Scientific Investigation, Data Analysis and Evidence-Based Reasoning
This section covers scientific investigation and data analysis. The exam tests whether you can design a test, quantify uncertainty, distinguish precision from accuracy, and judge whether evidence supports a claim.
Core rules
- A testable hypothesis makes predictions that could be shown wrong. Define variables, controls and sampling strategy before collecting data.
- Replicates estimate natural variability; calibration checks instruments against known standards; blanks and duplicates expose contamination or drift.
- Precision is reproducibility; accuracy is closeness to the true value. Random errors scatter results; systematic errors shift them.
- Independent uncertainties combine in quadrature: the square root of the sum of squares.
- Correlation does not establish causation. A plausible mechanism, temporal order and controlled comparison strengthen causal inference.
Worked example
Two tide gauges record trends of 3.1 plus or minus 0.4 mm/yr and 1.9 plus or minus 0.4 mm/yr over the same period. The difference is 1.2 mm/yr. The combined uncertainty is the square root of 0.4 squared plus 0.4 squared, about 0.57 mm/yr. The difference is about 2.1 combined uncertainties, suggestive but not decisive at the 95 percent level. Before attributing local sea-level rise, check datum shifts, instrument changes and common-mode errors. Reasoning: compare the effect size with its uncertainty, then audit possible systematic errors.
Traps
- Reporting many decimal places as if that equals accuracy.
- Treating a high R-squared value as proof of causation.
- Extrapolating beyond the calibrated range of an instrument or model.
- Adding independent uncertainties linearly instead of in quadrature.
- Ignoring sampling bias, such as measuring only fair-weather days.