Accidental error is reduced with a more precise instrument (measurements become thinner) and with more repeatability or reproducibility (precision). Consider a common laboratory experiment in which you must determine the acid content in a vinegar sample by observing the volume of sodium hydroxide solution needed to neutralize a certain volume of vinegar. You experience it and you get value. Just to be on the safe side, repeat the process on another identical sample of the same bottle of vinegar. If you have actually done this in the laboratory, you will know that it is very unlikely that the second study will produce the same result as the first. In fact, if you do a series of replication tests (i.e. identical in all respects), you will probably get scattered results. Suppose you did an experiment to determine the water`s boiling point and get a value of 99.3 degrees Celsius. Uncertainty in a given measure is the confidence interval around the measured value, so the measured value is sure not to be outside that specified interval. Uncertainties can also be expressed with a probability. In this case, the measured value has the probability of being within the confidence interval. A particularly common example is a standard deviation (SD) for the average of a random sample.

The « value ± 1 SD » format means that if you repeat the measurement, 68% of the time your new measurement falls in that interval. « The smaller the difference between the measured value of repeated measurements of the same amount, the greater the accuracy. » To calculate the percentage error for measuring aluminum density, we can replace the indicated values of 2.45 g/cm3 with the experimental value and 2.70 g/cm3 with the assumed value. The accepted value is a number or value that scientists and the public consider to be true. An individual measurement may be accurate or imprecise depending on the proximity of the actual value. Suppose you are doing an experiment to determine the density of an aluminum sample. The accepted value of a measurement is the true or correct value based on a general agreement with a reliable reference. For aluminum, the accepted density is 2.70 g/cm 3. The experimental value of a measurement is the value measured during the experiment. Suppose you determine in your experiment an experimental aluminum density value of 2.42 g/cm3. The error of an experiment is the difference between experimental values and accepted values. Accuracy is the proximity of a measure to fair value for this measurement.

The accuracy of a measurement system refers to the proximity of the concordance between repeated measurements (repeated under the same conditions).