EMA+3800_6800+Presentation+4 New

EMA+3800_6800+Presentation+4 New - The Blocking Principle...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
The Blocking Principle Text Reference, Chapter 4 Blocking and nuisance factors The randomized complete block design or the RCBD Extension of the ANOVA to the RCBD Other blocking scenarios…Latin square designs
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
The Blocking Principle Blocking is a technique for dealing with nuisance factors A nuisance factor is a factor that probably has some affect on the response, but it’s of no interest to the experimenter … however, the variability it transmits to the response needs to be minimized Typical nuisance factors include batches of raw material , operators, pieces of test equipment, time (shifts, days, etc.), different experimental units Failure to block is a common flaw in designing an experiment (consequences?)
Background image of page 2
The Blocking Principle If the nuisance variable is known and controllable , we use blocking If the nuisance factor is known and uncontrollable , sometimes we can use the analysis of covariance (see Chapter 14) to remove the effect of the nuisance factor from the analysis If the nuisance factor is unknown and uncontrollable (a “lurking” variable) , we hope that randomization balances out its impact across the experiment Sometimes several sources of variability are combined in a block, so the block becomes an aggregate variable
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Blocking as A Tool: Example In comparing different ceramic products , for example, each must first be fired in a furnace , but the furnace may not be large enough to handle more than a few samples at a time. Since we know that differences among furnaces represent an important source of variability. Care must therefore be taken to have all treatments represented in each furnace (Block) , The experimental design is called a randomized block design .
Background image of page 4
Randomized block design Blocks of ground, shifts of workers, furnace heats, patients, and laboratories—represent blocking variables . We include them as part of the experimental design The studied variables are the treatments. We randomly assign the treatments to the blocks The experimental design is called a randomized block design .
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Given k treatments and n blocks: Y . 1 Y. .2 Y . .j Y . .k Y . . Treatments 1 2… j k 1 y 11 y 12 . . . y 1j . . . y 1k Y 1. 2 y 21 y 22 . . . y 2j . . . y 2k Y 2 . Blocks . . . . . . . . . . . . . . . . . . n y n1 . . . y n2 . . . y nj . . . y nk Y n.
Background image of page 6
ANOVA table should be used with the model y ij = μ + β i + τ j + ε ij ; ε ij NID (0, σ 2 ), ; where: μ = grand mean; β i = block effects τ j = treatment effects; ε ij = errors
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
EXAMPLES : Two types of fuels were tested in an attempt to establish whether real differences in car mileage results from using a modified formula. Ten vehicles were available for the tests. It is a good idea to use both formulas for each vehicle, since any observed difference in mileage could then only be due to errors of observations and the possible true differences in formula effect. This simple experimental design
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 72

EMA+3800_6800+Presentation+4 New - The Blocking Principle...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online