Replication (statistics)


Replication (statistics)

In engineering, science, and statistics, replication is the repetition of an experimental condition so that the variability associated with the phenomenon can be estimated. ASTM, 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 measurements of the same item: they are dealt with differently in statistical experimental design and data analysis.

For proper sampling, a process or batch of products should be in reasonable statistical control; inherent random 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.
* 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 data analysis methods and yield different conclusions.

ee also

* sample size
* test method
* design of experiments
* Degrees of freedom (statistics)
* Statistical process control

Bibliography

* ASTM 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, [http://www.itl.nist.gov/div898/handbook/]
* Pyzdek, T, "Quality Engineering Handbook", 2003, ISBN 0824746147
* Godfrey, A. B., "Juran's Quality Handbook", 1999, ISBN 007034003


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Replication — may refer to:;Science * Self replication, an organism making a copy of itself or replicating oneself * Self replicating machines * DNA replication or DNA Synthesis, the process of copying a double stranded DNA molecule * Semiconservative… …   Wikipedia

  • replication — [rep΄li kā′shən] n. [ME replicacioun < MFr replication < L replicatio < pp. of replicare: see REPLY] 1. a folding back; fold 2. a reply, or answer; esp., a reply to an answer 3. repetition of a sound; echo 4. the act of repeating,… …   English World dictionary

  • List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… …   Wikipedia

  • Degrees of freedom (statistics) — In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.[1] Estimates of statistical parameters can be based upon different amounts of information or data. The number… …   Wikipedia

  • Sampling (statistics) — Sampling is that part of statistical practice concerned with the selection of individual observations intended to yield some knowledge about a population of concern, especially for the purposes of statistical inference. Each observation measures… …   Wikipedia

  • Balanced repeated replication — is a statistical technique for estimating the sampling variability of a statistic obtained by stratified sampling. Outline of the technique # Select balanced half samples from the full sample. # Calculate the statistic of interest for each half… …   Wikipedia

  • Official statistics — on Germany in 2010, published in UNECE Countries in Figures 2011. Official statistics are statistics published by government agencies or other public bodies such as international organizations. They provide quantitative or qualitative information …   Wikipedia

  • Comparison of statistics journals — This is a comparison of peer reviewed scientific journals published in the field of statistics. Contents 1 General information 2 Impact, indexing, abstracting and reviewing 3 Notes 4 …   Wikipedia

  • Descriptive statistics — quantitatively describe the main features of a collection of data.[1] Descriptive statistics are distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aim to summarize a data set, rather than use the… …   Wikipedia

  • Mathematical statistics — is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis. The term mathematical statistics is closely related to the term statistical theory… …   Wikipedia


Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”

We are using cookies for the best presentation of our site. Continuing to use this site, you agree with this.