Experimental Design

 

Randomised Complete Blocks

-          Tukey Test for Additivity – tests whether 2 factors interact

-          Efficiency of blocking variable

o   Number of replications per treatment required with CRD to achieve same variance

-          Control extraneous sources of variation

o   Ie day of week

-          Regardless of whether block is significant. Including it will reduce MSE

-          RCD – assumes no interaction

-          affect the response, but not of primary interest to researcher  à nuisance or confounding factors

-          heterogenous experimental units divided into homogenous subgroups / blocks

-          separate restricted randomisations – one for each block

-          different blocks as heterogenous as possible

-          each block constitutes a replication of the experiment

-          two types of blocking criteria

o   characteristics associated with experimental unit

§  age, gender, job experience

o   characteristics associated with experimental setting

§  observer, time / date , batch

-          blocking variable is observational à cause and effect inferences problematic

-          Data may not fit RCB

o   unequal error variability by blocks

o   unequal error variability by treatments

o   time effects

o   block – treatment interactions

-          use of more than one blocking variable

 

 

Latin Squares

-          Efficiency of blocking variable

o   Example – Latin Square is not more efficient that CRD : Score of 1.04 à it would only be necessary to take 4% larger sample (ie one observation) to achieve same precision as Latin Square

-          Advantages

o   Greater reduction in variability of experimental error

o   For repeated measures – useful to take account order position effect

§  2 blocks

·         subject / order of treatment

-          Disadvantages

o   Restrictive assumptions à no interaction

o   Number of classes of blocking variable must be equal to number of treatments

-          Humans etc / order effect

-          à use of 2 blocking variables in complete block design

-          Latin Square

o   r treatments

o   two blocking variables, each with r classes

o   each row and column contain all treatments à each class of each blocking variable constitutes a replication.

 

 

Factorial

-          Interaction / main effects