Impact of Covid Crisis On Students This report provides an analysis on the life of students based on the survey data collected from the cohort of Data2001 and Data2002. With a focus on the impact of Covid crisis and the life of ordinary student lives.
The analysis will be based on 4 aspects:
1. whether the number of COVID tests taken by a student follows a poisson distribution
2. whether females are more likely to live with their parents than males
3. A test on the population mean of the weekly exercise hours of students
4. Does the time a student spent on daily exercising agree with result of the 2011-2012 health survey of average daily duration of physical activity collected by the Australian Bureau of Statistics
The class survey consisting of 29 questions gathered 211 responses. This report mainly focuses on discussing the number of Covid-tests taken by students, living arrangement and weekly/daily exercise hours of students.
In this report, the missing values that are either defined as NA or empty string were removed before conducting the relevant tests. The code for cleaning was adapted from the code of Tarr (2021).
Discussion
The survey data was not a random sample of the Data2x02 student. The sample selection of the survey was not made randomized but voluntary. This has introduced many biases.
1. Undercoverage bias could be potential as there were students neglecting important Ed announcements. This made them miss out on the survey. The variable ‘What year of university are you in?’ could be affected as many of the first-year students are new to the Ed system. The group was hence not well represented in the survey.
2. Non-response bias took place as some of the students were inactive to be involved with the survey. They were more willing to concentrate on personal matters such as studying, working and socializing
3. Question order bias was introduced by “How do you assess your mathematical ability” and “How do you self assess your R coding ability?”. Furthermore, the successive order could have the latter one affected. Studies(1) have proven people tend to relate a specific question with a general question. In addition, the mathematical ability and R coding ability both assess the learning outcome of a student. Students who had a weaker background in Math tended to also say they were weak in R coding to make their answers internally consistent.
The numeric response questions include ‘How tall are you?’ and ‘What do you believe is the average entry salary in Australian Dollars of a data scientist who has just completed their undergraduate degree in data science?’ should specify a unit of measurement to make the responses consistent to improve. Furthermore, the question ‘How are you finding DATA2002 so far?’ should be answered in numbers instead of using difficulty level. Different people have different understandings of the standard of ‘easy’ or ‘difficult’. Answering the question on a scale of 1-10 would be more appropriate. This allows the survey to collect more expandable responses.
Analysis
Poisson Distribution
In the first section, we look at how has affected the lives of the students with the data of Covid tests
Furthermore, data shows there are 126 students who have taken 0 Covid test during the last 2 months and the detailed table shows below.
Furthermore 0 1 2 3 4 5 6 7 8 10
In addition, 126 40 16 4 5 9 1 1 4 2
Because none of the responses stated that they have taken 9 covid tests we need to manually add a 0 between 8 and 10 to make the vector length consistent with our expected outcome in the later goodness of fit test.
a = vector(mode = “numeric”,length = 11)
a = as.vector(display)
Furthermore [1] 126 40 16 4 5 9 1 1 4 0 2
In the initial phase of analyzing the number of Covid tests, the missing values from the variable are removed. We are able to calculate the mean parameter �� which is 1.02 and the expected cell counts as follows.
By summing up the occurrences of the numbers from 0-10 in the data, we are able to visualize the distribution. The observed counts are shown by the bars. While the red dots represent the expected cell counts under the null hypothesis of a Poison distribution. The number of COVID tests does not follow a Poisson distribution according to the graph. This is because the expected frequencies and observed frequencies are less consistent.
Hypothesis: The number of COVID tests a student has taken in the past two months follow a Poisson distribution vs : The number of COVID tests a student has taken in the past two months does not follow a Poisson distribution
Assumptions: independent observations
The cells where the expected number of counts is < 5 violates an assumption that �� = ���� ≥ 5 which are 3,6,7,8,10 and need to be combined so �� ≥ 3 = 4 + 5 + 9 + 1 + 1 + 4 + 2 = 26, �� ≥ 3 = 17.8
After combining the columns with the expected number of cell counts < 5, we’re left with 4 goal outcomes (0, 1, 2, 3 and 3+), the test statistic will follow a chi-squared distribution with 4−1−1=2 degrees of freedom as we have estimated the mean parameter ��
Test statistic: �� = ∑(ି)మ
ୀଵ . Under ��, �� ∼ ��ିଵ
Observed test statistic: �� = 70.90525 p-value: ��(��ଶଶ ≥ ��) = 0
ଶ approximately.
Decision: Since p-value is less than 0.05, we reject the null hypothesis. We conclude that the data is not consistent with the null hypothesis that the number of COVID tests a student has taken in the past two months follow a Poisson distribution.
Whether females are more likely to live with their parents than males
Males are traditionally considered more independent than females. Moreover, an exploration of whether females are more likely to live with their parents will provide an insight into the topic. In the meantime, the living environment is an essential topic in students’ life. Accompanying family members become rather difficult when they are not living together. A investigation into the topic will give us a deeper understanding of how students’ lives differ depending on their gender during the Covid crisis.
During the data cleaning of the gender variable, Non-binary gender is removed as this analysis is focusing on the differences between males and females.
The responses under living_arrangement(“What are your current living arrangements?”) are categorized into two types: 1. Living with their parents 2. Not living with their parents
Let ������ be the probability of an observation falling in the (i,j)th category. ����. = ∑ ��
ଶୀଵ ���� and ��.�� = ∑ ��
ଶୀଵ ����
Such that ��11 = ��(�� = ������������ℎ��������������, �� = ������������) = ��(�� = ������������ℎ��������������)��(�� = ������������) = (��. 1��1. )
After cleaning we end up with the following table:
Not with parents With parents
Female 15 59
Male 42 87
From the mosaic plot, we have an overview of the data. Independence is shown when the boxes across categories all have the same areas, however they do not have the same areas in this case as shown from the graph.
Test of independence
Hypothesis: ��: The distribution of whether or not living with their parents is the same for both gender vs ��ଵ: The distribution of whether or not living with their parents is not the same for both gender
Assumptions: independent observations and �� = ���� ≥ 5 The expected cell count is > 5 which fulfills the assumption where �� = ���� ≥ 5
Female male
Not with parents 20.8 36.2
with parents 53.2 92.8
Test statistic: �� = ∑ ∑ (ೕିೕ)మ
ୀଵ
ଶ approximately.
ୀଵ . Under ��, �� ∼ ��(ିଵ)(ିଵ)
ೕ
Observed test statistic: �� =$2.9338
p-value: ��(��ଵଶ ≥ ��) = 0.08674
Decision: Since the p-value = 0.08674 > 0.05, we do not reject H0. There is insufficient evidence to conclude that the distribution of whether or not living with their parents is not the same for both gender i.e. The chance of living with parents do not depend on one’s gender.
Population mean of the weekly exercise hours of students
Apart from the focus on the students’ living environment under Covid, physical health should also be a center of focus. This is due to the fact that Covid has made out-door activity less frequent. Studying the time students spend on exercise with various activity restrictions will provide us with a wider view about the impact of Covid.
The question “How many hours each week do you spend exercising?” are consisting of 203 responses after NA values have been removed as we are analyzing based on existing values.
Since exercising 80 hours a week is physically questionable and we are analysing based on the normal population. it is reasonable to remove the outlier.
We can also calculate the mean value and standard deviation of the data that we use for our testing. Mean = 4.38 SD = 3.55
Before we conduct our one sample t test, we shall generate a Q-Qplot and boxplot to check if the data fulfills the assumption of normal distribution. With its five number summary (“minimum”, first quartile (Q1), median, third quartile (Q3), and “maximum”) of the boxplot, we see that the Maximum hours are 20 and its Q1 and Q3 are sitting in 0-10 we can also interpret this as the majority of the students taking the survey are exercising 0-10 hours a week. Meanwhile, we see that the median is roughly in the middle of the box, suggesting the data follows a normal distribution. The QQ plot on the right also indicates a normal distribution
The Australian government has recommended 2.5 to 5 hours of moderate intensity physical activity for adults, we can take the mean of 2.5 and 5 to become our hypothesized value for the one-sample t test. So hypothesized value = (2.5 + 5)/2 = 3.75
We want to know whether the mean is statistically different from the value. Hypothesis: H: �� = 3.75 vs Hଵ: �� ≠ 3.75
Assumptions:
�� ∼ௗ ��(��, ��ଶ)
As our sample is large enough we can safely say that the normality assumption is satisfied and the graph also indicates a clear normal distribution.
Test statistic:
�� =��‾ − �� ��
√��
∼ ��ିଵ ���������� ��
And the degree of freedom are 202-1 = 201 Observed test statistics:
�� =��‾ − ��
��
√��
p-value: ��(��ଶଵ ≤ 2.51) = 0.13 Decision:
qt(c(0.9,0.95,0.975),202)
=4.38 − 3.75 3.55
√202
= 2.51
## [1] 1.285757 1.652432 1.971777
At the level of significance a = 0.05, We reject H because test statistic ��0 = 2.51is larger than the critical value 1.97. We conclude that �� ≠ 3.75
t.test(x$Stab,mu = 3.75, alternative = “two.sided”)
##
Furthermore ## One Sample t-test
data: x$Stab
t = 2.5072, df = 201, p-value = 0.01296
Furthermore alternative hypothesis: true mean is not equal to 3.75 ## 95 percent confidence interval:
3.883830 4.869635
Furthermore ## sample estimates:
mean of x = 4.376733
How many hours a day do students spend doing exercise?
Concluding with the test of the population mean, studying how one’s exercise cycle has changed will add in the depth of our analysis. Lastly, we can do this by comparing the survey data with the health survey data in the past year.
In order to compare the data from the survey to the result of the 2011-2012 health survey conducted by ABS. We convert the weekly-exercise time to daily-exercise time. Moreover, this is done by dividing the responses under:
‘How many hours each week do you spend exercising?’ by 7. Furthermore, the data are further categorized into a rough time range. Where category 0-0.5 includes 0 minute to 29 minutes, 0.5-1 includes 30 minutes to 59 minutes, etc. In addition, the average_daily_exercise looks like this after the cleaning steps are performed.
0 0-0.5 0.5-1 1-1.5 1.5-2 2-2.5 2.5-3 3+
22 67 65 41 1 4 2 1
Moreover, by examining the statistics obtained from the health survey, we obtain the following proportions of daily exercise time for the population aged above 18 and we can see that most of the population spent about 0-0.5 hours exercising per day in 2011-1012.
Physical activity(%)
0 20.3
0-0.5 39.2
0.5-1 21.4
1-1.5 10.0
1.5-2 3.7
2-2.5 2.0
2.5-3 0.9
3-3.5 0.6
3.5-4 0.2
4-4.5 0.3
4.5-5 0.1
5+ 1.3
In the class survey data we do not have any response spending 3-5 hours doing exercise per day, we therefore combine the proportions of ‘3-3.5’ ‘3.5-4’ ‘4-4.5’ ‘4.5- 5’ ‘5+’ into ‘3+’, so the health survey data will be:
Physical activity(%)
0 20.3
0-0.5 39.2
0.5-1 21.4
1-1.5 10.0
1.5-2 3.7
2-2.5 2.0
2.5-3 0.9
3+ 2.5
Under the circumstance, a chi-square-test will be appropriate, let ���� be the probability in the �� hours such that �� = 0, 0-0.5,0.5-1,1-1.5,1.5-2,2-2.2.5,2.5-3,3+ We have two hypothesis:
Null hypothesis: �� = 20.3% ��(ି.ହ) = 39.2% ��(.ହିଵ) = 21.4% ��(ଵିଵ.ହ) = 10.0% ��(ଵ.ହିଶ) = 3.7% ��(ଶିଶ.ହ) = 2.0% ��(ଶ.ହିଷ) = 0.9% ��ଷା = 2.5%
Alternative hypothesis”: The proportions of exercise hours in the class survey do not follow the model. i.e. at least one equality does not hold
To analyse the hypothesis, we firstly draw a a visualization of the observed outcome of daily-exercise hour vs the expected outcome of daily-exercise hour from the health surveys:
In our assumptions, �� = ���� ≥ 5, however the last three cells have their expected number of counts less than 5 which violates an assumption. We hence need to combine the last three cells so the combined outcome fulfills the assumption.
We see the observations for 2+ hours are similar in the observed outcome. But again, two outcomes are different in 1.5-2 hours
chisq.test(new_y,p= new_dd)
Furthermore Chi-squared test for given probabilities
In addition data: new_y
Furthermore X-squared = 49.824, df = 5, p-value = 1.506e-09
Chi-squared goodness of fit test
Hypothesis: ��: �� = 20.3% ��(ି.ହ) = 39.2% ��(.ହିଵ) = 21.4% ��(ଵିଵ.ହ) = 10.0% ��(ଵ.ହିଶ) = 3.7% ��(ଶିଶ.ହ) = 2.0% ��(ଶ.ହିଷ) = 0.9% ��ଷା = 2.5%
��ଵ: In addition, the proportions of exercise hour in the class survey do not follow the model. i.e. at least one equality does not hold
Assumptions: independent observations and �� = ���� ≥ 5
Test statistic: �� = ∑(ି)మ
ୀଵ . Under ��, �� ∼ ��ିଵ
Observed test statistic: �� = 49.824 p-value: ��(��ଶଶ ≥ ��) = 0
ଶ approximately.
Decision: Since the p-value = 0 < 0.05, we reject H0. There is strong evidence against in the data against ��, the class survey data does not agree with the proportions introduced by the health survey
From the chi-square test, we perceive that the daily exercise hour of students is no longer consistent with the data obtained from the 2011-2012 Health survey. Particularly, there are more people exercising more than 0.5 hours a day.
Limitations and Conclusion
This report concludes with the findings that 1. The Covid-tests an individual has taken during the past 2 months do not follow a poisson distribution 2. Gender does not affect the chance that a student is living with their parents 3. The daily exercise cycle of students have changed since 2011-2012
Apart from the biases discussed in the introduction, the main limitation comes from the question ‘How many hours each week do you spend exercising’, the result after converting the numeric into a specific range (e.g. 1.2 hours to 1-1.5 hours range) might be inaccurate as requiring a numeric response can be too strict for this type of question. Instead, range can reduce potential inaccuracies caused by strict standards.
Appendix
(1) https://academic.oup.com/poq/article
abstract/55/1/3/1819909?redirectedFrom=fulltext NORBERT SCHWARZ, Furthermore, FRITZ STRACK, HANS-PETER MAI, ASSIMILATION AND CONTRAST EFFECTS IN PART WHOLE QUESTION SEQUENCES: A CONVERSATIONAL LOGIC ANALYSIS, Public Opinion Quarterly, Volume 55, Issue 1, SPRING 1991, Pages 3–23, https://doi.org/10.1086/269239
Impact of Covid Crisis On Students : Furthermore, Impact of Covid Crisis On Students
Leading Artificial Intelligence and Financial Advisor – Rebellion Research
