card is corrected reading. Walk the arrows once: set the input, apply the rule, then read the result with its unit.
The retained audit below checks several chapter fixtures. This model keeps those stated values fixed and changes only validation raw reading, so the numeric fixture does not switch without explanation.
Derive the baseline in four named moves
- 1
Name the input. The chapter baseline is 21.45 deg C.
- 2
Name the relationship. corrected = raw x 1.0817308 - 2.379808
- 3
Substitute with units. 21.45 x 1.0817308 - 2.379808 = 20.823 deg C
- 4
Read the result. Keep the unit beside the value. Use it only inside the technical boundary on this page.
Predict, then change validation raw reading
Try Predict the direction of corrected = raw x 1.0817308 - 2.379808. Test another validation raw reading, then compare corrected reading.
Observe A third point can expose curvature that the two fitted endpoints cannot represent. Reset validation raw reading to 21.45 and compare corrected reading.
Explain A third point can expose curvature that the two fitted endpoints cannot represent.
Check yourself
What should you do before trusting a moved-control result?
What does this small model leave out?
Fit corrected = raw × scale + offset from raw 2.20 at 0 °C and raw 43.80 at 45 °C, then test the unused raw 21.45 point against 22.5 °C.
The fitted scale and offset are 1.0817308 and -2.379808, yet the validation result is 20.823 °C—an error of 1.677 °C against a 0.5 °C limit.
Two endpoints force a straight line through the calibration baths but cannot represent mid-range curvature; an independent third point exposes that model error.
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’s1.0817and-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.
Technical boundaries: This three-reading exercise excludes reference-instrument uncertainty, repeatability, hysteresis, chamber gradients, ageing drift, humidity coupling, sample size, and uncertainty propagation.