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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Blocking (statistics) | 3/3 | https://en.wikipedia.org/wiki/Blocking_(statistics) | reference | science, encyclopedia | 2026-05-05T09:49:20.919707+00:00 | kb-cron |
Yij is any observation for which X1 = i and X2 = j X1 is the primary factor X2 is the blocking factor μ is the general location parameter (i.e., the mean) Ti is the effect for being in treatment i (of factor X1) Bj is the effect for being in block j (of factor X2)
=== Estimates === Estimate for μ :
Y
¯
{\displaystyle {\overline {Y}}}
= the average of all the data Estimate for Ti :
Y
¯
i
⋅
−
Y
¯
{\displaystyle {\overline {Y}}_{i\cdot }-{\overline {Y}}}
with
Y
¯
i
⋅
{\displaystyle {\overline {Y}}_{i\cdot }}
= average of all Y for which X1 = i. Estimate for Bj :
Y
¯
⋅
j
−
Y
¯
{\displaystyle {\overline {Y}}_{\cdot j}-{\overline {Y}}}
with
Y
¯
⋅
j
{\displaystyle {\overline {Y}}_{\cdot j}}
= average of all Y for which X2 = j.
=== Generalizations === Generalized randomized block designs (GRBD) allow tests of block–treatment interaction, and has exactly one blocking factor like the RCBD. Latin squares (and other row–column designs) have two blocking factors that are believed to have no interaction. Latin hypercube sampling Graeco-Latin squares Hyper-Graeco-Latin square designs
== See also ==
Algebraic statistics Block design Combinatorial design Generalized randomized block design Glossary of experimental design Optimal design Paired difference test Dependent and independent variables Blockmodeling Paired data Block bootstrap Controlling for a variable
== References ==
This article incorporates public domain material from the National Institute of Standards and Technology
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