This standard specifies the commonly used experimental design terms. This standard applies to the experimental design terms involved in various standards and technical documents. It should also be used as a reference for the experimental design terms involved in various research reports and works. GB/T 3358.3-1993 Statistical Terminology Part 3: Experimental Design Terms GB/T3358.3-1993 Standard download decompression password: www.bzxz.net
This standard specifies the commonly used experimental design terms. This standard applies to the experimental design terms involved in various standards and technical documents. It should also be used as a reference for the experimental design terms involved in various research reports and works.

National Standard of the People's Republic of China
Statistical terms
Part III: Terms for experimental design
Terms for statistics
Part I: Terms for experimental designSubject content and scope of application
This standard specifies the commonly used experimental design terms. GB/T3358.3-93
Replaces GB3358
This standard applies to the experimental design terms involved in various standards and technical documents. The experimental design terms involved in various research reports and works should also be used as a reference.
2 Referenced standards
GB/T3358.1 Statistical terms Part I - General statistical terms
3 General terms
3.1 Design of experiments, experimental design The planning of experiments mainly refers to the selection of factors to participate in the experiment, the determination of the levels of each factor, and the selection of the level combination to be tested. 3.2 Factor factor
Controllable causes or their combinations that may affect the test results and are investigated in the test. Synonyms: factor
3.3 Level level
A given value of a factor, or a specific measure, or a specific state. Synonyms: level
Example: In the test to investigate the effects of variety, fertilizer amount, and field management measures on crop yield, variety, fertilizer amount, and field management measures are all factors; each variety, fertilizer amount, and field management measure used is a level of the corresponding factor. 3.4
Treatment
A combination of factor levels implemented in the test. 3.5 Experimental unit experiment unit implementation---the combination of raw materials, equipment, operators, time and space conditions, etc. required for a treatment. 3.6 Block
All experimental units are divided into several groups according to the similarity of other experimental conditions other than treatment. Each group is called a block. The number of experimental units in a block is called the block size (blocksize). Note: Blocks can be regarded as factors, called block factors. Each specific block is one of its levels. 3.7 Experimental error Experimental error Error in experimental results caused by reasons other than factors and block factors (including various random reasons) 3.8 Complete replication replication
Approved by the State Administration of Technical Supervision on August 28, 1993 and implemented on May 1, 1994
GB/T 3358.3-~93
All treatments in the experiment are repeated equally. In the same replication, all treatments should be implemented in the same group; for different replications, they can be implemented in different blocks. 3.9 Partial replication Partial replication Replicate some treatments.
3.10 Duplication
Repeated implementation of a treatment under the same conditions
3.11 Randomization
The distribution of treatments to each experimental unit according to a random mechanism. Response
The expectation of the experimental results under given experimental conditions. 3.13 Main effect
A measure of the difference between the average responses of each level of a factor. The difference between the average response of all treatments at the !th level of a factor and the average response of all treatments is called the main effect of the !th level of the factor. 3.14 Interaction
A measure of the effect produced by the combination of the levels of two factors. The interaction effect between two factors is called the "two-factor interaction effect" or "first-order interaction effect". The interaction effect between three factors is called the "factor interaction effect" or "second-order interaction effect". The rest are similar. Example: Consider a two-factor experiment (A and B), A takes I levels, B takes J levels, and K complete repetitions are performed. The experimental result Y can be expressed as:
Y=+=u++++,
i = 1,2,.,I,j= 1.2,.-,J,k - 1,2,.,K=02=02=0
where e is the experimental error when A takes the ith level, B takes the ith level, and the th repetition, and its mean is zero. is the main effect of A at the ith level, is the main effect of B at the ith level, is the interaction effect of factors A and B at the :th level of A and the ,th level of B, and the expectation of Y# is the response when A takes the ;th level and B takes the th level. 3.15 confounding
Some main effects of factors, or the interaction effects between factors, are mixed with the main effects or interaction effects of other factors or block factors and cannot be distinguished.
3.16 contrast
a linear combination of parameters (e.g., main effects of factors or interactions between factors) whose coefficients are not all zero but whose sum is zero.
Example: For the example in 3.14, as long as the constant α1 and α sum to zero, 3.17 orthogonal contrastorthogonal contrasttwo contrasts whose coefficients are orthogonal.
ai is a contrast,
Example: For the example in 3.14, if the two contrasts α and > b, and αb, = 0, then they are orthogonal.
3.18 explanatory variableexplanatoryvariablea variable (or its determinant) that affects the outcome of an experiment, regardless of whether the choice of its level can be controlled by the experimenter. 3.19 response variableresponsevariable
a random variable used to represent the outcome of interest in the experiment. 82
3.20 Assumed model
assumd model
GB/T 3358.3--93
An assumed functional relationship between the response and the explanatory variable. 3.21 Residual
The difference between the test result of the response variable and the estimated value of the response. 3.22
Response surfaceresponse surface
The geometric representation of the assumed model.
3.23 Evolutionary operation (EVOP) A sequential test method that is implemented step by step in the normal production process to find the optimal value of the response. Experimental arrangement terminology
Completely randomized design A design in which all treatments are randomly assigned to each experimental unit with equal chance. Block design
A design in which all experimental units are divided into a number of blocks. 4.3 Complete block design completeblockdesign A block design in which all treatments are arranged in each block, and none of them are repeated or are equally repeated. Randomized complete block design4.4
In each block, all treatments are randomly arranged to each experimental unit according to equal chance. 4.5 Latin square
A square matrix of n rows and n columns is formed by several non-embarrassing symbols (letters or numbers), so that each symbol appears once in each row and column. Such a square matrix is ​​called an n-order Latin square.
Example: The following is a 3-order Latin square:
4.6 Latin square design Latin sqaure design The rows and columns of the n-order Latin square represent the levels of two factors respectively, and the symbols in the Latin square represent the n levels of the third factor. This three-factor experimental plan containing n experiments is called an n-order Latin square design. Example: The following is a 4-order Latin square design: row factor
column factor
The first and second factors are represented by rows and columns respectively, and the levels of the third factor are represented by A, B, C, and D. This experimental plan contains 4\-16 experiments, and its experimental conditions are (1,1,A), (1,2,B),, (4.4,C). 4.7 Orthogonal Latin square, Graeco-Latin squares If the number of ordered pairs formed by the same position of the symbols in two Latin squares of the same order do not alternate with each other, then the two Latin squares are said to be orthogonal. When the Latin squares of the same order are orthogonal to each other, the Latin squares are said to be mutually orthogonal. 83
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Example: The following two 3-order Latin squares are non-intersecting: B
4.8 Orthogonal Latin square design When there are m orthogonal n-order Latin squares, the row and column numbers of the Latin squares represent the n levels of two factors respectively. The symbols of the m Latin squares represent the levels of the other m factors respectively. This (m+2)-factor experimental plan containing n experiments is called an orthogonal Latin square design. Example: The following is a 4-factor 3-order Latin square design: Column factor
Row factor
The first factor and the second factor are represented by rows and columns respectively, the levels of the third factor are represented by A, B, and the levels of the fourth factor are represented by a, β,.
Note: In an orthogonal Latin square design, all combinations of levels of any two factors appear and only appear once. 4.9 Incomplete block design Incomplete block design The total number of treatments is greater than the block size, and each treatment appears at most once in the first block. 4.10 Balanced incomplete block design (BIB) design An incomplete block design that meets the following three conditions: (a) Each block contains the same number of experimental units; (b) Each treatment has the same number of repetitions; (c) Any two treatments are arranged in the same block the same number of times. Note: When the number of treatments is the same as the number of blocks, it is called a symmetrical balanced incomplete block design. Youden square
A type of block design derived from the Latin square. Its construction method is: delete some rows (or some columns) from the Latin square so that when the columns (or rows) are used as blocks, a symmetrical balanced incomplete block design is formed. 4. 12 Split-plot design In a two-factor experiment, the experiment is carried out in batches (or blocks) according to the different levels of the factor, and all levels of the other factor are arranged in each batch (block).
Note: Split-plot design can be extended to cases with more than two sub-plots. 4.13 Mixture design Mixture design Several ingredients are mixed, and the response depends only on the proportion of each ingredient, but is independent of the total amount of the mixture. Each treatment is represented by the proportion of each ingredient. This type of experimental design is called a mixture design. 4.14 Factorial experiments Factorial experiments are used to examine the main effects of factors and the interaction effects of interest. All or part of the level combinations of each factor are used as treatments so that the effects of interest can be estimated.
Synonym: Factorial experiment
Note: When the experiment includes all level combinations of factors, it is called a full factorial experiment, otherwise it is called a partial implementation. Example: For an experiment with three factors A and B, each with two levels A.AB, B2, Ct, C2, when all level combinations BC84
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A,B,CABC,A,B,C2ABC,2BC2,ABC,ABC are implemented in the experiment, it is a complete factorial experiment; if only the level combinations AB,C,AB,C2,ABC1,A,BC are implemented in the experiment, then it is a 1/2 implementation. 4.15 Orthogonal array orthoganal array is a table used to arrange multi-factor experiments. In addition to the row number (experiment number) and column number (used to arrange factors), the table is composed of other symbols (generally represented by numbers), in which the number of occurrences of different symbols in each column is the same, and the number of occurrences of different symbol pairs formed by corresponding positions in any two columns is the same. Example 1. The following orthogonal table L (2) consists of the numbers 1 and 2, with a total of 8 rows and 7 columns: 7
Using 1: (2') at most 7 2-level factorial experiments can be arranged. Example 2. The following mixed orthogonal table L (4×2) has a total of 8 rows and 5 columns, of which the first column consists of the numbers 1, 2, 3, and 4, and the remaining 4 columns consist of the numbers 1 and 2.
Using L (4×2*), 1 4-level and at most 4 2-level factorial experiments can be arranged. Orthogonal design
A multi-factorial experimental design, for any two of the factors, is an equal-repeated complete factorial experiment. t factorial experiment4. 17
A factorial experiment with 17 factors and t levels for each factor. Composite design composite design
An experimental design for fitting a quadratic response surface of multiple factors, composed of the origin (repeated several times), the experimental points of a 2" factorial experiment with -1 and +1 as the levels of each factor, and two symmetrical points on each coordinate axis with a length of α (a given positive number).
4.19 Nested design
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A two-factor design, the level of factor B depends on the level of another factor A, hereby referred to as factor B nested factor A.
Note: Nested design can be extended to the case of more than two factors. Example: A takes two levels A.A2. For A, B takes two levels B11B2+ For AB takes two levels B1··B: There are five treatments: ABAB2AB21B2242B25 Terminology of analytical methods
5.1 Method of least multiplication method of least squaresA method of estimating unknown parameters in a model by minimizing the sum of the squares of the differences between each observation and its response. 5.2 Fixed effect modelfixed effectmodelA model in which the main effects of all factors and the interaction effects between factors are unknown constants. Note: This model is applicable to situations where the levels of all factors are completely determined and not randomly selected. 5.3 Random effect modelrandom effect modelA model in which the main effects of all factors and the interaction effects between factors are random variables. Note: This model is applicable to situations where the levels of all factors are randomly selected. 5.4 Mixed modelmixed model
A model in which some effects are random and other effects are fixed. 5.5 Contrast analysiscontrast analysisA method used to estimate the parameters of a model and perform hypothesis testing on a pre-specified set of controls. 5.6 Multiple comparisonsmultiple comparisonsA method of giving simultaneous confidence intervals for some or all of the effects and inferring from them whether the effects of interest are equal.
5.7 Covariate
A variable whose value cannot be controlled in the design of the experiment, but which can be measured in the experiment and whose effect on the experimental results must be considered in the analysis.
Example: The experimental units may differ in the content of a certain chemical component. The experiment cannot adjust this content, but it can be measured and its influence on the experimental results is small. The content of this chemical component is a covariate. 5.8 Analysis of covariance covariance A method of estimating and testing the effect of a treatment when one or more covariates affect the experimental results. 86
Partial replication
Incomplete block design
Residuals,
Single treatment replication
Control analysis
Multiple comparisons
Composite design
Fixed effects model
Mixed model
Mixture design:
Assumed model.
Interaction effects·
Explanatory variables·
Latin square
Latin square design
Split plot design
Balanced incomplete block design
GB/T 3358.3-93
Appendix A
Chinese index
(Supplement)
Block design
Experimental unit
Experimental design
Experimental error
Randomization·
Randomized complete block design
Random effects model
Nested design
Optimization operation:
Complete replication||tt| |Complete block design
Completely randomized design
Factoral test
tFactoral test-
Response variable·
Response surface·
Covariate
Covariance analysis
“Yao Dun formula·
Factoral test
Orthogonal table
Orthogonal control·
Orthogonal Latin square
GB/T3358.3-93
Orthogonal Latin square design
Orthogonal design·bzxZ.net
Main effects
Least squares
Analysis of covariance
Assumed model
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Appendix B
English index
(Supplement)
balanced incomplete block (BIB) design block
block design
complete block design
completely randomized designcomposite design
confounding
contrast
contrast analysis
covariate
design of experiments
duplication
evointionary operation (EVOP)experiment unit
experiinental design
explanatory variable
txperimental erro
factor
factorial experiments
lixed effect rmodel -
Graeco-Latin squares
incomplete block design
interaction
Latin sgual
Latin sqaure design
main effect
method of least squares
mixed model
mixture design
multiple comparisons
nested design
orthogonal array
orthogonal contrast
orthogonal design
orthogonal Latin squares
orthogonal Latin square designpartial replicatior
random effect model
randomization
randomized complete block designreplication
residual
response
response surfac
response variable
split-plot design
+ factorial experiment
treatmcnt
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Youden square
Additional remarks:
GB/T 3358.3---93
This standard is proposed by the National Technical Committee for Standardization of Statistical Methods. 11
This standard was drafted by the working group of the Subcommittee of Terminology, Symbols and Statistical Tables of the National Technical Committee for Standardization of Statistical Methods. The main drafters of this standard are Chen Xiru, Xiang Kefeng, Wu Qiguang, Tao Bo and Feng Tuyong.
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