Systematic Error, Controls and the Design of a Measurement · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Random scatter versus built in bias

Science · Scientific Inquiry · ages 22-24
Name ______________________   Date ____________

  1. A scale misses by 3 grams on a 180 gram standard. What is the relative error?

    • About 1.7 percent
    • Exactly 3 percent
    • About 183 percent

  2. You repeat a measurement many times and average. Which part of the error does this shrink?

    • The systematic offset
    • The random scatter
    • Both parts equally

  3. In a null test the signal must read zero, so a nonzero answer exposes a systematic offset.

    Circle one:   True   False

  4. A lab hides the group labels until the analysis is finished. What danger does this guard against?

    • Expectation steering judgment toward a wanted result
    • Random noise in the instruments
    • Too few readings in the sample

  5. You average one hundred readings and a 2 unit offset remains exactly in place. What kind of error is it?

    • Random, because averaging failed
    • A mistake in arithmetic
    • Systematic, because it survived averaging

  6. Your error budget lists sources of 5 units, 1 unit, and 0.2 units. Which do you attack first?

    • The 0.2 unit term, to be thorough
    • The 1 unit term, as a compromise
    • The 5 unit term, because it dominates the total

  7. A scale misses by 2 grams on a 200 gram standard. Relative error is the miss divided by the expected value, in percent. Type the relative error.

    Answer: ______________

  8. A rose trial plants fertilizer A on the wet side of the field and fertilizer B on the dry side. What is the right fix?

    • Average more roses on each side
    • Randomize plots across the field and keep an untreated control group
    • Water the A side even more
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Random scatter versus built in bias W1-mt_rGjB_JcsLJ-s1

  1. About 1.7 percent · Relative error divides the miss by the expected value: 3 over 180 is about 1.7 percent.
  2. The random scatter · Averaging tames random scatter, while a built in offset sits exactly where it started.
  3. True · The zero expectation leaves any nonzero reading with only one explanation: bias.
  4. Expectation steering judgment toward a wanted result · Blinding stops researchers from reading ambiguous results with bias.
  5. Systematic, because it survived averaging · Random scatter would have shrunk, so a survivor that repeats every time is systematic.
  6. The 5 unit term, because it dominates the total · The dominant term decides the answer, so shrinking small ones barely moves the total.
  7. 1 · 2 over 200 is one hundredth, which is 1 percent.
  8. Randomize plots across the field and keep an untreated control group · Water is a systematic difference here, so only randomization plus a control separates it from the fertilizer effect.
Worksheet · LightMySky