BUSI 820: ASSIGNMENT 3
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Assignment 3 Quantitative Analysis: Descriptive Statistics, Ordinal Scale, and Dichotomous
Variable Assignment
BUSI 820 Quantitative Research Methods
February 2, 2025
BUSI 820: ASSIGNMENT 3
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Table of Contents
SPSS Problems 3
A3: Chapter 4, Problem 4.1. 3
Figure 1...………………………………………………………………………………….4
A3: Chapter 4, Problem 4.2. 4
Figure 2….………………………………………………………………………………4-5
A3: Chapter 4, Problem 4.35
Figure 3...………………………………………………………………………………….5
Results………………………………………...………………………………………….……….6
Figures 4-10.……………………………………………………………………………7-8
A3: Chapter 4, Problem 4.49
Figure 11.………………………………………………………………………………...10
References 11
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SPSS Problems
A3: Chapter 4, Problem 4.1. For the variables with five or more ordered levels, compute
the skewness. Describe the results. Which variables in the dataset are approximately
normally distributed/scale? Which ones are ordered but not normal?
The variables with five or more ordered levels include positive evaluation institution,
major, facilities, and social life, as depicted in figure 1. These variables follow an ordered level
system where 1 signifies strong agreement, 2 indicates disagreement, 3 is neutral, 4 represents
agreement, and 5 denotes strong agreement. Other variables in the set possess less than three
ordered levels. These variables produce outputs such as the number of subjects (n), range,
minimum and maximum scores, mean for each variable, standard deviation, variance, skewness
statistic, and the standard error of the skewness. The valid?n?value is 49, symbolizing the total
number of participants in the data set. It's crucial to remember that a skewness value within the
range of plus/minus one indicates a normal distribution range. If the skewness value falls outside
this range, the distribution is not normal. A skewness value greater than one in the positive range
implies a right-skewed distribution, while a value less than negative one indicates a left-skewed
distribution (Morgan et al., 2020). As per Morgan et al. (2020), all four measured variables fall
within the normal distribution, as illustrated in figure 1. It can be shown with all four variables
are within the normal distribution scale of plus/minus one range. Drawing from the information
given in the preceding section, it can be inferred that they all fall within the normal distribution.
However, if we consider zero as the benchmark for neutral distribution, any value below or
above it could indicate a slight skewness. Furthermore, the primary variable, in some instances,
may not have sufficient data, which could potentially lead to signs of skewness (Morgan et al.,
2020).
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Figure 1
Descriptive Statistics Variables with 5 or More Ordered Levels
A3: Chapter 4, Problem 4.2. Do a stem-and-leaf plot for the same-sex parent’s height split
by sex at birth. Discuss the plots.
Referencing the below Figure 2, the first number of heights in the stem-and-leaf plot
represents same-sex parents, while the leaf is depicted by the last number (Morgan et al., 2020).
The collected data was complete, with no missing information, and the measurements were
interpreted in inches (1"). The median height for males and females was 72" and 62"
respectively. The largest concentration of males was around 74/75", while for females it was
approximately 62". From the participants in the study, the tallest individual was a male
measuring 76", and the shortest was a female at 62". Both measurements fall within the normal
distribution range. There was one male outlier with a height of 69", and no female outlier at 61".
However, there was one female outlier at 58". These findings suggest that males are generally
taller than females.
Figure 2
Stem-and-leaf Plot Same-Sex Parent’s Heigh Split by Sex at Birth
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A3: Chapter 4, Problem 4.3. Which variables are nominal? Run Frequencies for the
nominal variables and other variables with fewer than five levels. Comment on the results.
Referencing Figure 3 below, the variables that are nominal include sex-at-birth, marital status,
subject with children, television shows-sitcoms, television shows-movies, television shows-
sports, television shows- news shows, and age group. These nominal variables all have less than
five levels.
Figure 3
Statistics of Nominal Variables
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Frequency charts utilize percentages to depict the results gathered from the total number
of participants who selected a specific category, participated in each category, and the
cumulative percentage in each category. The results are as follows, frequency reports for the
mentioned nominal variables were run, please refer to Figures 4-11 below, when referencing the
results.
Regarding participant demographics sex-at-birth, males constitute 52% of the
participants, while females make up the remaining 48%. For marital status: 36.7% of the
participants are married, while 63.2% are not. One unit was not accounted for in this category.
Results for parenthood showed the participants are almost evenly split in this category, with 48%
not having children and 52% having children. Lastly, age: 30% of the participants are 30 years or
older, while the majority, 70%, are younger than 30. Notably, 17 participants are under the age
of 22.
Regrading television viewing habits, 36% of the participants do not watch sitcoms, while
a majority of 64% do. It is evident that more participants do not watch movies, 64%, compared
to those who do at 36%. For sports, the participants are almost evenly split in this category, with
48% not watching sports and 52% watching. Lastly, more participants do not watch news, 54%,
compared to those who do, 46%. Further insights can be obtained by examining the gender
distribution among each television show category and making comparisons. According to the
data, sitcoms are the most-watched category, while movies and news are the least popular.
Figure 4
Frequency Report Sex-at-birth
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Figure 5
Frequency Report Marital Status
Figure 6
Frequency Report for Subject with Children
Figure 7
Frequency Report for Television Shows-Sitcoms
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Figure 8
Frequency Report for Television Shows- Movies
Figure 9
Frequency Report for Television Shows- Sports
Figure 10
Frequency Report for Television Shows- News Shows
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A3: Chapter 4, Problem 4.4. Do boxplots for student height and for hours of study.
Compare the two plots.
The frequency table provides a comprehensive overview of the responses from all
participants. It reveals a normal distribution of data, which is a key characteristic of a well-
balanced dataset. The median value, which is the middle value when the data is arranged in
ascending order, is notably high at 67.3". The range of the data, which is the difference between
the highest and lowest values, spans from 60" to 75". The mode, or the most frequently occurring
value, is 64". The boxplot, Figure 12 below, which is a graphical representation of the five-
number summary (minimum, first quartile, median, third quartile, and maximum), shows a
normal distribution of study hours. This suggests that the data is symmetrically distributed
around the median. On the other hand, the histogram, which is a graphical representation of the
frequency of data, exhibits a right skewness. This indicates that there are a few unusually large
values in the dataset, which pull the mean towards the right of the median. The median study
hours per week is 15.62, indicating that when the study hours are arranged in ascending order,
the middle value is 15.62 hours. The range of study hours is quite wide, varying from a minimum
of 2 hours to a maximum of 38 hours per week. The mode, or the most frequently reported study
duration, falls within the 10-12 hours per week bracket. Interestingly, only about 2% of the
students reported studying for as little as 2 hours per week. There was also an outlier in the
dataset, with one student reporting an unusually high study duration of 38 hours per week. This
outlier could potentially skew the data and should be taken into account when interpreting the
results.
Figure 11
Boxplots for Student Height and Hours of Study
student
height
in
inches
hours
of
study
per
week
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References
Morgan, G. A., Barrett, K. C., Leech, N. L., & Gloeckner, G. W. (2020).?IBM SPSS for
introductory statistics: Use and interpretation?(6th ed.). Routledge.
