October 9

STAT1103 / STAX1103 S2 2022 Research Report

For your research report assessment task, you are to write up an empirical, quantitative psychology
research study as if you were the researcher who conducted it. The structure and requirements of
this report align with the APA guidelines for writing empirical research papers (see resources in
iLearn as well as the “How to Write Psychology” textbook).
This document will provide you with the details you need to write up your research report. Your
tutorial time will work through some of this content. Your job for the research report is to write this
up in proper psychology report format: you cannot copy and paste this content [with the exception
of the aim and hypotheses] into your report!
Have a good read through this document, as well as all the Research Report Resources (posted on
iLearn). You will also be given a dataset (via iLearn), containing the data obtained from the study.
Starter References
Gee, N.R., Mueller, M.K., & Curl, A.L. (2017). Human-animal interaction and older adults: An
overview. Frontiers in Psychology, 8(1416), 1-7. https://doi.org/10.3389/fpsyg.2017.01416
Mueller, M.K., King, E.K., Callina, K., Dowling-Guyer, S., & McCobb, E. (2021). Demographic
and contextual factors as moderators of the relationship between pet ownership and health.
Health Psychology and Behavioural Medicine, 9(1), 701-723.
https://doi.org/10.1080/21642850.2021.1963254
Sharpley, C., Veronese, N., Smith, L., Lopez-Sanchez, G.F., Bitsika, V., Demurtas, J., Celotto,
S., Noventa, V., Soysal, P., Turan Isik, A., Grabovac, I., & Jackson, S.E. (2020). Pet ownership
and symptoms of depression: A prospective study of older adults. Journal of Affective
Disorders, 264, 35-39. https://doi.org/10.1016/j.jad.2019.11.134
You need to read all these papers as part of your research report preparation (find them on Leganto)
and should cite all in your report. You also need to find additional resources for your research report
preparation. There is NO set number of papers to read and cite!!
Study Aim and Hypotheses
The study investigated whether human-animal interactions can improve wellbeing in older adults.
The specific hypotheses are:
1. People will report lower levels of depression 6 months after adopting a pet compared to
baseline levels of depression
2. People will report lower levels of anxiety 6 months after adopting a pet compared to
baseline levels of anxiety
3. People who adopted a dog will report lower levels of depression 6 months after the
adoption compared to those who adopted a cat
4. People who adopted a dog will report lower levels of anxiety 6 months after the adoption
compared to those who adopted a cat

Note: the aim and hypotheses are the only things from this document that CAN be written word-for-
word into your report. Your report must cover all of these hypotheses.

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AFIN3028: Financial risk management
16 October 2022 11:55pm AEST.

Assignment questions

1. Your first task is to provide an analysis of the effectiveness of dynamic hedging of an options
position.
a. A trader sells 100,000 European call options on a non-dividend paying stock when
stock price is $49, strike price is $50, risk-free interest rate is 5% p.a., stock price
volatility is 50% p.a., and time to maturity is one year. The trader wants to charge
25% more than the no-arbitrage price. How much should the trader charge?
Note: the no-arbitrage price in this case is the Black-Scholes price.
(1 mark)
b. Assume the stock price follows a geometric Brownian motion with expected return,
μ = 0, and volatility σ = 0.5, simulate two price trajectories using
{( ) } 2 exp 0.5 tt t S S μ σ σε t t +∆ = − ∆+ ∆ ,
where ε is a standard normal random variable, Δt=1/252 (daily increment), and time
horizon is one year. For the first price trajectory, we want the price at maturity to

be less than the strike price, i.e., ST < K, such that the call option closes out-of-the-
money. For the second price trajectory, we want the price at maturity to be greater

than the strike price, i.e., ST > K, such that the call option closes in-the-money. Plot
the two price trajectories on the same graph.
Note: since the price trajectories are randomly generated, you may need to repeat
the simulation multiple times until you find one that fits the criterion.
(2 marks)
c. For each of the price trajectory in Part (b), perform delta-hedging similar to Table
8.2 and Table 8.3 on pp.167-168 of the textbook. What are the hedging costs for
the case in which option closes out-of-the-money, and for the case in which option
closes in-the-money, respectively?
(5 marks)

2. Your second task is to estimate expected shortfall (ES) for a portfolio of stocks and bonds
using the “historical simulation” approach. Your portfolio has 80% of funds invested in the
AORD equity index and 20% invested in the RSM (a diversified bond ETF). You are provided
with the daily prices from 1/07/2019 to 31/03/2020.
a. Use the “exponential weighting” method (Section 13.3.1) to estimate the one-day
97.5% ES for the portfolio.
Note: in our context each scenario is represented by the “rate of return” instead of
“value”. For instance, the simulated rate of return under the i
th scenario would be given by
for each market variable. Hence, the ES should also be estimated as a rate of return.
(3 marks)
b. Use the “volatility-scaling” method (Section 13.3.2) to estimate the one-day 97.5%
ES for the portfolio. The daily volatilities for AORD and RSM should be estimated by
GARCH (1,1). You may assume the initial variance (v1) for the first daily return and
the long-run variance (VL) are both equal to the sample variance. The parameters, α
and β, should be estimated by maximum likelihood method for each market
variable.
Note: As in Part (a), each scenario should be represented by rate of return. In the
case of volatility-scaling, the simulated rate of return under the i
th scenario is given
by
σi is the estimated volatility for the ith scenario, σn+1 is the volatility forecast for next
trading day.
(5 marks)

3. Your third task is to estimate ES for a portfolio of stocks and bonds using the “Model-
Building” approach. Your portfolio has 80% of funds invested in the AORD equity index and

20% invested in the RSM (a diversified bond ETF). Assume conditionally the returns of AORD
and RSM follow a bivariate normal distribution. We estimate the daily volatilities and the
correlation using the EWMA model with λ = 0.94. Plot the daily volatilities for AORD and

RSM on the same graph. Plot the daily correlations on a separate graph. Estimate the one-
day 97.5% ES for the portfolio.

Note: You are not required to use maximum likelihood to estimate λ, we simply assume λ =
0.94. You may assume the initial variance for the first rate of return is equal to the sample
variance, and the initial covariance is equal to the sample covariance.
(4 Marks)

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MATH3871 Bayesian Inference and Computation
14 Oct

1. Inference: Let ✓ be the true proportion of people over the age of 40 in your community
with hypertension. Consider the following thought experiment:
(a) Though you may have little or no expertise in this area, give an initial point estimate
of ✓.
(b) Now suppose a survey to estimate ✓ is established in your community, and of the first
5 randomly selected people, 4 are hypertensive. How does this information a↵ect
your initial estimate of ✓?
(c) Finally, suppose that at the survey’s completion, 400 of 1000 people have emerged
as hypertensive. Now what is your estimate of ✓?
2. Multivariate Priors: Let x1,...,xn 2 Rd be n iid d-dimensional vectors. Suppose that
we wish to model xi ⇠ Nd(μ, ⌃) for i = 1,...,n where μ 2 Rd is an unknown mean
vector, and ⌃ is a known positive semi-definite covariance matrix.

(a) Adopting the conjugate prior μ ⇠ Nd(μ0, ⌃0) show that the resulting posterior dis-
tribution for μ|x1,...,xn is Nd(ˆμ, ⌃ˆ) where
and

(b) Derive Je↵reys’ prior ⇡J (μ) for μ.
Hint: If you need help with vector di↵erentiation, you can find out about this on various
places on the internet. One such place is https://en.wikipedia.org/wiki/Matrix calculus.

3. Importance Sampling: There are many ways to compute or estimate ⇡. A very sim-
ple estimation procedure is via importance sampling. Suppose that samples x1,...,xn

were obtained uniformly inside a square with side length 2r (see diagram), where each
xi = (x(1)
i , x(2)
i ) for i = 1,...,n.

r

2

Now define bi = 1 if xi is also inside the circle of radius r, and bi = 0 otherwise. Then
pˆ = 1
n
Pn
i=1 bi is an estimate of the ratio of the area of the circle to the area of the square.
Given that we know the true value of p for this setting, we can then obtain an estimate
of ⇡.
(a) Show that the estimate of ⇡ is given by 4ˆp.
(b) Estimate ⇡ using n = 1, 000 samples.
(c) Using the central limit theorem, determine the Monte Carlo sampling variability of
⇡ˆ (i.e. derive the asymptotic distribution of ˆ⇡ as n gets large).
(d) Construct a histogram of 1, 000 estimates of ˆ⇡, each based on n = 1, 000 samples.
Superimpose the Monte Carlo sampling variability distribution from part (c) under
the assumption that the true value for p=0.7854, and verify that it matches the
experimental result.
(e) Without using the true value of p, based on the Monte Carlo sampling variability,
determine what sample size, n, is needed if we require to estimate ⇡ to within 0.01
with at least 95% probability.
(Hint: You will need to use a value for p in order to obtain this value. Choose the
value of p that gives the most conservative value of n, so that you can be sure that
you have estimated ⇡ to the desired accuracy.)

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PSYU/X2248 2022
Sunday 16 October 2022 at 11.55pm (AEDT)

Background
The Uncanny Valley1

is a psychological phenomenon referring to the fact that our affinity/fondness for an
artificial object (e.g., animations, robotics, humanoid, simulated dolls) increases when its appearance or
action becomes more like humans (e.g., see the “climbing-up” part of the curve in the illustrative figure
below); however, as the appearance or action of the artificial object continues to become human- or life-like,
our affinity to that object drops into a “valley” (i.e., the uncanny valley; e.g., see the “dipping” part of the
curve) – we feel a sense of eeriness, or sometimes even uneasiness, when seeing those human-like (but not
quite) artificial objects; and only when the artificial object becomes almost identical to a real human, our
affinity towards it increases again.

Fig. 1. An graphic illustration of the Uncanny Valley phenomenon; graph adapted from

https://magagpa.wordpress.com/tag/uncanny-valley

With the rapid technological advancements in robotics and the prevalence of using digital avatars in video
games, films, online customer service etc., a large body of research has been devoted to understanding why
such an effect occurs. These efforts have been fruitful but also resulted in mixed accounts for the
phenomenon. For example, some researchers suggest that it is the abnormal facial features associated with
the artificial face, e.g., a pair of overly enlarged eyes on the artificial face, rather than the overall impression
of human likeness, make us feel uneasy (e.g., Seyama & Nagayama, 2007). Other researchers assume that
the effect of the uncanny valley emerges from one’s categorisation difficulty and the “conflict” feeling
associated with it. For example, a “rabbit-duck” (as shown in Figure 2) can be categorised as either a rabbit
or a duck, and due to its categorical ambiguity, it is perceived as odd looking. Similarly, the conflict we
experience with a human-like robot (it is a robot, but it looks like a human, too) generates an eerie and
uneasy feeling (see Moore, 2012; Ferrey et al., 2015). More interestingly, Gray and Wegner (2012) proposed

1 The phenomenon was first described by Japanese robotic scientist Masahiro Mori.

that some robots are unnerving because they strike people as having a mind or having human experiences,
and it is the human experience attribute that contributes to our uneasy feeling.

Fig. 2. An example of the “rabbit-duck” bistable image; image adapted from
https://en.wikipedia.org/wiki/Rabbit%E2%80%93duck_illusion

To further explore this idea, Gary and Wegner (2012) tested whether the perceived experience of machines
influences raters’ uneasiness (Experiments 2) 2

. More specifically, they examined if a machine gives the
uneasy impression if it has the attribute of experience (e.g., having emotions, being able to sense or feel),
has the attribute of agency (e.g., having the capacity to do something), or has neither experience nor agency
attribute. Gary and Wegner hypothesised that only when the machine is perceived as having experience
(rather than having agency), it gives raters an uneasy feeling.
In the experiment, participants were asked to read descriptions of the “Delta-Cray supercomputer,” with
descriptions differing across experimental conditions. Specifically, in the experience condition, the computer
was described as able to feel some form of “hunger, fear and other emotions”; in the agency condition, the
computer was described as being able to “independently execute actions and self-control”; and in the
control condition, the computer was only described as “like a normal computer, but much more powerful.”
(NB. This experiment used a within-subject design in that each participant viewed all three conditions of
descriptions). Gary and Wegner’s results showed that participants gave the experience condition
significantly higher uneasiness ratings than the other two conditions, while the ratings in the other two
conditions did not differ significantly, in line with their hypothesis.
An honours student found this uncanny valley phenomenon very interesting, particularly the idea that the
perceived human experience (and not agency) is one of the sources contributing to the uncanniness feeling.
The student decided to replicate and extend Gray & Wegner’s (2012) findings in three follow-up studies (i.e.,
the following Study 1, Study 2, and Study 3). Please take a careful read of the research design and hypothesis
for each study, and ensure you conduct all necessary summaries and analyses yourself. Remember that
often, researchers need to run more summaries etc., behind the scenes than what will end up in a research
report results section.
In the assignment itself, ensure for each of the three studies that you present (a) summaries of all
demographic variables (for the sample as a whole), (b) necessary assumption testing, (c) the statistical
2 They also investigated the impact of perceived lack of experience in humans on participants’ uneasiness rating in
Experiment 3, but here we focus on the manipulations and results from Experiment 2.

analyses themselves needed to address the research hypotheses, and (d) any necessary summaries to
interpret these results and link back to the research questions.
Study 1
As a first step, the honours student researcher aimed to synthesise the factors that are known to influence
viewers’ uncanniness feelings based on the previous literature. More specially, the student investigated the
factors of abnormality of the facial features, participants’ categorisation difficulty, the perceived experience,
and the perceived agency of the robot.
To do this, the honours student used 90 short animated robot video clips as their stimuli. These video clips
were gathered from previous studies that demonstrated the existence of the uncanny valley effect (i.e., the
red line in figure 1, or, with the animated robots appearing more human-like, participants felt creepier or
uneasier). Twenty participants’ rating data (10 females and 10 males, with a mean age of 20.5, SD = 4.5)
were collected via an online survey. In the survey, participants were asked to rate the following five aspects
of each video clip:
1. Rate how many abnormal facial features they noticed in the animated robot (using an actual human
face as the judging criterion);
2. Put the animated robot into a “living” or a “nonliving” category, and rate the difficulty in making that
decision (measured on a 0-10 scale, with a higher score indicating greater difficulty);
3. Rate the degrees they think the animated robot can experience and feel;
4. Rate the degrees they think the robot can act (with 3 and 4 similarly measured on a 0-10 scale, with
a higher score indicating a higher level of experience or agency);
5. Rate how much the animated robots in the video clip give them an unnerving/uneasy feeling
(measured on a 1-100 scale, with a higher score indicating a higher level of unnerving or uneasy
feeling).
Using this data, the student investigated whether the abnormality of the facial features, participants’
categorisation difficulty, the perceived experience, and the perceived agency jointly predicted the uneasy
feeling participants may have experienced in Study 1. Based on the previous literature, the student
hypothesised that all the factors mentioned above but the perceived agency should significantly predict
uneasy feeling, with the perceived experience having the strongest effect.
“Study1.dta” includes the rating data (averaged across the 20 participants) for the 90 video clips. In the
dataset, the “id” was the ID of each video clip; the number of abnormal features was labelled as “nfeatures”;
the difficulty associated with categorisation was labelled as “catdiff”; the perceived level of experience was
labelled as “experience”; the perceived level of agency was labelled as “agency”; the unnerving/uneasy
rating was labelled as “unnerving”.

Study 2
In Study 2, the student aimed to conceptually replicate Gary and Wegner’s Experiment 2 (2012) using
different experimental stimuli, measurements, and a different design. Forty-five animated robot video clips
selected from Study 1 were used in Study 2. Among the 45 animated robots (in the video clips), 15 were

rated as having high experience but low agency (i.e., the experience condition), 15 as having low experience
but high agency (i.e., the agency condition), and the final 15 had low ratings on both experience and agency
(i.e., the control condition). Participants’ fixation times on the animated robot while watching the video clips
were recorded by a non-invasive eye-tracking device and used as an index of how much they felt unnerved
about the animated robot – participants would avoid looking at the animated robots when they felt uneasy,
therefore, resulting in shorter fixation times on the animated robots. Finally, the student employed a
between-subject design (cf. the within-subject design in Gary and Wegner’s, 2012) so that each participant
only viewed 15 video clips in one of the three conditions and did not feel fatigued by the end of the
experiment.
Following Gary and Wegner’s results, the student hypothesised that participants’ average fixation times on
the animated robots across the 15 videos in the experience condition should be shorter (avoid looking
because of the unnerving feeling) than those in either the agency or the control condition. However, the
average gaze times on the animated robots should not differ between the agency and control conditions.
Sixty participants (university students) took part in this experiment in total, with each participant being
randomly assigned to one of the three video clip groups (i.e., the experience, the agency, and the control
group).
As shown in dataset “Study2.dta”, each participant has one data point (a single row per participant), and
there are 4 variables. Participants’ gender was labelled as “gender”, age as “age”, the type of videos they
viewed was labelled as “vdtype”, and the average fixation times on the animated robots across 15 videos
was labelled as “avgfd”, with higher scores on this variable represents longer fixation times (in seconds)
looking at the animated robots.
Study 3
For the final study, the honours student was interested in exploring whether the uncanny valley effect (i.e.,
viewers deem robots with human experience creepier than robots without human experience) may manifest
itself differently for viewers with different video game experiences. The student hypothesises that
experienced video game players are often exposed to all kinds of digital avatars that fall within the uncanny
valley, and this familiarity with digital avatars may lessen any uncanny valley effects one experiences (e.g.,
Seyama & Nagayama, 2007).
In the final study, this student used two of the three video types: video clips with animated robots perceived
as having high experience but low agency (i.e., the experience condition), and video clips with animated
robots perceived as having low experience and agency (i.e., the control condition) from Study 2. The video
clips rated as having high agency but low experience were dropped to simplify the study. As in Study 2, a
between-subject design was used such that each participant only viewed one of the two video types.
Extending Study 2, Study 3 recruited participants from two participant groups: experienced video game
players and novices, thereby employing a 2 (video clip types: experience vs. control) × 2 (participant groups:
experienced video game players vs. novices) design. A total of 80 participants took part in Study 3 (20
participants in each of the four groups). Participants’ average fixation times on the animated robots were
recorded while viewing the video clips and used as an index for uneasiness.

The student expected a main effect of video types: there should be shorter average fixation times on the
animated robots in the experience than in the control video clips; a main effect of participant group:
experienced video game players should have longer average fixation times on the aminated robots than that
of the video game novices; and most importantly, the student predicted an interaction between the video
types and participant groups – specifically, the difference between the two video types (i.e., the uncanny
effect) in the averaged fixation times on the animated robots would be smaller for experienced video game
players than novices.
As shown in dataset “Study3.dta”, each participant has one data point (a single row per participant). There
are 6 variables: participants’ gender was labelled as “gender”, age (numeric) as “age”, the type of videos as
“vdtype”, the participant group as “ppgroup”, each unique combination of the video type and the participant
group was labelled as “condition”, and the average fixation times on the animated robots across 15 video
clips was labelled as “avgfd”.
Your task
Please help the honours student researcher conduct the appropriate analysis for each of the three studies,
including all necessary statistical steps (e.g., necessary descriptive statistics, assumptions checking, statistical
analysis etc.) before interpreting the results.
References
(NB. You are not expected to read the references; however, some students might find the references helpful
in terms of providing additional background information.)
Ferrey, A. E., Burleigh, T. J., & Fenske, M. J. (2015). Stimulus-category competition, inhibition, and affective
devaluation: a novel account of the uncanny valley. Frontiers in psychology, 6, 249.
Gray, K., & Wegner, D. M. (2012). Feeling robots and human zombies: Mind perception and the uncanny
valley. Cognition, 125(1), 125-130.
Moore, R. K. (2012). A Bayesian explanation of the ‘Uncanny Valley’effect and related psychological
phenomena. Scientific reports, 2(1), 1-5.
Mori, M. (2012). The uncanny valley. In K. F. MacDorman, & N. Kageki (Trans.), IEEE robotics and automation,
19(2), 98-100 (Original work published in 1970).
Seyama, J. I., & Nagayama, R. S. (2007). The uncanny valley: Effect of realism on the impression of artificial
human faces. Presence, 16(4), 337-351.