The aim of this workshop is to give you some experience using standard statistical treatments of data using statistical software. The package we will use for this workshop is Minitab. It is the package used as the standard statistical software by the Mathematics and Statistics courses at RMIT and Chemistry also has a site licence for it. Most of the analyses in this workshop can be done using Excel but Excel is not very user-friendly for statistical analyses. The analyses in Minitab can be done from simple pull-down menus and there is a good on-line help facility. You can copy-and-paste data from Excel into Minitab. For the assessment you should enter your results into the attached pro forma.
Before you attempt the case studies in this assignment you should try the worked examples in modules 1-4
Case Study 1
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Analyst A
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Analyst B
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6.42
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6.40
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6.41
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6.54
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6.43
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6.52
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6.38
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6.58
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The above results were obtained by two analysts using a new method for determination of Nickel in a standard reference alloy containing a certified value of 6.49% Ni
For this data we want to determine the standard statistics:- (i) mean (ii) variance (iii) standard deviation and (iv) confidence intervals for the mean. This data enables us to answer the following questions:-
(a) Which analysis is the most accurate? (i.e. closest to the certified value)
(b) Which analysis is the most precise? (i.e. which has the smallest spread, or variability, of values
As well we can use the t-test to answer the following:-
(c) Is there any evidence, with either analyst, of a systematic error? I.e. does either average differ significantly from the certified value?
(d) Do the results of each analyst differ significantly?
Analysis: Basic Statistics
1. Open up Minitab by clicking on the Minitab icon on your desktop
2. When you open the program you will notice it is divided into two areas - the data area (lower screen) and the output area. Enter data from the above table in columns C1 and C2.
Warning: make sure you start entering data in row 1 NOT in the cell immediately below the column heading (C1 etc). This cell is reserved for column labels (you may put a label here like 'Analyst A'). Also make sure you don't enter a column label in row 1. The whole column will then be formatted as text (C1-T) and cannot be used for analysis. If this happens delete the whole column and start again (clicking on 'C1' will highlight the whole column).
3. To get descriptive statistics click on Stat => Basic Statistics => Display Descriptive Statistics to get the basic statistics dialog box. Highlight C1 and C2 on the left and then click 'Select'. Alternatively you can click in the Variable box and type C1 C2 . Then click OK and the output will appear in the output window. From the output data enter the values in the pro forma. Note that the output does not give the variance but you should be able to calculate it from the standard deviation.