PSYC1004A 2022-2023 1st Semester
Assignment 1
PSYC1004A Introduction to Quantitative Methods in Psychology
Assignment 1 – Basic statistical concepts [Total Marks: 51]
Due date: September 28th 2022, at 11:55pm
Wong Ching Tung Elle
3035926045
Tutorial 003
:
•
Please submit a soft-copy of your assignment to your tutor’s submission box
on Moodle by the deadline. If you have handwritten work, please scan and
combine it with your assignment into one file and submit it to Moodle (and
make sure your handwriting is easily readable).
•
The total mark of a late submitted assignment (if accepted) will be reduced by
5% per calendar day lapsed. Submissions more than six calendar days after
the deadline will not be accepted and you will receive zero marks for that
assignment.
•
For hand calculations (i.e., manual calculations), please show your calculation
steps (e.g., how numerical values are substituted into a formula) and round the
numerical values in your answers to three decimal places.
•
The data collection scenarios and numerical information in the questions are
factitious. Please take “sample” in the questions as referring to a random,
representative sample of the population concerned, unless otherwise stated.
Question 1: [Total: 6 marks]
A university invited 923 of their current full-time students to participate in a surveybased research project, and subsequently 718 of the invited students returned their
completed survey questionnaires. However, 86 of those respondents did not
complete the key questions and their data were therefore excluded from the analysis.
The questionnaire included, but was not limited to, questions asking for the following
information of the students: Their age (rounded to the nearest year), gender, year of
study, Faculty, satisfaction with their academic results, happiness, and frequency of
skipping lectures.
a. What was the sample size for the data analysis of this research? [1 mark]
632
University students
b. Can the mean ratings of the sample on happiness be used to estimate the
mean ratings of the part-time students in the university? Explain why or why
not in no more than two sentences. [3 marks – no marks for “can” or “cannot”
answers without explanation] It cannot Because the population
.
is
different part
,
higher happiness
time students may give owner or
level hand so the mean ratings will be
tiÑii%iiitaY%?
-
different from fun
.
1
,
PSYC1004A 2022-2023 1st Semester
Assignment 1
c. The variable “frequency of skipping lectures” was measured by a multiplechoice rating question with a six-point rating scale from “0” (I have never
skipped any lecture of my courses), “1” (I have skipped a small proportion of
lectures of my courses), to “5” (I have skipped more than half of my lectures of
my courses). The researcher argued that the scores on this question were
ratio data, since if a participant rated zero for this question, the score indicated
no lecture was skipped. Is this justification reasonable? Explain your answers
in no more than two sentences. [2 marks – no marks for “yes” or “no” answers
without explanation]. No it is an ordinal data because I -5 those
,
the
numbers can be ranked to convey order on
lectures)
number of lectures skipped .gg 5 ( skipped more than half of
my
_
'
.
,
is ranked
'
than I l
'
higher and meaning skip more lectures
lectures )
skipped a small proportion of
.
Question 2 [Total: 12 marks]
Determine the level of measurement (nominal, ordinal, interval, or ratio) for the
variable boldfaced in each of the following items. For each answer, explain your
rationale in no more than three sentences. (For each item, no marks will be given for
answers without explanation.)
a. A person’s reaction time on a word recognition task, as a measure of word
recognition latency. [3 marks] Ratio Because the measure in latency
converts order on Saeed of recognizing a word for example longer latency period
or longer reaction time mean slower recognition for words an d. hat an
for example thedifference in latency time
equal interval property ,
10 behinds is the same as 10 to 15 seconds and possess a
between 5 to
0 minutes or latency period theoretically
meaningful zero , for example
a word
he can reckon
time for a
person to recognize
means it takes no
instantly
b. A household’s monthly income bracket range (measured by >0-10,000;
>10,000-20,000; >20,000-30,000) as a measure of household financial
wealth. [3 marks] Ordinal The household 's monthly income conveys order
of household financial wealth but the bracket range does not have an
the difference in financial wealth
equal interval property for example
Cannot be assumed to be the same
and 510000 -20000
between 70-10000
30000
20000 and > noooo
710000
between
as that
.
←
,
,
-
,
,
.
.
.
-
-
.
-
c. The ethnicity of participant as measured by having them select from a set of
provided options (1 = Indian, 2 = Chinese, 3 = Pakistani, etc.). [3 marks]
Nominal The measure 1,2 } act as labels and represent
i
.
different
ethnicity and do not represent orders
2
.
PSYC1004A 2022-2023 1st Semester
Assignment 1
d. A student’s numerical GPA score, as a measure of his/her academic
capability. [3 marks]
Interval Because the GPA
.
sure
3.0 GPAs are
conveys order of academic capability for example
0
academic
ranks higher than 2- GPA meaning higher
interval property for example
capability and has an banal
the same as
the difference in GPA score between 2.0 -3.0 is
that between 3N to 4.0
,
,
-
,
.
Question 3: 21 marks
A high school examined some statistics of a sample of their students’ scores on the
same exam paper to estimate the corresponding school-population values. The
scores in the sample are shown in the table below:
Exam paper scores
Males
80
73
82
86
71
91
75
Females
74
93
81
78
75
82
79
a. Calculate two central tendency measures of the exam scores for each gender
that reflect the typical score values but do not necessarily reflect the
frequencies of the score values. According to each of the two central tendency
measures used, which gender has a higher typical exam score? [9 marks]
Males
mean :
fot*
Females mean
=
79.714
74493481-178-175482-179
:
to 286
.
males median
For mean
for median
,
:
to
Females median : 79
females has
,
malls
has
a
higher typical exams
higher typical exam score
core ,
a
3
while
.
PSYC1004A 2022-2023 1st Semester
Assignment 1
b. Which gender has a higher variability in terms of variance? Calculate the
variance of each gender to support your answer. [5 marks]
to N=4 -4061
Males Variance
Males
aborting
-10N -1=52.571
avoiding
variance
Females variance
Females
according
variance
SO Malet has
according
-74.204
N -1=39.905
to N
to
higher variability
a
.
c. Is there a statistical outlier in the female group of the sample? Work out your
answer based on the Tukey’s hinges and the criteria of a boxplot. [7 marks]
female paper scores
74,75 78,79 81,82193
First arrange
the
,
N'-7
The quartile
765
,
,
,
so the median
position
the 3rd
:
order :
position -17-11112=4
(4+1)/2=2.5
quartile
in
=HHs
eg the 1st quartile
median:
=
,
81.5
79
451¥
,
thedata and
from the rest of
An outlier is a score very different
the box plot can display outliers
g
-7 g. g
Inter quartile rangel 2AM v81.5
.
,
-
{§
85
go
75
70
I
§
-1
-
.
.
:-.
.
€1
There's an outlier as
the highest value of the
data is 93 which exceed
\
,
the upper fence and tower
fence As 93
.
than
.
-
lower fence -16.5-5×1.5=69
81.5-15×1.5=89
4
¥74
lower
fence
before
minimum
upper
larger
89
which is the upper fence , it
is the statistical outlier
-
-
is
fence :
the upper three 93
before
maximum
.
_
,
PSYC1004A 2022-2023 1st Semester
Assignment 1
Question 4 [Total: 12 marks]
The table below shows the average hours slept per day over the past week of a
sample of students. Students were split by whether they are residents of the
university’s hostels.
Number of hours slept
Not resident of a university hostel
Resident of a university hostel
6.4
13
7
7.9
6.7
7.9
8.7
7.4
5.8
7.3
7.3
3.2
5.6
6.5
7.6
5.8
8.6
4
8.3
7
a. Calculate the z-scores of the non-hostel-resident student #2 and the hostelresident student #8 on the average hours slept per day over the past week
(their raw scores are in bold), with reference to their respective sample groups.
Show your calculation steps. Sample summary statistics should be used for
the calculations. [8 marks]
Mean of non hostel resident student :
based on NE 1. Off
resident
student
hostel
SD
non
729
-
of
-
based
C
2- score
-
✓
on
N
-
1) ÷ 1.
126
(7.9-7,29) / 1. Off
:O
.
571
b.
resident student
hostel
of
Mean
resident student l based
of
hostel
SD
=
-
N -11=2 627
v6.91 ) / 2.492=-0.445
Score :( 5 I
.
2-
or
91
on
or
(7.9-7.29)/1.126=0.542
based
NJ 2.492 , l
:
b. For non-hostel-resident student #2 and hostel-resident student #8, calculate
their individual data points’ squared deviations from their respective sample
means. [1 mark]
Non hostel resident student # 8=0.374
Hostel resident student #i. = 1.23M
-
-
5
on
(5,8-6.91)/2.64=-0.423
,
-
,
PSYC1004A 2022-2023 1st Semester
Assignment 1
c. Relative to their respective sample groups, who (non-hostel-resident student
#2 or hostel-resident student #8) was less atypical on the average hours slept
per day over the past week? Explain your answer in no more than two
sentences. [3 marks – no marks for an answer without explanation].
The hostel resident student
less
atypical
because it has a lower 2- score which implies it is
nearer to the uhlan the typical hours slept of
hostel resident students given the data
-
#
I
was
,
,
.
6