MATH 558 Design and Analysis of Experiments Assignment 1
MATH 558 Design and Analysis of Experiments Assignment 1
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From the paper ’ The importance of experimental design in proteomic mass spectrometry experiments; some cautionay tales ‘written by Jianhua Hu, Kevin R. Coombers, Jeffery S. Morris, and Keith A. Baggerly, which was published in the journal of Briefings in Fuinctional Genomics and Proteomics in 2005, read the following: 1). Case study 4: Doing things right (pg 327) 2). Comments (following case study 4) 3). Discussion 4). Advice for statisticians. (a) Which experimental design principals were used in the experiment discussed in case study 4? Describe (in context of the experiment). (b) Make a list of recommendations given in the section ‘Advice for statisticians’. (c) How far do you think these recommendations apply to experiments in other areas of Science?
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An experiment 1 was performed to see the affects of sulphur on reducing scab disease on potatoes. Sulphur increases the acidity in the soil which helps cure the disease. The purpose of the experiment was to choose the right amount of sulphur per acre. The amounts of sulphur used were 0, 300, 600 and 1200 per acre. The applications were applied in Fall and Spring. There were seven treatments in all: F3 , F6 , F12 , S3 , S6 , S12 , 0. The response to be analysed was scab index which is the surface area of the potato that is infected by the scab. It is obtained by randomly selecting 100 potatoes, grading each on a scale of 0 to 100 infected, and taking the average. The experimental design is given below. (a) Give the analysis of variance table for this data.
F3 9 0 12 010 S3 7 F3 9 S12 7 S3 9 0 18
S6 18 F12 10 S6 24 S12 17 F12 4 F6 10 S3 21 0 24 F6 18 0 30 F6 18 S12 16 S12 17 S6 19 0 30 F12 5
S3 30 F6 16 0 24 S6 12 F3 16 F12 4 0 26 F3 4
(b) Is there any evidence that the mean scabbiness is different according to different treatments? Justify your answer. (c) Estimate the mean scabbiness produced by each treatment. (d) What is the standard error of the above estimates? (e) What is the standard error of the difference between the means? Note: The questions in (2) are taken from Bailey, pg 42.
