11. Measurement and data processing

11. Measurement and data processing

11.1 Uncertainties and errors in measurement and results

Nature of science:

• Making quantitative measurements with replicates to ensure reliability - precision, accuracy, systematic, and random errors must be interpreted through replication.

Understandings:

• Qualitative data includes all non-numerical information obtained from observations not from measurement.

• Quantitative data are obtained from measurements, and are always associated with random errors/uncertainties, determined by the apparatus, and by human limitations such as reaction times.

• Propagation of random errors in data processing shows the impact of the uncertainties on the final result.

• Experimental design and procedure usually lead to systematic errors in measurement, which cause a deviation in a particular direction.

• Repeat trials and measurements will reduce random errors but not systematic errors.

Applications and skills:

• Distinction between random errors and systematic errors.

• Record uncertainties in all measurements as a range (±) to an appropriate precision.

• Discussion of ways to reduce uncertainties in an experiment.

• Propagation of uncertainties in processed data, including the use of percentage uncertainties.

• Discussion of systematic errors in all experimental work, their impact on the results and how they can be reduced.

• Estimation of whether a particular source of error is likely to have a major or minor effect on the final result.

• Calculation of percentage error when the experimental result can be compared with a theoretical or accepted result.

• Distinction between accuracy and precision in evaluating results.

11.2 Graphical techniques

Nature of science:

• The idea of correlation - can be tested in experiments whose results can be displayed graphically.

Understandings:

• Graphical techniques are an effective means of communicating the effect of an independent variable on a dependent variable, and can lead to determination of physical quantities.

• Sketched graphs have labelled but unscaled axes, and are used to show qualitative trends, such as variables that are proportional or inversely proportional.

• Drawn graphs have labelled and scaled axes, and are used in quantitative measurements.

Applications and skills:

• Drawing graphs of experimental results including the correct choice of axes and scale.

• Interpretation of graphs in terms of the relationships of dependent and independent variables.

• Production and interpretation of best-fit lines or curves through data points, including an assessment of when it can and cannot be considered as a linear function.

• Calculation of quantities from graphs by measuring slope (gradient) and intercept, including appropriate units.

11.3 Spectroscopic identification of organic compounds

Nature of science:

• Improvements in instrumentation - mass spectrometry, proton nuclear magnetic resonance and infrared spectroscopy have made identification and structural determination of compounds routine.

• Models are developed to explain certain phenomena that may not be observable—for example, spectra are based on the bond vibration model.

Understandings:

• The degree of unsaturation or index of hydrogen deficiency (IHD) can be used to determine from a molecular formula the number of rings or multiple bonds in a molecule.

• Mass spectrometry (MS), proton nuclear magnetic resonance spectroscopy (¹H NMR) and infrared spectroscopy (IR) are techniques that can be used to help identify compounds and to determine their structure.

Applications and skills:

• Determination of the IHD from a molecular formula.

• Deduction of information about the structural features of a compound from percentage composition data, MS, ¹H NMR or IR.