Reference no: EM131322999
Learning Outcomes
Select an experimental design appropriate to a particular scientific system, create the design matrix and analyse the results.
Implement appropriate multivariate techniques using statistical software. Compare, contrast, appraise and evaluate the results from the application of multivariate methods to datasets.
A. Trihalomethanes (THMs) are disinfection by-products formed when chlorine is added to disinfect water for drinking. Excessive levels of THMs in drinking water are found to be harmful to human health. Two regional companies carried out a set of experiments in order to investigate how characteristics of the pre-processed water may affect level of THMs present after the disinfection process. Each company undertook 12 experiments on water samples with different levels of pH and Total Organic Carbon (TOC). THMs levels were measured after the disinfection process. The table below summarizes the THMs measurements (in/).
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Low pH
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High pH
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Low TOC
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High TOC
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Low TOC
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High TOC
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Company 1
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65.0, 65.5, 65.5
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66.7, 67.0, 66.5
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72.6, 72.0, 72.0
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73.8, 72.2, 72.0
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Company 2
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65.0, 66.0, 64.5
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67.4, 66.0, 67.0
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72.6, 73.0, 72.5
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73.5, 73.8, 73.0
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(a) Explain carefully the type of experimental design used and construct the full design matrix for this experiment.
(b) Analyse the data fully using SPSS. Include an evaluation of all significant effects using the contrast coefficients.
(c) Use your analysis to write a short conclusion.
B. Glass can be characterised by the chemical composition and optical properties. In forensic science, research has been carried out to investigate if these characteristics can be used to determine the origin of a glass fragment
(for example whether the fragment was originated from a vehicle window or from a glass container). The glass dataset on Blackboard contains measurements of 66 glass fragments found in various crime scenes. For each fragment, the optical property is measured by the Refraction Index (RI) and the chemical composition is broken down into four types of oxides, namely percentages of sodium oxide (Na), aluminium oxide (Al), silicon oxide (Si) and calcium oxide (Ca). The last two variables in the dataset type and typeNum indicate the origin of the glass fragments (1=from window; 2=from glassware and 3=from vehicle).
Use SPSS to obtain a random sample of 55 glass fragments from the dataset.
Your task is to investigate whether glass fragments can be classified by type of origin (i.e. windows, glassware or vehicles) using the chemical composition and optical property. You are expected to choose two appropriate multivariate analysis techniques for the classification purpose. Compare and contrast the two chosen methods.
Include a critical evaluation of your results. Out of the two chosen methods, recommend one that can be used in the future to classify glass fragments from a crime scene. Justify your recommendation.
I have already obtained 55 glass fragments at random in the file attached to this assignment under
Attachment:- Assignment GlassDataset.rar
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What is the name of the statistic used in an anova
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An anova partitions the total variance into four components
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