Accuracy & Precision

1. Calculate the percentage error of a result

2. Define and distinguish between “accuracy” and “precision”

3. Characterize the accuracy and precision of experimental results

Accuracy

Accuracy: Tells us how close a measurment is to the true value (literature value).

Measuring Accuracy

Absolute Error: The difference between the experimental value and literature value.

Accuracy can also be measured using percentage error (relative error), which is computed like so:

Danger

Remember to include the sign for both absolute error and percentage error. A positive percentage error implies that the experimental value was larger, while a negative percentage error implies the experimental value was smaller.

Types of Inaccuracy

Systematic Error: An issue that will consistently impact results in the same way (i.e. if a scale is broken and always measures a value 5 grams over the actual value).

Random Error: Meanwhile, a random error doesn’t impact an experiment in a consistent way (i.e. fluctuating scale readings, varying humidity/pressure in a room impacting results).

Fortunately, repeating an experiment many times essentially eliminates random error. However, multiple trials will not eliminate systematic error.

Precision

Precision: The smallest difference that a measuring device can measure (i.e. an object measured with a scale with precision of ±0.1g would have a true mass in the ±0.1g range of the scale’s reading).

Measuring Precision

Precision can be measured with relative precision which is computed as follows:

Absolute Margin of Error (MoE): The range of possible values.

Relative Margin of Error: The range as the precentage of the final result.

Note

Relative precision can be increased either by increasing the amount of material measured or using a measuring device with more precision.

So Is My Result Accurate?

A measurement is accurate if it is within the experimental MoE of the literature value. For instance, if an obelisk of processed meat has a true mass of 50.001g, but was measured to have a mass of 50.0±0.1g, it would be considered accurate, because 50.001g is inside the range 50.0±0.1g. Likewise, if it was measured to have a mass of 100±80g, the resutl would be considered accurate since 50.001 falls inside that range. However if the mass was measured to be 30.000±0.001g, the result would precise, but inaccurate because 50.001 does not fall inside that range.