CEGE0044: Engineering Data Analysis
Coursework 2 – Statistical Tests

Due: See Moodle for deadline
Submission method: Moodle
Late submissions will be penalised according to standard UCL regulations

In this coursework, you will be asked to carry out a variety of statistical tests on given data sets.

Instructions for generating your personal dataset:
Download the spreadsheet EDA_CW2_Data_2022.xlsx using the link on Moodle. Enter your five-
character candidate number in lower case and upper case in the cells indicated (e.g. abcd1 and
ABCD1). You will see a data set. Copy the data and paste it into a new spreadsheet that will form
the basis of your submission. You should do this using “paste special” and select “values”. This
will freeze the data and avoid later complications.

About the data
The data represents a set of ellipsoidal heights of mean sea level, derived from observations made
by a satellite altimeter over a calibration site (from multiple passes over several months).

These values have been found from a radar measurement of the height of the satellite above the sea
surface, ; the height of the satellite above the ellipsoid, ℎ; and a tidal correction, . Then the
height of mean sea level, ℎ, is given by the expression:

ℎ = ℎ − −

See diagram below.




ℎ
ℎ
Ellipsoid
Mean Sea Level
Sea surface
It is estimated that the tide has been found with a standard deviation of 0.05 m. The raw altimetry
measurements, , are thought to have been made with a standard deviation of 0.10 m. The height
of the satellite has been computed from the coordinates of the satellite using the expression:

ℎ = (
2 + 2 + 2)
1
2 −

where is the radius of the Earth, and is a known constant (6400 km). The and coordinates
have each been found with a standard deviation of 0.07 m; the coordinate has been found with a
standard deviation of 0.11 m. The exact position of the satellite changes slightly with each pass,
but the following representative values will be sufficient for error analysis:

Parameter Approximate value (m)
4430000
155000
5674000

You will see that there are two sets of data: a primary one and a smaller secondary one. The
secondary one was collected during a later period, when it is believed that high solar activity may
have affected the quality of the measurements.

Task: You are required to carry out the following analysis, making clear in your submission what
steps you have undertaken and why, and giving the derivations of any equations that you use for
these purposes:

A. Carry out a complete analysis of the primary data set, rejecting any outliers, finding the mean
() and standard deviation (), and determining whether the data are normally distributed or
not.

B. Find the mean () and standard deviation of (), and reject any outliers from, the secondary
data set (you do not need to test this one for normality).

C. Determine whether the high level of solar activity has, as predicted, had any effect on the
secondary data set, when compared to the primary one. This should be from the point of view
of both whether the mean value is significantly different, and whether the data is significantly
noisier.

D. Predict what the standard deviation of the mean sea level ought to be, by considering the
contributions of the measurements that go into determining it, and comment on whether this is
consistent with the value that you determined from the primary data set.

You are required to submit the following two items:
▪ A report containing information on all relevant statistical tests, summaries of data, diagrams,
analysis, etc. Marks will be awarded for presentation, as well as for getting the correct answer
and following the right procedures. This report is limited to four sides of A4 and should be
in PDF format. The file should be named: EDA_CW2_XXXX1 where XXXX1 is you
candidate number.

▪ The spreadsheet that you used to derive all the information in your report. We shall use this
to check how the computations were carried out in case of errors and so on, but the PDF report
should stand on its own without needing to refer to the spreadsheet.