CEG2002: Statistics for Civil Engineers

Practical 1

 

Instructions

 

1.    Read through the section “About Minitab”, and follow the instructions for “Getting started”. 

 

2.    Answer all questions. 

           

3.    This practical is not assessed – but you should work through all questions, saving your work at the end of the session for future use. 

 

 

About Minitab

 

Minitab is an easy-to-use statistical package which can carry out a wide variety of statistical tasks.  You may use Minitab in many different courses during your time as a student, for many different purposes, so it is worth putting a little effort into familiarising yourself with the basics at an early stage.  That way, you will be able to adapt to more sophisticated uses of the package later on in your course.  There are three basic kinds of object Minitab works with:

 

Data column: This is the most frequently used object type in Minitab.  Columns are denoted C1, C2, C3 etc.  They each store a collection of observations relating to a particular variable. 

 

Constants: These are denoted K1, K2, K3 etc., and each stores a single number of interest. 

 

Data arrays: These are matrices of numbers, and are denoted by M1, M2, M3 etc. 

 

All of the data columns, constants and data arrays relating to a particular problem are stored in a working environment called a worksheet.  Worksheets can be saved to and loaded from disk, for later use.  Several worksheets may be opened simultaneously, and these can be saved together as a project. 

 

Minitab has both a command language and a menu driven interface.  This module will concentrate on the latter, which is more intuitive, especially for the beginner.  The easiest way to see Minitab in action is to work through this practical and the exercises within. 

 

 

Getting started

 

Logging onto Windows 7

 

Before you can use Minitab, you must log into the Windows system. 

 

Load Minitab

 

Load Minitab by selecting Start – All Programs – Minitab – Minitab 16 Statistical Software...  This should load the Minitab application, which may take a few seconds. 

 

You should now have a spreadsheet (“data window”) ready to input data.  In Minitab, there are two main windows; the session window and the Worksheet window.  The Worksheet allows you to view and edit the data columns of the current worksheet.  It is normally empty on startup, so the first step is to load the data in.  Always enter data in the white boxes – the grey boxes are for column titles.  Use the arrow keys to move around the worksheet. 

 

 

 

You should write your solutions to the following questions in a Microsoft WORD document (this is how the computing part of the Statistics assignment will have to be written up).    Remember to include a title at the top of the page – e.g. “CEG2002 Practical 1”.  Don’t copy and paste the entire Minitab output into your solutions – just the relevant bits!  And don’t forget to save your work!

 

  1. Enter the sea levels given at the end of this question into column 1.  Check that it has been entered correctly.  You do not need to enter the years, but the sea levels should be entered in chronological order (i.e. first row is 2.508 for 1954 and last row is 2.413 for 1994).  Label the column “sea level” in the grey box above the data. 

 

a)    Obtain simple numerical summaries of the sea level data by selecting Stat – Basic Statistics – Display Descriptive Statistics and entering C1 in variables.  Click OK.  Write down the mean and standard deviation of the sea levels in your solutions.  What are the maximum and minimum sea levels?

 

b)    Create a histogram of the sea levels by clicking on Graph – Histogram – Simple – OK.  Enter C1 as your graph variable.  Click on Labels and enter a title for your histogram – e.g. “John Smith’s Histogram of sea levels”.  click OK and OK again.  Right click on the Graph, and click on Copy Graph.  Now paste this into your WORD document, and make a few comments on the graph. 

 

c)    Data collected over time is useful plotted as a time series plot.  Click on Graph – Time Series Plot – Simple – OK.  Enter C1 in Series, give your plot a title, and click OK.  Copy and paste this graph into your solutions. 

 

d)    Another useful graph is a box and whisker plot.  Click on Graph – Boxplot – Simple – OK.  Enter C1 as your graph variable, give your plot a title, and click OK.  Copy and paste this graph into your solutions.  What is the median sea level from your boxplot?  What about the maximum/minimum sea levels (roughly)?

 

e)    Often, we want to produce one column from another for re-analysis.  Left click the cursor over the session window (the white window at the top).  Click on Editor – Enable Commands.  Notice the MTB> prompt; this enables you to type commands into Minitab instead of using the drop down menus.  Try square-rooting the sea level observations by typing

LET C2 = SQRT(C1)

 

This square roots all the observations in column 1 and puts them into column 2.  Label column 2 with something like “SquareRoot”. 

 

 

f)     Try logging the sea levels by typing

LET C3 = LOGE(C1)

 

This logs the sea levels in column 1 and puts them in column 3.  Label column 3. 

 

g)    Produce histograms of the square-rooted sea levels and the logged sea levels, and copy and paste these into your solutions.  Comment on the shape of the square-rooted and logged sea levels.

 

Saving and retrieving worksheets and projects

 

When you have been using Minitab, you will often want to save the contents of your Worksheet for future use.  To save a Worksheet, first click on it in order to make it active, and then select File – Save Current Worksheet As.  Make sure that your current drive is H: (which appears as your user name) and give an appropriate name for the file before clicking on OK.  On the Windows 7 clusters, drive H: is synonymous with My Documents, so you may save your work in My Documents if you prefer – it makes no difference.  Note that saving a Worksheet only saves the Worksheet contents.  It does not save any plots you have produced, or the contents of the session window.  To save your complete workspace, including the session window, all open worksheets, and any plots, select File – Save Project As.. and select an appropriate directory and file name.  This can be reloaded at a later stage by selecting File – Open Project.. or by clicking on the small yellow “open file” icon on the Minitab toolbar.  Projects are often more convenient than worksheets for a “project” you are working on.  However, they are less useful for long term data storage, as the project files tend to be very large, and so you may eventually run out of disk storage space. 

 

 

 

 

 

 

 

Sea level data:

The following data are annual maximum sea levels (in m) at Lowestoft, U.K., from 1954 – 1994. 

 

1954

2.508

 

1968

1.856

 

1982

1.952

1955

1.954

 

1969

2.709

 

1983

2.688

1956

1.831

 

1970

1.996

 

1984

2.053

1957

1.865

 

1971

2.262

 

1985

1.869

1958

1.941

 

1972

1.832

 

1986

1.721

1959

1.903

 

1973

2.470

 

1987

1.913

1960

1.929

 

1974

1.810

 

1988

1.871

1961

2.381

 

1975

1.850

 

1989

2.305

1962

1.265

 

1976

2.680

 

1990

2.236

1963

1.612

 

1977

1.961

 

1991

1.880

1964

1.856

 

1978

2.346

 

1992

1.645

1965

2.131

 

1979

1.659

 

1993

2.641

1966

1.917

 

1980

1.932

 

1994

2.413

1967

1.948

 

1981

2.020

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  1. Download data file for the course

 

Visit the following website for this course (or click the link from Blackboard)

http://www.staff.ncl.ac.uk/j.q.shi/teaching/CEG2002/

Click the name corpuschristi.MTW to download the data file. You can do so by clicking ‘Save’ and then save the file in your H: drive (or any other desk you want to save your files in), e.g., the file is saved as “H:CEG2002/corpuschristi.MTW’.     

 

Open Worksheet

 

In Minitab, click on file and Open Worksheet.  Look in the drive you saved the data file (e.g., H: and then double click on CEG2002, the folder we saved the files in), and select corpuschristi.MTW.  Click Open and OK.  You should now have a worksheet open in Minitab with data in two columns; the data in C2 are annual maximum wind speeds in miles per hour recorded at Corpus Christi (Texas, USA), over a period of 32 years from 1944 to 1975 (inclusive).  Years are given in C1. 

 

(a)   Produce a histogram of these wind speeds (C2), and copy and paste this into your solutions.  Describe the shape of the histogram – is it symmetric or asymmetric?

 

(b)  Obtain simple numerical summaries of the wind speed data (use Stat – Basic Statistics – Display Descriptive Statistics).  With reference to the shape of the histogram in part (a), would you use the mean or the median as a suitable measure of location?  Write your choice (either the mean or the median) in your solutions.  Similarly, should you use the standard deviation or the interquartile range as a measure of spread?  Write your choice (standard deviation or interquartile range) in your solutions.  Justify your choices. 

 

(c)   Calculate the probability of the maximum wind speed in any given year being less than or equal to 55 miles per hour (do this by simply counting the number of years which have a maximum wind speed less than or equal to 55, and dividing by the total number of years), and write this down in your solutions.  This is your “frequentist” estimate. 

 

(d)  Now use Minitab to obtain an accurate calculation of this probability, assuming the data follows a Normal distribution (Use Calc - Probability Distributions – Normal, enter the mean wind speed and standard deviation in the appropriate boxes, and then enter the Input constant as 55). Write this probability down in your solutions. This is your “Normal theoretical” estimate. 

 

(e)  Repeat the instructions in part (d), but this time assume the wind speed data follows an exponential distribution (Use Calc – Probability Distributions – Exponential, enter the mean wind speed in the Scale box, and then enter the Input Constant as 55).  Write this probability down in your solutions.  This is your “Exponential theoretical” estimate. 

 

(f)   How well do your “frequentist” and “theoretical” estimates compare?  Which of the theoretical estimates do you trust most?  Why? 

 

 

Exiting and logging out

 

When you are finished working with Minitab, it is important that you exit the program and then log out of the Windows 7 network properly; this will ensure that all of your work is saved properly and that your files are not corrupted.  To exit Minitab, select File – Exit.  You will have an opportunity to save your project – you may wish to save this to your H: drive, which is your own personal file space, and will be available to you whichever machine you use, on any Windows  cluster.