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Systematic Errors, Calibration & Controls (IPhO Experimental)

IPhO experimental lesson on systematic errors: identifying bias, calibrating instruments, designing controls, and writing strong evaluations.

  • International Physics Olympiad preparation

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Repeating measurements reduces random uncertainty, but it does not fix bias. Many IPhO experiment deductions come from spotting the likely systematic errors, stating their direction of effect, and proposing a calibration or control that would remove them.

Prerequisites (quick refresh)

1. Definitions (Must Know)

  • Random uncertainty: scatter between repeats (noise). Reduced by repeats/averaging.
  • Systematic error: consistent bias (offset or scale factor). Not reduced by repeats.
  • Zero error (offset): instrument reads x₀ when true value is 0.
  • Scale factor error (gain): instrument readings are multiplied by a factor (e.g. “1.02 times true”).
  • Calibration: comparing an instrument against a reference standard to correct offset/gain.
  • Control variable: quantity held constant to isolate the effect being tested.
  • Method of reversal: perform the measurement in two opposite configurations to cancel a bias.

2. Key Ideas (What Earns Marks)

High-scoring evaluation statements
  • Name the systematic error, not just “human error”.
  • State direction of effect: “would make g larger/smaller”.
  • Propose a concrete fix: calibration, reversal, null method, shielding, or a changed measurement method.
  • Separate random vs systematic improvements (more repeats helps only random).

3. Detailed Explanations

A. The two most common systematic shapes

  1. Offset: xₘₑₐₛ = xₜᵣᵤₑ + x₀
    Fix: measure x₀ and subtract; or use a difference method that cancels x₀.

  2. Scale factor: xₘₑₐₛ = k xₜᵣᵤₑ
    Fix: determine k with known standards (two-point calibration), then divide by k.

Many real instruments have both: xₘₑₐₛ = kxₜᵣᵤₑ + x₀.

B. Controls: what “keep everything else constant” really means

Controls are not just “do it carefully”. They are design choices:

  • keep geometry fixed (same alignment, same contact points)
  • keep environment fixed (temperature, airflow, vibrations)
  • keep the method fixed (same timing method, same person, same threshold definition)
  • if you cannot keep it constant, measure it and correct for it

C. Reversal cancels bias

If a bias changes sign under reversal, averaging the two configurations cancels it.

Examples:

  • swap current direction to detect/average out a stray magnetic field
  • flip a component to cancel parallax alignment bias
  • reverse the motion direction to check for friction asymmetry

4. Common Mistakes

  • Writing “reaction time” as the main issue even when timing is automated (or negligible).
  • Claiming “take more readings” fixes a systematic error.
  • Listing 5 vague improvements instead of 1 to 2 concrete, high-impact ones.
  • Not stating direction of effect (this is often an easy mark).
  • Calibrating with only one point when both offset and gain errors are plausible.

5. Exam Tips

  1. In your conclusion, include one sentence on whether results agree with theory within uncertainty.
  2. In evaluation, name one dominant systematic and one dominant random uncertainty separately.
  3. If you suspect an offset, design a measurement where the true value should be zero (baseline check).

6. Worked Examples (use Toggle)

1) Two-point calibration: correct both offset and scale factor

Suppose a temperature sensor reports Tₘₑₐₛ but may have both an offset and gain error:

Tₘₑₐₛ = kTₜᵣᵤₑ + T₀.

You measure two reference points:

  • ice-water: Tₜᵣᵤₑ = 0°C gives Tₘₑₐₛ = 1.2°C
  • boiling water: Tₜᵣᵤₑ = 100°C gives Tₘₑₐₛ = 103.0°C

Then

1.2 = k(0) + T₀ ⇒ T₀ = 1.2,
103.0 = k(100) + 1.2 ⇒ k = 1.018.

So the corrected temperature is

Tₜᵣᵤₑ = (Tₘₑₐₛ - 1.2)/1.018.
2) Method of reversal: cancel a stray magnetic field in a coil experiment

You are measuring the magnetic field from a coil using a Hall probe. A stray background field B_b adds:

Bₘₑₐₛ = B_coil + B_b.

Reverse the current so the coil field flips sign:

B₊ = +B_coil + B_b, B₋ = -B_coil + B_b.

Subtract:

B_coil = (B₊ - B₋)/2,

and the background cancels automatically. This is a clean, mark-winning control.

7. Mind Stretchers (use Toggle)

1) Direction of effect: identify whether the bias pushes your parameter up or down

You measure a pendulum period T with a stopwatch. Your reaction time adds a constant delay τ to each timing, so the measured period is larger:

Tₘₑₐₛ = Tₜᵣᵤₑ + τ.

If you compute g = 4π² L/T², does this systematic make your g too large or too small?

Hint: g ∝ 1/T².

8. Practice

  1. Your voltmeter reads 0.03 V when the leads are shorted. Identify the systematic error type and state a correction.
  2. In a friction experiment, the cart moves slightly slower each run as the track warms. Is this random or systematic? Propose a control or redesign.
  3. You suspect a constant background light level affects a photodiode reading. Describe a “baseline subtraction” method.

Back to IPhO Experimental Skills Hub

Answer key and feedback

  • If measured L is systematically too large while T is unaffected, g = 4π²L/T² is systematically too large by the same fractional amount. State the sign before applying a correction.
Syllabus and review details

No official syllabus alignment is listed for this lesson.