blocking

(noun)

A schedule for conducting treatment combinations in an experimental study such that any effects on the experimental results due to a known change in raw materials, operators, machines, etc., become concentrated in the levels of the blocking variable.

Related Terms

  • nuisance factors
  • null hypothesis
  • ANOVA

Examples of blocking in the following topics:

  • Randomized Block Design

    • Block design is the arranging of experimental units into groups (blocks) that are similar to one another, to control for certain factors.
    • In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another.
    • An example of a blocking factor might be the sex of a patient; by blocking on sex, this source of variability is controlled for, thus leading to greater accuracy.
    • The general rule is: "Block what you can; randomize what you cannot. " Blocking is used to remove the effects of a few of the most important nuisance variables.
    • An example of a blocked design, where the blocking factor is gender.
  • Principles of experimental design

    • Blocking.
    • Under these circumstances, they may first group individuals based on this variable into blocks and then randomize cases within each block to the treatment groups.
    • This strategy is often referred to as blocking.
    • For instance, if we are looking at the effect of a drug on heart attacks, we might first split patients in the study into low-risk and high-risk blocks, then randomly assign half the patients from each block to the control group and the other half to the treatment group, as shown in Figure 1.15.
    • Blocking is a slightly more advanced technique, and statistical methods in this book may be extended to analyze data collected using blocking.
  • Comparing Three or More Populations: Randomized Block Design

    • Nonparametric methods using randomized block design include Cochran's $Q$ test and Friedman's test.
    • The blocks were randomly selected from the population of all possible blocks.
    • The procedure involves ranking each row (or block) together, then considering the values of ranks by columns.
    • Given data $\{ x_{ij} \} _{nxk}$, that is, a matrix with $n$ rows (the blocks), $k$ columns (the treatments) and a single observation at the intersection of each block and treatment, calculate the ranks within each block.
    • Replace the data with a new matrix $\{ r_{ij} \} _{nxk}$ where the entry $r_{ij}$ is the rank of $x_{ij}$ within block$r_{ij}$ i.
  • Experimental Design

    • Blocking: Blocking is the arrangement of experimental units into groups (blocks) consisting of units that are similar to one another.
    • Blocking reduces known but irrelevant sources of variation between units and thus allows greater precision in the estimation of the source of variation under study.
    • When this is not possible, proper blocking, replication, and randomization allow for the careful conduct of designed experiments.
    • Outline the methodology for designing experiments in terms of comparison, randomization, replication, blocking, orthogonality, and factorial experiments
  • Experiments exercises

    • (c) Does this study make use of blocking?
    • If so, what is the blocking variable?
    • (c) Has blocking been used in this study?
    • If so, what is the blocking variable?
    • (c) Yes, the blocking variable is age.
  • Statistical Graphics

    • They include plots such as scatter plots , histograms, probability plots, residual plots, box plots, block plots and bi-plots.
  • Random Sampling

    • For example, while surveying households within a city, we might choose to select 100 city blocks and then interview every household within the selected blocks, rather than interview random households spread out over the entire city.
  • ANOVA Design

    • The protocol's description of the assignment mechanism should include a specification of the structure of the treatments and of any blocking.
    • More complex experiments with a single factor involve constraints on randomization and include completely randomized blocks.
  • Distribution-Free Tests

    • Cochran's $Q$: tests whether $k$ treatments in randomized block designs with $0/1$ outcomes have identical effects.
    • Friedman two-way analysis of variance by ranks: tests whether $k$ treatments in randomized block designs have identical effects.
  • Plotting Points on a Graph

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