Measurement Accuracy and Precision

Central Value of a Set

  • Definition of central value: The central value of a set should be determined to understand the data accurately.

Accuracy

  • Definition: Accuracy indicates the closeness of the measurement to the true or accepted value.

  • Expression of Accuracy: It is expressed by the difficulty to determine because the true value is usually unknown.

Precision

  • Definition: Precision refers to the agreement among several results obtained from repeated measurements. It indicates consistency across those measurements.

  • Example: Two measurements may have the same way of accuracy but varying precision.

    • Measurements: 4.13, 13.1, 12.9, 13.0, 13.0 show good precision but varying accuracy.

    • In contrast, measurements like 11, 10, 9, 9, 11, 1, 13 showcase good accuracy but poor precision.

    • Notation: Measurement 'A' has poor precision but good accuracy, whereas measurement 'B' has good precision but poor accuracy.

    • True value is considered to be 11.

Determinate Errors vs. Indeterminate Errors

Determinate Errors (Systematic Errors)

  • Characteristics:

    1. Have a definite value.

    2. Possess an assignable cause.

    3. Exhibit the same magnitude for replicate measurements made under identical conditions.

    4. Lead to bias in measurement results.

  • Example of Determinate Errors:

    • Data example: 13, 13.1, 12.9, 13.0, 13.0 indicates that errors are consistent in one direction.

Indeterminate Errors (Random Errors)

  • Characteristics:

    1. Unpredictable nature.

    2. Non-correctable through standard correction methods.

    3. Can be reduced by averaging multiple measurements.

    4. Can be treated mathematically using statistical methods.

    5. Always present in measurements.

  • Question: Why can't indeterminate errors be eliminated?

    • Answer: Because they do not have an assignable cause.

Types of Determinate Errors

Categories:

  1. Instrumental Errors: Errors resulting from the measuring instrument itself.

  2. Method Errors: Errors arising from the method of measurement used.

  3. Personal Errors: Errors that occur due to individual actions or subjective interpretation while measuring.

Figures of Merit (Performance Characteristics of Instruments)

  • Definition: A number derived from measurements used to evaluate an instrument or analytical technique.

  • Figures of Merit include:

    • Accuracy

    • Precision

    • Bias

    • Sensitivity

    • Detection Limit

    • Dynamic Range

    • Minimal Selectivity

    • Linearity

Measurement and Errors

  • The concept of absolute measurement:

    • No analytical instrument measurement is absolute, meaning that:

    1. There are two types of errors: determinate and indeterminate (random).

    2. Systematic errors have an assignable cause that can be traced and corrected, whereas random errors have causes that cannot be traced and corrected.

  • Error Definition: Refers to the difference between a measured value and the "true" or known value.

  • Estimated uncertainty: Error often denotes the estimated uncertainty associated with a measurement or experiment in implied form.

  • Realization: It is impossible to perform a measurement without error, emphasizing that errors are inevitable.

Improving Measurement Reliability

  • Recommendations for reliability and variability in measurements:

    • Measurements must be carried out in replicates (multiple instances of the same measurement under identical conditions).

    • Replicates should celebrate samples of the same kind and be processed through analysis in an exact manner.