Scientific Methods and Experimental Skills: Experimental Design, Data Analysis, Error Analysis, Modeling, Scientific Reasoning
This domain is assessed inside every other task. The Abitur expects a described setup, a clean data table, a linearised graph with slope and unit, an uncertainty statement, and a critical comment on the model.
Experimental design
State hypothesis, independent and dependent variable, and the quantities held constant. Match the instrument to the effect: a stopwatch read to ±0.2 s is useless for one swing but adequate for ten. Repeat measurements and vary the parameter over the widest safe range.
Data analysis
Tables with symbol, unit and consistent significant figures. Linearise before fitting: T² against l, U_G against f, ln A against t, p against 1/V, s against t². The slope carries the unit of y/x and the physics - for T² = (4π²/g)·l the slope is 4π²/g. Report R² and check the intercept against theory.
Uncertainty
Random errors average out; systematic errors (zero offset, calibration) do not. For z = x·y or x/y, relative uncertainties add; for z = xⁿ, multiply by |n|. Quote x ± Δx with matching decimals and a unit.
Worked example
A pendulum with l = 0.800 ± 0.002 m gives T = 1.795 ± 0.005 s from ten swings. Then g = 4π²·l/T² = 4π²·0.800/1.795² = 9.80 m/s². Relative uncertainties: 0.002/0.800 = 0.25 % and 2·(0.005/1.795) = 0.56 %; combined in quadrature, 0.61 %. So Δg = 0.06 m/s² and g = (9.80 ± 0.06) m/s², consistent with 9.81 m/s².
Modelling and critique
Name the idealisations: point mass, massless spring, frictionless track, ideal gas, negligible air resistance. State where each holds and which observation would falsify the model. Order-of-magnitude checks and unit checks catch most slips before they cost marks.
Traps
- Quoting a slope without a unit.
- Averaging away a systematic offset.
- Over-precise results such as g = 9.80347 m/s².
- Presenting R² = 0.99 as proof that the model is correct.
- Omitting how a quantity was actually measured.