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The branch of [[Mathematical statistics|mathematical statistics]] dealing with the rational organization of measurements subject to random errors. One usually considers the following scheme. A function <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031390/d0313901.png" /> is measured with random errors, these being dependent on unknown parameters (the vector <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031390/d0313902.png" />) and on variables <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031390/d0313903.png" />, which, at the experimenter's choice, may take values from some admissible set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031390/d0313904.png" />. The purpose of the experiment is usually either to estimate all or some of the parameters <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031390/d0313905.png" /> or functions of them, or else to test certain hypotheses concerning <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031390/d0313906.png" />. The purpose of the experiment is used in formulating a criterion for the design's optimality. The design of an experiment is understood to mean the set of values given to the variables <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/d/d031/d031390/d0313907.png" /> in the experiment.
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The branch of [[Mathematical statistics|mathematical statistics]] dealing with the rational organization of measurements subject to random errors. One usually considers the following scheme. A function $f(\theta,x)$ is measured with random errors, these being dependent on unknown parameters (the vector $\theta$) and on variables $x$, which, at the experimenter's choice, may take values from some admissible set $X$. The purpose of the experiment is usually either to estimate all or some of the parameters $\theta$ or functions of them, or else to test certain hypotheses concerning $\theta$. The purpose of the experiment is used in formulating a criterion for the design's optimality. The design of an experiment is understood to mean the set of values given to the variables $x$ in the experiment.
  
 
====References====
 
====References====
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  V.V. Nalimov,  N.A. Chernova,  "Statistical methods of designing extremal experiments" , Moscow  (1965)  (In Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  V.V. Fedorov,  "Theory of optimal experiments" , Acad. Press  (1972)  (Translated from Russian)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  C. Hicks,  "Basic principles of experiment design" , Moscow  (1967)  (In Russian; translated from English)</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top">  D. Finney,  "An introduction to the theory of experimental design" , Univ. Chicago Press  (1960)</TD></TR></table>
 
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  V.V. Nalimov,  N.A. Chernova,  "Statistical methods of designing extremal experiments" , Moscow  (1965)  (In Russian)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  V.V. Fedorov,  "Theory of optimal experiments" , Acad. Press  (1972)  (Translated from Russian)</TD></TR><TR><TD valign="top">[3]</TD> <TD valign="top">  C. Hicks,  "Basic principles of experiment design" , Moscow  (1967)  (In Russian; translated from English)</TD></TR><TR><TD valign="top">[4]</TD> <TD valign="top">  D. Finney,  "An introduction to the theory of experimental design" , Univ. Chicago Press  (1960)</TD></TR></table>

Revision as of 14:43, 14 September 2014

The branch of mathematical statistics dealing with the rational organization of measurements subject to random errors. One usually considers the following scheme. A function $f(\theta,x)$ is measured with random errors, these being dependent on unknown parameters (the vector $\theta$) and on variables $x$, which, at the experimenter's choice, may take values from some admissible set $X$. The purpose of the experiment is usually either to estimate all or some of the parameters $\theta$ or functions of them, or else to test certain hypotheses concerning $\theta$. The purpose of the experiment is used in formulating a criterion for the design's optimality. The design of an experiment is understood to mean the set of values given to the variables $x$ in the experiment.

References

[1] V.V. Nalimov, N.A. Chernova, "Statistical methods of designing extremal experiments" , Moscow (1965) (In Russian)
[2] V.V. Fedorov, "Theory of optimal experiments" , Acad. Press (1972) (Translated from Russian)
[3] C. Hicks, "Basic principles of experiment design" , Moscow (1967) (In Russian; translated from English)
[4] D. Finney, "An introduction to the theory of experimental design" , Univ. Chicago Press (1960)
How to Cite This Entry:
Design of experiments. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Design_of_experiments&oldid=19314