37252: Design and Analysis of Experiments - Chemistry Assignment Help

Assignment Task :

Question 1 

(a) Randomisation is used to minimise dependence between response measurement, in line with the assumption of independence A balanced design is one in which each treatment is tested the same number of times while an unbalanced design is one where not all treatments are tested the same number of times  

(b) Blocking is required when there are more treatments than there are homogenous experimental units  Blocks are created as combinations of the levels of blocking factors where the experimental units within each block are homogenous  

(c) Confounding occurs when modelling effects are indistinguishable from each other For example, confounding occurs when blocks contain fewer experimental units than treatments, such as in the case of 2k designs where each of the 2m blocks contain only 2k−m experimental units In this case some experimental effects will be confounded with the blocks 

(d) Treatments are assigned to experimental units while the response variable is measured from the measurement units  An example of this could be an experiment to assess the sugar content of tomatoes grown in plots where each plot receives a different treatment. In this case the plots are the experimental units but the tomatoes themselves are the measurement units

Question 2

(a) The assumptions are that the errors terms have zero mean, constant variance (which we label σ2 and are independent from each other, that is eij~N(0 ,σ2) i.i.d.  

Normality can be assessed with a range of normality tests such as Shapiro-Wilk, Cramer von Mises, Anderson-Darling etc.; constant variance across groups defined by treatments can be assessed with Levene’s test of equal variances and independence (via autocorrelation) can be test assessed with the Durbin-Watson test

Question 3

(a) Not assessed  

(b) A fractional factorial design is one in which not all treatments are tested, giving rise to aliasing or confounding of effects   The main advantage is that not all treatments have to be tested leading to lower costs [1 mark]. If the experiment is designed properly, the significance of the main effects (and perhaps low-order interaction effects) can still be ascertained at the cost of some high-order interaction effects, which in many (most?) cases are not of much interest to experimenters  

(c) A “regular fraction” is one in which treatments have been assigned according to p defining contrast equations or equivalently defining relations involving p generator effects [1 mark]. Irregular fractions are those where treatments are assigned on an ad-hoc basis  . 

(d) The defining contrasts are the set of generator effects and their associated generalised interaction effects

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