Fundamental Principles

Fundamental Principles

1. Replication

   • allows us to form an unbiased estimate of the error variance by pooling the individual variances from each treatment under certain assumptions
   • as the number of treatments and replication increases, the df of residual variance increases
     • and so the critical point of the t-distribution approaches an asymptote
       • so there is a benefit to having sufficient replication to enable the variance to estimated with some precision
         • replication decreases the variances of our estimates of means
     • we want more than 20df
   • if the variability among the treatment means is not larger than the experimental error variance, the treatment differences are probably due to the differences of the experimental units assigned to each treatment
   • avoids the danger of basing inferences on 'rogue' observations or outliers that are not typical of the effect of a treatment

2. Randomisation

   • enables a valid estimate of residual variance to be made and significance tests to be performed
   • form of insurance that guard against bias and other disturbances that may occur
   • several forms of bias
     • systematic bias
     • selection bias
     • accidental bias
     • cheating
   • important to randomise even when we don't expect any bias to be present
   • once the units for the trial have been selected, it is entirely a matter of chance which unit receives which treatment
     • the selection of one particular treatment-unit combination should have no influence on the treatment received by the unit that is adjacent in space or time

3. Blocking

   • eliminate 'known' sources of variation in material
   • so we can compare treatments on homogeneous material
   • exploit the variation to our advantage

4. Representativeness

   • we want to make inferences about a wider population
   • the extent to which the experiment and experimental material is representative of the units or material for which inferences are to be made