Experimental design types

A question is this type if and only if it asks to describe, provide examples of, or justify the use of specific experimental designs (randomized blocks, Latin square, completely randomized).

2 questions · Standard +0.3

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OCR MEI S4 2009 June Q4
24 marks Standard +0.3
4
  1. Describe, with the aid of a specific example, an experimental situation for which a Latin square design is appropriate, indicating carefully the features which show that a completely randomised or randomised blocks design would be inappropriate.
  2. The model for the one-way analysis of variance may be written, in a customary notation, as $$x _ { i j } = \mu + \alpha _ { i } + e _ { i j }$$ State the distributional assumptions underlying \(e _ { i j }\) in this model. What is the interpretation of the term \(\alpha _ { i }\) ?
  3. An experiment for comparing 5 treatments is carried out, with a total of 20 observations. A partial one-way analysis of variance table for the analysis of the results is as follows.
    Source of variationSums of squaresDegrees of freedomMean squaresMean square ratio
    Between treatments
    Residual68.76
    Total161.06
    Copy and complete the table, and carry out the appropriate test using a \(1 \%\) significance level.
OCR MEI S4 2011 June Q4
24 marks Standard +0.3
4
  1. Provide an example of an experimental situation where there is one factor of primary interest and where a suitable experimental design would be
    1. randomised blocks,
    2. a Latin square. In each case, explain carefully why the design is suitable and why the other design would not be appropriate.
  2. An industrial experiment to compare four treatments for increasing the tensile strength of steel is carried out according to a completely randomised design. For various reasons, it is not possible to use the same number of replicates for each treatment. The increases, in a suitable unit of tensile strength, are as follows.
    Treatment
    A
    Treatment
    B
    Treatment
    C
    Treatment
    D
    10.121.19.222.6
    21.220.38.817.4
    11.616.015.223.1
    13.615.019.2
    [The sum of these data items is 256.8 and the sum of their squares is 4471.92 .] Construct the usual one-way analysis of variance table. Carry out the appropriate test, using a \(5 \%\) significance level. RECOGNISING ACHIEVEMENT