Random scatter versus built-in bias

Science · Scientific Inquiry · ages 22-24

Name ______________________ Date ____________

A scale reading differs by 3 g from a 180 g reference standard. What is the absolute relative error, expressed as a percentage?
- About 1.7 percent
- Exactly 3 percent
- About 183 percent
You average independent repeats with stable, zero-mean random errors and a shared fixed offset. Which contribution becomes smaller as more readings are averaged?
- The shared systematic shift of the mean
- The random uncertainty of the mean
- The scatter of each individual reading
A single nonzero reading in a null test proves a systematic offset, even when random noise is present.
Circle one: True False
A lab hides treatment identities while analysts choose their method, then reveals them after the analysis is fixed. Which risk does this procedure reduce?
- Expectation-driven analysis choices
- Random instrument noise in every reading
- Uncertainty caused by too few observations
Calibration establishes that a scale adds a fixed 2 units to every value in its tested range. Averaging 100 readings leaves this shift in the mean. How is the 2 unit contribution classified?
- A random fluctuation that averages away
- A difference caused only by rounding
- A fixed systematic offset
An uncertainty budget adds output bounds of 5, 1 and 0.2 units. Each can be reduced by the same fraction at the same cost. Which contribution should you reduce first to lower the total most?
- The 0.2 unit contribution to the bound
- The 1 unit contribution to the bound
- The 5 unit contribution to the bound
After correcting a known scale offset, a budget lists output uncertainty bounds of 0.6 g for calibration, 0.2 g for resolution and 0.1 g for temperature. Use the stated rule of adding these bounds. Enter the total bound in grams as a number.
Answer: ______________
A rose trial uses fertilizer A only on wet plots and B only on dry plots. The aim is to compare A with B. Which redesign addresses the moisture confounding?
- Keep A on wet plots and increase the number of roses
- Randomize A and B within each wet or dry zone
- Keep B on dry plots and repeat every growth measurement

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

About 1.7 percent · Divide the absolute difference by the reference value and multiply by 100: 100 × 3 / 180 = 1.666...%, or about 1.7%.
The random uncertainty of the mean · Averaging more independent readings reduces random uncertainty of the mean under these assumptions. It does not reduce individual-reading scatter or remove a shared fixed offset.
False · The predicted signal is zero, but random noise can produce a nonzero reading. Interpret the estimated signal using its uncertainty before investigating a possible systematic departure.
Expectation-driven analysis choices · Blinding makes it harder to favor a preferred treatment when choosing an analysis. It does not change instrument noise or the number of observations.
A fixed systematic offset · The calibration establishes a shared +2 shift. Because every reading contains it, their mean contains the same fixed systematic offset.
The 5 unit contribution to the bound · Under the additive-bound rule, an equal fractional reduction saves most units when applied to the largest contribution, 5 units.
0.9 · All entries are output bounds in grams. Under the stated additive-bound rule, 0.6 + 0.2 + 0.1 = 0.9 g.
Randomize A and B within each wet or dry zone · Using both fertilizers with random assignment within each moisture zone breaks their deliberate link to wet or dry conditions. More roses or repeated readings alone retain that link.