Precision in processed data by Chris Paine Bioknowledgy
Processing data in Biology! Simply calculating a mean and standard deviation on raw data is not always the best solution: ! If we are dealing with enzymes a reaction rate (1/time) is often a better way to present and analyse data ! If we have a starting mass/length and then after time has elapsed an ending mass/length then % change ([end – start] / start x 100) gives a better comparisonN.B. practical examples of both calculations will be given during the course
What about precision and uncertainty?! Your raw data had units and uncertainty what about the processed data? There are two options: ! Workout a reasonable level of precision and uncertainty and justify it when you write up DCP ! If you can’t workout a reasonable level of precision then say so and again explain your reasoning
A general rule of thumb! If your raw data has a maximum of 3 significant figures then your processed data should have no more than 3 significant figures too! Uncertainty is expressed as decimal places and should be based upon the maximum significant figures found in the raw data
% Change in mass example! If your raw numbers show an initial mass of 3g (±1g) and a final mass of 106g (±1g)! The percent change would be to 3 sf (significant figures) as your raw data has a maximum of 3 sf (i.e. 106g) The percentage change is calculated as 34.333333% (0.3 recurring) = [end – start] / start * 100 = [106 – 3] / 3 * 100! The largest percent change is 34.3% (expressed to 3 sf) therefore the precision can be expressed to 1 dp
Reaction rate example! If your raw times vary from 10s (±0.5s) to 332s (±1s)! The reaction rate again should be expressed as 3sf as your raw data has a maximum of 3 sf (i.e. 106g) reaction rate (1/s * 1000) = 1/332 * 1000 = 3 reaction rate (1/s * 1000) = 1/10 * 1000 = 100 In this case the scaling factor produces reaction rates between 3 and 100 therefore 3sf produces a precision of 0 dp N.B. 1000 is a scaling factor used to avoid decimal places. Scaling factors are optional, you may include one of an appropriate value where deemed necessary.
What about uncertainty?! Uncertainty can be expressed on raw data - this should be sufficient for equipment error analysis! Uncertainty gets more complicated other forms of processed data, as it varies from measurement to measurement, the general rule is to omit uncertainty on processed data! If the mean and standard deviation are included then the uncertainty will reflect that of the data the calculations are based on