Added
Individual Assignment

You can submit an individual Word document (no more than four A4 pages) in which you shortly
describe a more thorough and sophisticated statistical analysis of the data you
collected for your individual robot.

The document should be titled “Added
Individual Assignment” and contain at least the sequence of behavioural
activities you collected from your “focal” robot, both as raw data and
summarised in a transition matrix.

The methods for behaviour analysis are
covered in the slides and accompanying Excel Workbook “Analysis of Robot
Behaviour” and the spreadsheet “seqdep” (plus guidelines) (Course Work
Assignments > Robotics > CW3 > Supporting Documentation & Tools).

The workbook “Analysis of Robot
Behaviour” consists of four spreadsheets that contain valuable information
about the chi square test for dependency between behaviour acts and similarity
(distance) between behaviour profiles as used in behaviour analysis and how to compute them.

The first sheet (“Example Light
Signal vs Movement”) illustrates the first 25 slides of the accompanying set of
PowerPoint slides “Analysis of Robot Behaviour” and deals with the setup of a
simple chi square test for associations between (behavioural) events. By
clicking at the coloured cells you can see the functions that have been used
for the computations.

The second sheet (“Example Chi Sq
Distribution”) contains tables and plots of the Chi Square Distribution and
exemplifies the issues of statistical significance as mentioned on slides 15 –
25.

The sheet “Example Sequential
Analysis” is not only of use for this additional assignment but should also be
helpful for the analysis of robot data you are required to carry out for the
main part of CW3. By clicking on the green cells you can uncover the choice and
use of functions to generate transition matrices which you can then adapt and
apply to the data collected by the group. The sheet also carries out a simple chi
square test for sequential dependency, but this test does NOT bypass diagonal
zero’s; for a procedure that does take this in account you have to use the
spreadsheet “seqdep”. A comparison between the results of the “naïve” and
sophisticated (seqdep) test (applied to data of rat behaviour) is the topic of
the fourth spreadsheet (“Chi Sq Rat Data”) and refers to slides 57 - 63.

Finally, sheet 5 (“Similarity Rat
Data Profiles”) illustrated to compute
Euclidean and Correlation Distances as they are used in Cluster Analysis. Once
computed, you could a cluster analysis by hand (if you do not how to do this
automatically in R or MatLab) given the fact that the number of behavioural
elements you are dealing should be quite
small.

A note on
the use of “seqdep”.

“seqdep” (plus guidelines) is a spreadsheet for
doing a Chi Square test bypassing diagonal zero’s. Read the “guidelines” for a
description and explanation of its use. Be aware that the spreadsheet was set
up in an older version of Excel and depends on the use of macros, therefore do
not convert it in a newer version of Excel.

Suggestions
for things to include in the assignment

Choose one or more of the topics
below

I.
A Sequence Plot of the activities (0.5 mark).

II.
Combining activities
with the similar profiles (as assessed from a correlation matrix, a PCA or a cluster analysis) (3
marks).

III.
Chi Square Tests (bypassing diagonal zero’s) to check
whether the frequencies of transitions are statistically independent (3 marks).

IV.
If they are not:

·
An identification of those elements that follow each other
sequentially

more than expected by chance (0.5 mark)

·
Possible solutions to deal with overt dependency (0.5 mark)

·
A Markov State Space diagram based on the transition rates
after

correcting for dependency (0.5 mark)

V.
A Markov State Space diagram for various episodes (e.g. begin- and
end of the experiment (2 marks).

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