Drawing conclusions from evidence (age 12+)

Activities to try

1. 1

   Error bench: inject each error type and watch the data respond

   Why it works: Systematic and random error are diagnosed by how they move the data — an offset of the whole line versus scatter about it — and each demands a different remedy. Averaging defeats random error but is powerless against a miscalibrated instrument; a systematic zero-offset leaves the slope intact but shifts the intercept, so it must be corrected before a proportionality claim can be tested.

   1. Start from a clean results graph with a best-fit trend line.
   2. Use a systematic-error control (e.g. a zero-offset slider) that shifts the ENTIRE line parallel — every point moved the same way, like a balance that was never zeroed — and observe that the per-unit slope is preserved while the whole line moves off its original intercept.
   3. Note that for a through-origin (proportionality) claim this intercept shift matters: the offset must be corrected (recalibrated or subtracted) before checking whether the line passes through the origin.
   4. Use a random-error control (e.g. a scatter dial) that jitters points above and below the true trend.
   5. Run a 'repeat and average' action and watch random scatter shrink toward the trend line. If an offset is also switched on, the averaged points settle on the offset line, not the true line, so the systematic offset stays put however many repeats you run.
2. 2

   Classify, match, and conclude from data signatures

   Why it works: Error type is read from the data's signature, and 'evaluate' means proposing a remedy matched to that specific signature — not a generic improvement.

   1. Examine several datasets or graphs and classify each as showing systematic error (here, a zero-offset shifting the whole line parallel) or random error (scatter either side of the trend).
   2. Match each error type to its targeted remedy: systematic → recalibrate/zero, subtract the known offset, or fix the method; random → repeat and average or use a more precise instrument.
   3. Read a specific value off a graph (e.g. using a slider or gridline) and use it in a conclusion.
   4. From a set of candidate conclusions, select or construct the one that is quantitative and hypothesis-referenced, rejecting qualitative 'it went up' versions and ones that ignore the prediction.
   5. Identify an anomaly sitting off the best-fit line, and distinguish it from a line that fails to pass through the origin when it should (a systematic zero-error signature).
3. 3

   Mentor probe: diagnose and defend an error claim

   Why it works: A learner can articulate, under questioning, why a systematic offset is fixed by calibration/subtraction rather than repeats, why a constant per-unit step shows linearity but proportionality additionally requires passing through the origin, and can defend a conclusion with numbers tied to the hypothesis.

   1. Present your conclusion and have a mentor/examiner press for the specific numerical evidence behind it.
   2. Respond to a diagnostic prompt such as: 'Your line doesn't pass through the origin when it should — what kind of error is that, and would repeating fix it?'
   3. Answer follow-ups like: 'By how much does the reading change per unit — and does a constant step, on its own, establish strict proportionality (through the origin) or only a linear trend?', 'Would ten repeat readings remove a constant 2 cm zero-offset? Why or why not?', and 'If the readings instead scattered randomly by ±0.5 cm with no consistent offset, what would you do differently?'
   4. Explain how a systematic error changes a graph compared with a random error.