What are the best ways to report uncertainties and errors in a lab report?

1 What are uncertainties and errors?

Uncertainties and errors are the deviations of your measurements or calculations from the true or accepted values. They can arise from various sources, such as limitations of your instruments, human errors, random variations, or systematic biases. Uncertainties and errors can be classified into two types: random and systematic. Random errors are unpredictable and vary in magnitude and direction. They can be reduced by increasing the number of trials or using more precise instruments. Systematic errors are consistent and have a definite direction. They can be caused by faulty calibration, incorrect methods, or environmental factors. They can be corrected by identifying and eliminating the sources of error.

2 How to estimate uncertainties?

To estimate uncertainties, you need to use appropriate methods and units to express the range or interval of possible values that your measurements or calculations can have. Depending on the type and level of data you have, there are different methods you can use. For example, if you measure the length of a rod with a ruler that has millimeter divisions, your absolute uncertainty is ±0.5 mm. Alternatively, if you measure the mass of a sample 10 times and get an average of 12.3 g and a standard deviation of 0.2 g, your relative uncertainty is ±0.2/12.3 = 0.016 or 1.6%. Additionally, if you calculate the density of a sample using the formula d = m/v, where m is the mass and v is the volume, and both have uncertainties, you can use the formula d = sqrt[(dm/m)^2 + (dv/v)^2] to find the uncertainty of the density. Estimating uncertainties helps provide valuable insights for improving accuracy and reliability in your measurements and calculations.

3 How to report uncertainties?

To report uncertainties, you should use consistent and clear formats and conventions to indicate the level of confidence and significance of your results. For example, use the same number of decimal places or significant figures for your values and uncertainties, brackets, parentheses, or plus-minus signs to show the uncertainty, scientific notation or prefixes to avoid ambiguity or confusion, and percentage or fractional uncertainties to compare or combine results with different units or orders of magnitude. For instance, if you measure the mass of a sample as 12.3 ± 0.2 g and the volume as 10.5 ± 0.1 mL, you can write the uncertainties as 1.6% and 1.0%, respectively, or 0.016 and 0.010, respectively.

4 How to report errors?

To report errors, you should use appropriate methods and tools to analyze and evaluate the sources and effects of your uncertainties and errors on your results and conclusions. Graphs and charts are useful for visualizing and comparing data and uncertainties; for instance, error bars, scatter plots, or histograms can show the distribution and variation. Statistical tests and calculations can also be used to quantify and interpret data and uncertainties; for example, mean, median, mode, range, standard deviation, standard error, confidence intervals, t-tests, ANOVA, chi-square tests, correlation, or regression can measure and compare the central tendency, dispersion, difference, association, or relationship. Additionally, error analysis is necessary to identify and correct sources and types of errors; calibration curves, blank samples, control samples, reference standards, or quality assurance procedures should be used to check and adjust instruments, methods or samples for systematic errors.