Chaughule, Thorat - Statistical Analysis/Design of Experiments
(The experimental design is different if the goal of a particular study is to evaluate the
effect on various colour attributes during dehydration and may well be entirely different
if goal of a same particular study is to study the effect on all dehydration properties dur-
ing dehydration) So the experiment should be design in a way keeping in mind the final
response.
8.5.2. Factor Effects
A second important criterion in the selection of an appropriate statistical design is
likely effect of the factors. Inclusion of all relevant factors, when experimentally feasible,
is necessary to ensure that uncontrolled systematic variation of these factors will not
bias the experimental results. An accounting for uncontrollable systematic variation
through the measurement of covariates is necessary for the same reason. Anticipated
factor effects also influence the choice of a statistical design through their expected rela-
tionships with each another. If each factor is believed to affect the response indepen-
dently of any other factor or if joint effects of the factors are of secondary interest,
screening experiments can be used to assess the effects of the factors. If the effect of one
factor on the response depends on the levels of the other factors, a larger design is
needed. In general, an experimental design should allow the fitting of a model so that
the salient features of the response and its relationships with the factors can be identi-
fied. For example, the design should permit polynomial terms in the quantitative factors
to be included in the fitted model so that the response function can be assessed. The de-
sign should permit an assessment of the adequacy of the fitted model. If the fitted model
is judged to be an inadequate representation of the response function, the design should
form the basis for an expanded design from which more elaborate models (e.g., higher-
order polynomials) can be fitted. When assessing factor effects it is important to explore
the entire experimental region of interest. The combinations of factor levels used in a
statistical design should be selected to fill out the experimental region. If a factor is only
studied over a narrow portion of the experimental region, important effects may go un-
detected (Mason et al., 2003 ; Antony, 2003 & Montgomery, 2003).
8.5.3. Precision & Efficiency
Precision refers to the variability of individual responses or to the variability of ef-
fects that measure the influence of the experimental factors. Precision is a property of
the random variables or statistics and not of the observed values of those variables or
statistics. For example, an (observed) effect is said to be sufficiently precise if the stan-
dard deviation of the statistic that measures the effect is suitably small. In its simplest
form, an effect is simply the difference between two averages.
An observed effect is then said to be sufficiently precise if the standard deviation (or,
equivalently, the variance) of this statistic is sufficiently small. In practice, the value of
the standard deviation can be estimated from the data.
Blocking, repeat tests, replication, and adjustment for covariates can all increase
precision in the estimation of factor effects. Blocking increases precision (decreases va-
riability) by controlling the systematic variation attributable to non homogeneous expe-
rimental units or test conditions. Adjustment for covariates increases precision by eli-
minating the effects of uncontrolled factors from the variability that would otherwise be
attributed to random error.