Accuracy Versus Precision Target Range¶

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About This MicroSim¶

The four-quadrant target diagram is the standard way this distinction gets taught, and as a static picture it is memorised in about ten seconds and understood by almost nobody.

Here, bias and scatter are two separate sliders. They are separate because they are separate ideas:

Bias shifts the centre of the dot cloud away from the true value. That is inaccuracy. The instrument is consistently wrong.
Scatter controls how widely the dots spread around wherever that centre happens to be. That is imprecision. The instrument is unreliable one reading at a time.

You can produce all four quadrants yourself by moving two sliders, which is a much stronger claim than being shown four pictures.

The Calibrate button is the payoff. It measures the bias in the readings you have taken and subtracts it from every future reading. The bias collapses. The scatter does not move at all. That is the whole reason the two words exist.

How to Use¶

Set Bias and Scatter, then press Take 1 reading or Take 20.
Watch the target: dots fade with age, a red crosshair marks the mean of the readings, and a dashed orange circle shows one standard deviation.
Read the statistics panel. True value and mean of readings are printed as separate lines with the gap between them labelled bias, because that gap is what bias means.
Press Calibrate, then take twenty more readings. Compare the bias before and after. Then compare the scatter before and after.
The four preset buttons jump straight to each quadrant with a real-sensor description.

Iframe Embed Code¶

You can add this MicroSim to any web page by adding this to your HTML:

<iframe src="https://iowerx.github.io/pi-env-monitor/sims/accuracy-versus-precision-targets/main.html"
        height="602px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan¶

Grade Level¶

6-12

Duration¶

15-20 minutes

Bloom's Taxonomy Level¶

Analyze (L4)

Prerequisites¶

Reading a histogram
Knowing what an average is

Activities¶

Exploration (5 min): Press each of the four presets in turn. For each one, say out loud whether the sensor is accurate, precise, both or neither - before reading the verdict.
Guided practice (6 min): Choose Uncalibrated. Take 20 readings and write down the bias and the scatter. Press Calibrate, take 20 more, and write both down again. Which number changed?
Analysis (5 min): Set bias to 0 and scatter to 8. Take 1 reading, then 20, then 20 more. Does taking more readings make the average better? Does it make any single reading better?

Assessment¶

Predicts which fault a described sensor has before running it.
States that calibration repairs bias and cannot repair scatter.
Explains why averaging helps an imprecise sensor but not an inaccurate one.

References¶

JCGM 100:2008, Guide to the Expression of Uncertainty in Measurement (GUM) - the standard treatment of measurement error.
NIST/SEMATECH e-Handbook of Statistical Methods: measurement process characterization - bias and precision defined and worked through.
Wikipedia: Accuracy and precision
Wikipedia: Calibration