Accuracy and precision Knowledge-Based Study

Study notes

1. Defining Accuracy and Precision

   In scientific measurement, the terms accuracy and precision describe distinctly different aspects of measurement quality.

   • Accuracy: Reflects how close an experimental value or the average of several measurements is to the true, accepted reference value. An accurate measurement has minimal systematic deviation from the standard.
   • Precision: Reflects the degree of agreement or reproducibility among repeated measurements obtained under identical conditions. A precise set of measurements yields values clustered tightly together, regardless of whether they match the accepted value.

   A classic analogy involves a target: hitting the exact center (bullseye) demonstrates accuracy, whereas grouping multiple shots closely together in the same spot demonstrates precision.

   Sources of Error in Measurements

   The distinction between accuracy and precision is directly tied to the types of experimental error present in laboratory work:

   • Systematic Errors: These errors consistently skew measurements in one specific direction (always too high or always too low). Examples include an uncalibrated analytical balance, a buret with an incorrectly marked scale, or persistent parallax error. Systematic errors directly degrade accuracy while precision may remain high.
   • Random Errors: These errors arise from uncontrollable, unpredictable fluctuations in experimental conditions, such as slight ambient temperature shifts, mechanical vibrations, or human visual limitation in estimating the final digit. Random errors primarily limit precision by causing scatter in data.

   Repeating trials and calculating an average helps minimize the impact of random errors, whereas identifying and eliminating systematic errors restores measurement accuracy.

   Quantitative Evaluation in the Laboratory

   Chemists quantitatively assess both parameters using distinct mathematical tools:

   • Evaluating Accuracy: Accuracy is commonly assessed using percent error, calculated as:

   Percent Error = (|Experimental Value - Accepted Value| / Accepted Value) × 100%

   A lower percent error indicates greater accuracy.

   • Evaluating Precision: Precision is assessed by examining the variation among multiple trials, often reported as the range (difference between the maximum and minimum values) or the standard deviation of the dataset. A smaller range or standard deviation signifies higher precision.

   Example Scenario: A sample has an accepted mass of 5.000 g. A student measures the mass three times, recording 4.812 g, 4.811 g, and 4.813 g. Because the values are closely grouped, the technique shows high precision; however, because the average is significantly lower than 5.000 g, the measurement displays poor accuracy, suggesting a systematic error such as an improperly tared balance.