engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...

science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...

, and

statistics Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of ...

, replication is the repetition of an

experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome oc ...

al condition so that the variability associated with the phenomenon can be estimated.

ASTM ASTM International, formerly known as American Society for Testing and Materials, is an international standards organization that develops and publishes voluntary consensus technical standards for a wide range of materials, products, systems, an ...

, in standard E1847, defines replication as "... the repetition of the set of all the treatment combinations to be compared in an experiment. Each of the repetitions is called a ''replicate''." Replication is not the same as repeated

measurement Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared ...

s of the same item: they are dealt with differently in statistical

experimental design The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associ ...

and

data analysis Data analysis is a process of inspecting, cleansing, transforming, and modeling data with the goal of discovering useful information, informing conclusions, and supporting decision-making. Data analysis has multiple facets and approaches, enco ...

. For proper sampling, a process or batch of products should be in reasonable

statistical control Statistical process control (SPC) or statistical quality control (SQC) is the application of statistical methods to monitor and control the quality of a production process. This helps to ensure that the process operates efficiently, producing m ...

; inherent

random In common usage, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no :wikt:order, order and does not follow an intelligible pattern or combination. Ind ...

variation is present but variation due to assignable (special) causes is not. Evaluation or testing of a single item does not allow for item-to-item variation and may not represent the batch or process. Replication is needed to account for this variation among items and treatments.

Example

As an example, consider a continuous process which produces items. Batches of items are then processed or treated. Finally, tests or measurements are conducted. Several options might be available to obtain ten test values. Some possibilities are: * One finished and treated item might be measured repeatedly to obtain ten test results. Only one item was measured so there is no replication. The repeated measurements help identify

observational error Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics, an error is not necessarily a " mistake ...

. * Ten finished and treated items might be taken from a batch and each measured once. This is not full replication because the ten samples are not random and not representative of the continuous nor batch processing. * Five items are taken from the continuous process based on sound statistical sampling. These are processed in a batch and tested twice each. This includes replication of initial samples but does not allow for batch-to-batch variation in processing. The repeated tests on each provide some measure and control of testing error. * Five items are taken from the continuous process based on sound statistical sampling. These are processed in five different batches and tested twice each. This plan includes proper replication of initial samples and also includes batch-to-batch variation. The repeated tests on each provide some measure and control of testing error. Each option would call for different

methods and yield different conclusions.

Bibliography

E122-07 Standard Practice for Calculating Sample Size to Estimate, With Specified Precision, the Average for a Characteristic of a Lot or Process *
Engineering Statistics Handbook
, NIST/SEMATEK * Pyzdek, T, "Quality Engineering Handbook", 2003, . * Godfrey, A. B., "Juran's Quality Handbook", 1999, . {{DEFAULTSORT:Replication (Statistics) Design of experiments Sampling (statistics)

Example

See also

Bibliography