IAFOR Journal of Education: Technology in Education

Volume 10 – Issue 2 – 2022

The Link between Internet Connectivity and Missed Assessmentsin the Online Class Modality
Willington Onuh
De La Salle University-Dasmariñas, Dasmariñas City, Cavite, Philippines
Olivia M. Legaspi
De La Salle University-Dasmariñas, Dasmariñas City, Cavite, Philippines
Susan T. Mostajo
De La Salle University-Dasmariñas, Dasmariñas City, Cavite, Philippines
Don S. Malabanan
De La Salle University-Dasmariñas, Dasmariñas City, Cavite, Philippines
Rosario T. Reyes
De La Salle University-Dasmariñas, Dasmariñas City, Cavite, Philippines

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Abstract
Many published papers provide insights on factors affecting learning performance; however,they do not address how internet connectivity affects students’ capacity to meet assessment
and learning expectations. To address this gap in the literature, we draw from a survey of 257
students at the undergraduate level to investigate two questions: (a) To what extent doesinternet connectivity affect missed assessments? and (b) How do students vary through the
distribution of missed assessments? We used a count data model, specifically, negative
binomial (NB) regression, to determine incidence rate ratios and odds of missed assessments.
The NB results showed that students who indicated poor internet connectivity during thesemester had about a five times higher incidence rate of missed assessments than students who
did not indicate poor internet connectivity. Surprisingly, despite two-thirds of students
reporting poor internet connectivity, the chance of accumulating seven missed assessments
during the semester was very minimal. The results may provide insights to faculty andeducation policymakers at the institutional level on ways to design online learning to meetlearning expectations.
Keywords: internet connectivity, learning performance, missed assessments, online modality

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Since COVID-19 was declared a pandemic by the World Health Organization (WHO) in thefirst quarter of 2020, there has been no shortage of research papers on how it has transformed
learning in higher educational institutions around the world. Online learning in many parts of
the world, especially in developing countries, faced a number of constraints, such as access tointernet connectivity, financial resources to procure technological devices and physicalenvironment conducive for effective learning (Fishbane & Tomer, 2020; UNESCO, 2020;
Affouneh et al., 2020; Crawford et al., 2020; Limniou et al., 2021). Furthermore, because
online learning is dependent on digital tools, many schools implemented varying digitallearning activities based on resource capacity and platform limitations (Joshi et al., 2020).
While there are a number of new online learning technologies available in the market today toboost both learning and delivery capacity by faculty (Goh & Sigala, 2020), many schools lackthe capacity to procure these new technologies. Even when schools can afford such platforms,
students may not have adequate digital devices or a conducive environment to engage faculty(Arora & Srinivasan, 2020, Agarwal & Kaushik, 2020; Chick et al., 2020).
Experiences in online modalities are not entirely negative. An expansive body of researchshows positive effects of online transition on students (Babbar & Gupta, 2021; Muthuprasad
et al., 2021; Chisadza et al., 2021). Chisadza et al. (2021) identified clear opportunities withrespect to the shift to online learning. Babbar & Gupta (2021) measured benefits of online
learning in terms of innovations in the types of assessments used in higher education.
Muthuprasad et al. (2021) explored students’ preferences for various attributes of online classes
including online learning environment. They found that the main attraction to online classes
are flexibility and convenience brought by online learning. For the most part, it has become
increasingly possible for students to get into classes from the comfort of personalized spaces.
From all indications, digital inequality, described by Beaunoyer et al (2020) as “… access to
networks or connected devices, or when it comes to the skills required to navigate
computerized spaces optimally” (p. 1), remains a problem for online education in developed
and developing countries. Prior studies have shed light on various aspects of the problem ofdigital inequality: sustainability or environmental conditions in Mexico (Vargas et al., 2020);
internet connectivity and socio-economic class in Ireland (Cullinan et al., 2021); internet usage
and academic achievement in Indonesia (Soegoto & Tjokroadiponto, 2018); internet accessand power outage in Nigeria (Ivwighreghweta & Igere, 2014); low income students and online
education in India (Jain et al. (2021); limited laboratory-related courses and internet
connectivity in the Philippines (Rotas & Cahapay, 2020; Cahapay, 2020); academic
performance and access to WiFi in South Africa (Chisadza et al., 2021); and internet
connectivity and lower remote learning proficiency in the USA (Katz et al., 2021).
There has been almost no empirical work on the relationship between internet connectivity andmissed assessments except for Katz et al. (2021) which focused on the association between
internet connectivity and lower learning proficiency in an online modality. Given how theeducation sector around the world was forced to go online and the inherent problem ofbalancing quality and expectations of students’ compliance with online assessments, there is
an important gap to fill in understanding the full range of what might be necessary in designingonline learning. When many schools transitioned to an online modality, the traditional
institutional guidelines governing the conduct of class were formulated for face-to-facecontext. Applying these guidelines without clear understanding of underlying factors driving
student responses to assessments became a problem. Granting extensions to assessments
submitted after a deadline in face-to-face classes is a common issue faculty deal with all thetime. In online settings, missed assessments assume a different dimension because not only are

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digital devices needed, but also internet connectivity is required to drive the virtual meetingand facilitate timely submission of assessments. Understanding how internet connectivity isrelated to the number of missed assessments can serve as a reference for setting guidelines thatgovern expectations in online learning and outcomes as well as the administration of theseassessments.
To contribute to literature, the study investigated two questions: (a) To what extent doesinternet connectivity increase or decrease missed assessments? and (b) How do students varyin the distribution of missed assessments? We use a count data model which allows for discretevalues in regression estimation to examine the relationship between internet connectivity andnumber of missed assessments and analyzed odds of missing assessments. The goal is tounderstand a possible potential allowable number of missed assessments that students may
incur in an online modality without penalty. Overall, our focus on the relationship between
internet connectivity and missed assessments distinguishes our paper from the only similar
work done in the US using a unique data set from 30 universities from 19 states and the Districtof Colombia on internet connectivity and lower Remote Learning Proficiency (Katz et al.,2021).
Prior studies have made enormous contributions to online learning in the literature especiallyin the area of learning outcomes; however, this study may be the first to model missed
assessments of students in an online modality in higher education using a count data model.
We believe that the findings appeal to a broad spectrum of online advocates, readers andeducators including education policymakers.
The rest of the paper is organized as follows: Section 2 describes the data sources and summary
statistics including institutional context of missed assessments, Section 3 gives the empiricalstrategy including detailed theoretical and empirical formulation of the estimation process,Section 4 discusses the main results, and Section 5 offers concluding remarks and draws policy
implications.
Educational Setting and Data
Institutional Context of Assessments and System’s Theory in Education
Assessment is a key process of learning in higher education. In fact, assessment has been
described by Hodges et al. (2014) as “intrinsically linked to student learning and performance”(p. 189). Assessment as an integral part of higher education has been exhaustively studied andtheorized (Hodges et al., 2014) and its role in feedback mechanisms facilitating learning has
been well-documented (Graham et al., 2021). But as educational institutions transitioned fromthe traditional face-to-face to online classes, many schools were faced with two problems
occurring simultaneously: relevant data for suitable guidelines for online classes and adequate
digital infrastructure including stable internet connectivity (Chisadza et al., 2021; El Said,
2020).
There are three types of assessments that are commonly used in varying forms in online
modalities: formative, enabling, and summative. Formative assessment, as the name implies,
involves more frequent informal activities used in between teaching to gauge students’
understanding of lectures and does not count toward grades directly. It is used to prepare
students for either enabling or summative assessments (Burkhardt & Schoenfeld, 2018).
Enabling assessment is periodic and more frequent compared with summative assessment.

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Enabling assessment may be described as mini-summative in the sense that it gauges progressof learning on a much smaller scale at different points within the same module (e.g., consistingof few chapters). It is not uncommon to have two or three in one module depending on thesubject. Examples include multiple choice questions, short essays, debate exercises, etc. On
the other hand, summative assessment is usually designed to gauge overall grasp of the entire
module or multiple modules and may involve written examinations, written research papers or
well-designed projects (Guangul et al., 2020).
Overall, assessment has been described as a good measure of both quality and progress inonline learning (Babbar & Gupta, 2021). However, even when assessments have beendeveloped by experts to elicit a given performance, its usefulness will ultimately depend on
digital infrastructure and home conditions driving communications and feedback in both
directions (students and faculty) for smooth and unrestricted learning to take place (Yan &Carless, 2021). Yet not enough attention has been given to the effect of internet connectivity
on students’ ability to meet online assessment expectations. Assessments help faculty makebetter decisions on students’ progress (Carless & Winstone, 2020); however, when students
are unable to submit assessments in a timely manner due to poor WiFi reception or internet
connectivity, faculty may apply penalties indiscriminately which is contrary to how the
feedback mechanism should work. Kintu et al. (2017) notes that, “efficient use of a learning
management system and its tools improves learning outcomes in e-learning and blended
learning environments” (p. 5). Evidence of the challenges faced in an online modality due tolack of clear cut guidelines governing conduct has been documented (Guangul et al., 2020).
Our goal in this section is to situate online assessment within the literature of learning outcomesusing general systems theory applied to education to inform our empirical strategy in Section
3. In the conceptual framework (Figure 1), we propose that well-thought out institutionalguidelines for the online modality should be informed by inputs from missed assessments in a
feedback mechanism. System’s Theory in Education is anchored on General System Theory(GST) founded by Von Bertalanffy in the 1930s (Drac, 2015), which has been used extensively
in educational research to analyze educational output as a function of inputs at different levels(John, 2010; Garira, 2020). Systems theory acknowledges the universality of the feedback
mechanism as a necessary component to achieve desired learning outcomes. Viewed throughthis lens, institutional guidelines become part of a school’s inputs in an educational production
function in which minimizing the number of missed assessments is an objective function to beachieved for desired learning outcomes to occur (John, 2010).
We denote missed assessments as the sum of enabling and summative assessments students’failed to submit on deadline during a given semester. In reality, some students may miss only
one type of assessment, enabling or summative, and not necessarily both. Institutionalguidelines should be formulated with a clear understanding of what these rules are supposed toaddress. For example, how many missed assessments can be tolerated in online modality in agiven subject per semester? When and how should faculty intervene if there is a clear indicationthat the reason for missed assessment is not valid? These questions relate broadly to thespectrum of issues associated with formulating guidelines for effective learning outcomes.
Exhaustive discussion of factors affecting learning outcomes are diverse and complex(Malecka et al., 2020), and beyond the scope of this paper. The study’s goal is to highlight that
feedback mechanisms could be used to improve learning outcomes through integrating relevant
institutional guidelines. Figure 1 illustrates the relationships between institutional guidelines,
missed assessments and learning outcomes. When institutional guidelines are set arbitrarily,

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there is a possibility that they may create a ripple effect influencing enabling and summative
assessments, total number of missed assessments and learning outcomes
Figure 1
Proposed Relationship between Institutional Guidelines and Missed Assessments with
Feedback Mechanism

As shown in Figure 1, formative assessment does not count toward grade and is assumed toinfluence enabling assessment indirectly because many faculty members do not incentivize its
completion. It is used to prepare students for graded assessments such as enabling orsummative. Guangul et al (2020) noted that, “formative and summative assessments inconjunction with appropriate feedback systems are used to support learning in higher
education” (p. 521). Our framework (Figure 1) depicts the possible interplay between enablingand summative assessments. The double-headed arrow indicates that enabling assessment may
influence summative assessment, and can itself be influenced by summative assessment. Thisis primarily because a missed assessment is assumed to be cumulative, that is, inability tosubmit an enabling assessment may influence submission of a summative assessment and viceversa. As shown in Figure 1, the feed forward from [1] through [4] to [5] may occur in anenvironment where institutional guidelines are set arbitrarily. The dashed line depicts a system
which provides for a number of missed assessments to be used as input for policy changes at
the institutional level through a feedback mechanism. In case of well-thought out guidelines,
the possibility of [1] to [5] upper loop may be realized on efficiency grounds due to the absenceof impeding factors. Additionally, the feed forward from [1] through [4] to [5] may be
improved as well using a feedback mechanism. The proposed conceptual framework can beused to understand a system in which minimizing the number of missed assessments andimproved learning outcomes are objective functions. An empirical link between missed
assessments and internet connectivity may provide the starting point in addressing policychanges at the institutional level. We describe our data set and present summary statistics
below.

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Data Source and Summary Statistics
This study was based on the data collected from 257 undergraduate students enrolled in online
classes at a private university in the Philippines during the second semester of school year
2020-2021. The student participants were from two colleges (Education, CE and Business
Administration, CB) covering 4 programs (Education, Economics, Finance andEntrepreneurship). The two colleges were selected based on the professors’ willingness to join
the study and ability to handle the challenging data collection process. Participating facultyteach courses with term papers (with well-defined rubrics for evaluation) as part of the final
requirement. The rubrics used to evaluate the final requirement were comparable acrossprograms to reduce instructional heterogeneity.
Internet connectivity was measured through student binary answers [yes or no] to the question:
Have you missed an assessment deadline or online class due to poor internet connection? The
number of missed assessments was measured through the question: How many times in the lastsemester? The actual number of missed assessments and performance scores on the final classrequirement were generated from class records downloaded from the online platform. Students
were given at least one week to submit assessments. The online platform prevented submission
after the deadline. Other characteristics, such as personal and family background were collectedfrom students using survey questionnaire forms. Data collection was approved by the
University’s Ethics Review Committee. As expressed in the informed consent document,
participation in the survey was voluntary and included a statement regarding the right ofstudents to withdraw at any point during the data generation process without consequences.
There were no incentives given to any student for answering the questionnaire to avoid undue
influences and to minimize errors. Table 1 reports the definitions of socio-economic anddemographic characteristics of student participants.

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Table 1
Definition of Variables used in the Analysis
Variable nameDefinition
Dependent variable
Missed Assessment*
Number of missed assessments
Explanatory variables
Internet connectivity
Team participation
Performance
Age
Household size
GenderStudy hour
Father's Employed
Mother's Employed
Father's Education
Mother's Education
College of Business (CB)College of Education (CE)
Job
GPA
Team preferenceElectricity bill

Students who reported to have missed assessments due to poor internet
connection, value=1 if yes,0 otherwise
value =1 if the output is solo, 0 otherwise
Final score on paper
Age of respondent
Number of people in the household
value =1 if respondent is male, 0 otherwise
Number of hours per week in studying
value =1 if employed, 0 otherwise
value =1 if employed, 0 otherwise
value =1 if college graduate, 0 otherwise
value =1 if college graduate, 0 otherwise
value =1 if home college is Business, 0 otherwise
value =1 if home college is Education, 0 otherwise
value =1 if student has a part-time job, 0 otherwise
Current Grade Point Average (as of last semester)value =1 if student always prefer individual work not group, 0
otherwise
Estimated cost of family electricity bill per monthNote. *Summative and enabling assessments submitted after deadline

Table 2 reports descriptive statistics of students who participated in the study. The average
number of missed assessments was 2.6 (SD = 3.04), but ranged from 0 to 15. The minimum
number of graded assessments in a given semester was 12 (4 summative and 8 enabling).
Assessments were structured to ensure that one assessment did not carry too much weight in
the final grade. Formative assessments were not graded, but were commonly used by faculty
to provide students with an opportunity to practice skills as a lead-in to both enabling andsummative assessments. About 66% of students reported having poor internet connectivity,
while 34% did not report experiencing poor internet connectivity.

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Table 2
Descriptive Statistics
Variable
Poor internet connection (yes)Number of missed assessments
Gender (male)College of Business (yes)GPA
Working student (yes)Preference for group output (yes)Father is college graduate
Father has a job (yes)Mother is college graduate
Mother has a job (yes)Study hours/week
Household size
Electricity bill (monthly)
Age
Performance (Avg.score final paper)
Solo (individual output = yes)

Mean
0.66
2.60
0.31
0.79
3.35
0.19
0.67
0.63
0.79
0.68
0.59
23.88
5.21
4375.48
19.65
88.76
0.52

Std. Dev
0.47
3.04
0.46
0.41
0.64
0.67
0.46
0.48
0.40
0.46
0.49
20.52
2.53
2982.83
1.77
7.37
0.50

Min
0
0
0
0
1
0
0
0
0
0
0
1
0
600
15
70
0

Max
1
15
1
1
4
8
1
1
1
1
1
120
26
18000
35
97
1

Note. Monthly bill expressed in Philippine pesos (US$1=Php50).
Theoretical and Empirical Strategy
Formulation of Missed Assessments
Examining the link between internet connectivity and missed assessments presents special
econometric challenges. First, the number of missed assessments by students is a countvariable, therefore, treating it simply as continuous variable and applying linear regression will
result in biased estimates and may be improved using a count model such as Poisson (Greene,2003). Second, using the Poisson model does not guarantee unbiased estimates. This is because
missed assessments may not conform to the restrictive nature of the Poisson model. Greene(2003) points out, “Poisson has been criticized because of its implicit assumption that thevariance equals its mean” (p. 743). Assessments are typically cumulative, missing one
assessment increases the chance of missing another assessment as course requirements
progress over the duration of the semester. This may explain why the independence assumptionof the Poisson model is often violated (Sturman, 1999; Wooldridge, 2002).
To address this challenge, we first modeled missed assessments using the restrictive Poissonmodel to assess whether missed assessments conform to the standard Poisson’s assumption
which states that the of mean of missed assessments must equal its variance. Preliminary
analysis of the data indicated that the Poisson model did not apply. If the Poisson model wasapplicable, it would imply that missing one assessment does not necessarily increase thechances of missing another assessment. In reality, our data analysis implied that it does,
meaning that a less restrictive model like negative binomial is more appropriate for analyzing
missed assessments.

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Negative binomial is less restrictive and allows for the possibility that variance of missed
assessments can exceed the mean (Yirga et al., 2020). We modeled the number of missed
assessments of each student (yi) in the four programs during the semester using a negative
binomial model, which is assumed to take nonnegative integer values (i.e., 0 or greater thanzero). We assumed that y is a random variable which shows the number of times students havemissed assessments during the second semester, school year 2020-2021. The maximum
likelihood estimator using the Poisson distribution is used to estimate the mean. Essentially,
we are looking for the mean (lamda, λ) of missed assessments given the number of assessments(yi) missed by each student during the second semester. This problem can be said to follow the
Poisson distribution and each missed assessment has a Poisson distribution expressed as yi ~Pois (λ). The probability density function (PDF) of each missed assessment given the mean
parameter (λ) can be formally expressed in equation 1 including all relevant equations used in
the estimation process (Appendix 1). Our primary specification related the number of missed
assessments (y) to other explanatory variables (x’s) in which the key variable is internet
connectivity shown in equation 12 (Appendix 1).
Results and Discussion
We examined the link between internet connectivity and missed assessments in two ways:
differences between students reporting poor internet connectivity and those who did not reportpoor connectivity in our sample (Table 3) and incidence ratio (Table 4). Table 3 shows that themean number of missed assessments among students who reported poor internet connectivity
was 3.62 (SD = 3.12; higher than sample mean in Table 2), while among students who did notreport experiencing poor internet connectivity, which was about 0.80 (SD = 1.81) missed
assessment. The p-value is highly significant, which implies that between the two groups, thenumber of missed assessments was on average different. This first evidence provides the needfor further analysis using negative binomial in Table 4.
Table 3Comparison of students' characteristics using two sample t test
Variable
Poor Internet Connectivity
Yes
No
Mean
Std.D
Mean
Std.D
Missed Assessment
3.62
3.12
0.80
1.81
GPA
3.27
0.66
3.54
0.51
Study hours
22.53
18.84
26.60
23.40
Household size
5.18
2.22
5.27
3.07
Electricity bill4435.62951.624290.573059.73
Age
19.79
1.88
19.37
1.51
Performance
88.36
8.60
89.64
3.95
Note. ***1% ; *10%16t

-7.24 ***
3.35 ***
1.50
0.27
-0.36
-1.77 *
1.31

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Table 4Generalized binomial regression for missed assessments
Variable
Missed Assessment (Count = dependent)

IRRInternet connection(poor=yes)
AgeHome College (CBAA=yes)
Household size
Study hours
Group preference (Individual = yes)
Education of father (college=yes)
Education of mother (college=yes)
Job of mother (employed=yes)
Job of father (employed=yes)
Student (parttime job =yes)
Gender (male)Electricity bill

4.936
1.146
2.137
1.052
0.996
0.871
1.056
1.258
1.135
0.794
1.181
1.033
0.999

Constant

0.209 ***

LnalphaAlpha
LR test of alpha=0: chibar2 (01);Prob >= chibar2
Log likelihood
Number of observation
LR chi2 (12)Prob > chi2
Pseudo R2-0.4040.667
111.490.000-415.952
214
77.87
0.000
0.086

***
***
**
*

Std.
Error
0.927
0.064
0.695
0.032
0.004
0.139
0.197
0.251
0.187
0.159
0.124
0.174
0.001

Conf. Interval
(95%)
3.415
7.133
1.027
1.281
1.129
4.045
0.991
1.117
0.988
1.004
0.635
1.192
0.733
1.523
0.851
1.861
0.821
1.569
0.536
1.176
0.962
1.449
0.742
1.438
0.999
1.000

0.027

0.001

0.267

0.192
0.127

-0.779
0.458

0.084
0.972

Note. ***1%, **5% and *10%

The results of our empirical link between missed assessment and internet connectivity basedon equation 12 (Appendix 1) are presented in Table 4. But before evaluating the coefficients,
we tested the appropriateness of the negative binomial model. As discussed in the model
formulation (Appendix 1), negative binomial models assume that the conditional means are
not equal to the conditional variances. To test this assumption, we used a likelihood ratio test
that alpha equals zero. This test compares this model to a Poisson model. The lower left sectionof Table 4 shows the associated chi-squared value of 111.49 with one degree of freedom. The
probability value is highly significant, which suggests that alpha is non-zero and implies thatnegative binomial model is more appropriate than the Poisson model.
The coefficients in Table 4 are expressed as incidence rate ratios (IRR). Results indicated apositive and significant link between poor internet connectivity and missed assessments.
Students who reported to have poor internet connectivity had a 4.93 times higher incidence rateof missed assessments than students who did not report to have poor internet connectivity
holding other variables constant. On average, older students tended to have higher incidenceof missed assessments. To put it differently, a one-year increase in age tended to increase17

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missed assessments by 1.15 times (or about 15%). The incidence rate of missed assessments
for students from CB was 2.13 times higher than the incidence rate of students from CE.
Additionally, household size tended to increase the incidence rate of missed assessments.
Increase in household size by one increased the incidence of missed assessments by 1.05 times(or about 5%).
Perhaps relationships between internet connectivity and missed assessments is not surprising,
given that results from previous studies in online learning have alluded to it indirectly. In
particular, Joshi et al. (2020) showed that educational technologies are correlated with the levelof learning outcomes. Babbar and Gupta (2021) and Allen (2015) described assessments as the
key driver of quality in any educational system, and recommended requiring academic
institutions to focus on the integrity of assessments. Our results not only point attention tointernet connectivity as a barrier to online learning, but also highlight issues regarding
expectations and compliance by students with respect to online requirements. In Figure 2 andTable 5, we revisit the problem of missed assessments through visual illustration of predicted
odds given the sample of students in this study.
The findings on age indicate that missed assessments may increase with age. We found thiscounterintuitive since older students tend to be more mature and responsible. But, literature has
also shown that students of different age categories may be interested in different sets ofassessments (Aldrich et al., 2018), which may explain the differences in missed assessments.
Older students may also have additional non-school responsibilities related to work and/or
family. However, the link between age and missed assessments has not been explicitly
examined by previous studies and may require more research to understand the mechanisms
through which age affects missed assessments.
Less surprising is the incidence rate of household size and missed assessments. Thoughprevious studies may have linked household size to an array of factors including educational
goals, our interest lies on how size of household may impact the home environment setting in
online modalities, which in turn may influence students’ missed assessments. Household size
may be associated with home factors producing concurrent mechanisms with countervailing
effects. For example, an increase in household size may increase the number of people using
the internet at a given time which in turn may affect internet stability especially when
bandwidth is low.
To examine the probability and odds of missed assessments, we used information on meanvalues of missed assessments from Table 2 and a special command from Stata software toprobe further on the number of missed assessments by students. We calculated the odds ofmissed assessments by students, and used the calculated probabilities to generate Figure 2,
which visually illustrates the relationship between mean probability and number of missed
assessments in the sample. The computation of probability and odds of missed assessments inTable 5 provides useful quantitative information. For example, there is a 7% chance of not
missing assessments across all four programs in the sample, which tells us that it is possible tohave zero missed assessments in a given semester. While the zero missed assessment is not
impossible, it is not a realistic expectation for all students given what we know from Table 4.
However, looking at the other extreme, there is only about a 1% chance of missing sevenassessments in a semester. We can also examine Table 5 through cumulative probability(pcum), that is, the odds of a specific number of missed assessment. For example, the odds areabout 75% that students miss at least two but no more than four assessments, with the peak at
two (25% odds). We transformed Table 5 into a visual representation in Figure 2. In this18

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representation, the vertical axis records probability ranging from 0 to a little over 25% and thehorizontal axis records the number of missed assessments. As can be gleaned from Figure 2,
missed assessments peaked at number two. Notice how the number of missed assessments
decreases after number six missed assessments and progressively approaches zero. Figure 2
provides interesting insights regarding missed assessments and can help inform policy makers
regarding the number of missed assessments that may be deemed reasonable in any given
semester considering all possible scenarios including poor internet connectivity and other homefactors. As Figure 2 illustrates, the 7th missed assessment lies to the right and far away fromthe mean of the entire sample suggesting that the probability of accumulating the 7th missed
assessment is very low.
Table 5
Probability or Odds of Missed Assessments (2.6*)**

Number
0
1
2
3
4
5
6
7

Probability
0.074
0.193
0.251
0.217
0.141
0.073
0.031
0.011

Cumulative probability (pcum)
0.074
0.267
0.518
0.736
0.877
0.951
0.983
0.994

Note. *Mean of missed assessments; **number of missed assessments

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Mean of Probability

Figure 2
Number of Missed Assessments with Mean of Probabilities

Suppose that an institutional policy mandates the number of allowable missed assessments
during each semester to be arbitrarily set at one? This will be impractical given the underlying
forces which may increase missed assessments in a given semester. However, in order tocompel students to maintain a sense of responsibility and adhere to expectations regardless ofhome conditions, it may be reasonable to keep the number of allowable missed assessments to
between six and seven beyond which some level of penalty may be assessed in the form of
decreased score. Without clear-cut institutional guidelines, faculty are left with the burden of
having to figure out what may constitute valid reasons for missed assignments. As shown in
Figure 2, mean probabilities can help to inform institutional rules governing expectations ofstudents in online modalities.
Conclusion, Implications, and Recommendations
The unprecedented occurrence of COVID-19 pandemic compelled educational institutions tocarry out online learning modality which created challenges to school administrators, teachers,
and students particularly on the effective facilitation of the teaching-learning process. As thismethod relies heavily on internet connectivity, the current study delved into finding the link
between internet connectivity and students’ missed assessments. Results revealed that there isa positive and significant link between poor internet connectivity and missed assessments. The
findings also showed that other factors, such as age and household size are related to missed
assessments.
Our results have broader implications for the ongoing debate about how to design effective
online classes and the challenges of incorporating timely submission of assessments to aid
feedback between faculty and students, and most importantly to promote quality learning.

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While online class can never be a perfect substitute for face-to-face, institutional guidelines
must be forward looking to allow feedback and the possibility that online classes will persist
way into the future, even after the COVID-19 pandemic has ended (El Said, 2020). The analysis
we have presented here suggests that a key impediment to online learning may well beinstitutional guidelines that fail to take into account the larger picture of underlying factors
affecting students. The biggest takeaway from this research is that home environment, which
includes internet connectivity, greatly influences online learning. Finding an innovative way
to improve unstable internet connectivity is a key driver to promote both the quality andexpectations of learning. These may appear to be overstated since quality and expectations
were not directly measured in this study. In a more practical sense, the inability to summit
assessments in a timely manner, hampers the feedback mechanism that reinforces learning,which in turn may affect quality of learning.
The results offer other insights. For example, the probabilities of missed assessments calculated
in this study raises important questions regarding multiple claims of missed assessments giventhat the chances of the 7th missed assessment in a semester based on our sample is extremely
small. Our results present an opportunity for school administrators and advocates of online
learning to revisit rules governing the conduct and expectations in online modalities. In thesecond (2) section of this paper, we presented the educational context of assessments, we asked
two specific questions that faculty in any online modality may confront: how many missed
assessments can be tolerated in a given subject per semester or term?; and when and how should
faculty intervene if there is a clear indication that the reason for missed assessment is not valid?
These questions relate broadly to the spectrum of issues associated with formulating guidelines
for effective learning outcomes and deserve answers. One possible approach to answering thesequestions might involve implementing the type of framework proposed in Figure 1. Our results
provide a guide to institutional policymakers. Clearly, addressing issues regarding internet
connectivity is critical to any strategy aimed at improving learning outcomes.
Nevertheless, it is important to take note of the limitations of this study. Sample size is small,therefore both robustness and generalizability of the findings may benefit from expanding thesample size of this study. Although additional information such as dates present in online
classes, actual number of missed assessments, late submission of assessments and types ofassessments were generated from the online platform, other diverse and complex factors suchas study habits, learning attitude, digital skills, personality among others were not measured in
the survey instrument. Internet connectivity responses were based on students reported
experiences which we have no way of verifying in real time or during the period whenassessments were given. However, the methodology and model used in this study has provided
interesting insights and direction for future research. Future studies may utilize longitudinal or
bigger and more representative datasets to extend and test the robustness of findings. Quasiexperimental design may help to probe further on the relationship between internet connectivity
and missed assessments for different categories of students across schools.
Acknowledgements

We have benefitted immensely from the feedback and insightful comments of two anonymous
professors.

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Corresponding author: Willington Onuh
Email: willingtonoonuh@dlsud.edu.ph25

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Appendix 1
Modeling count data, starts with the most commonly used model, Poisson regression.
Following Greene (2003), the Poisson distribution with observation i can be
expressed as:

e- li liyi
Pr(Yi = yi | xi ) =, yi = 0,1, 2...
yi !

[1]

where, yi refers to missed assessment by each student in a semester, yi! is y factorial, and λi islamda which accounts for the mean incidence rate of missed assessments. The most prominentassumption of Poisson is that the conditional mean is equal to the conditional variance. The
variance-mean equality of Poisson distribution implies, var(y/x) = E(y/x). The mean parameterλi is related to (that is, a function of) regressors, xi as each yi is drawn from a sample, which isassumed to be random (i.e., independent and identically distributed). A common meanfunction, following Wooldridge (2003) and Greene (2003), is the loglinear model:
ln li = xi' b= b 0 + b1 xi1 + ... + b k xi k = b 0 + å j =1 b j xij
k[2]

since from equation 1

li = exp( x ' b ) i = 1,..., nEquation 2 models each student’s number of missed assessments as having a Poisson
distribution where the expected number (λ) is a function of regressors and the summation sign,∑!"#$ indicates the sum of missed assessments by all students. Equations 1 and 2 shows that
Poisson model is related to negative binomial and for the most part regarded as a special formof Poisson model.
Negative Binomial (Poisson-gamma) Regression Model
The main attraction of negative binomial (NB) is its flexibility allowing for the possibility forthe variance of missed assessment to be independent of the mean, which is not possible with
Poisson regression model. Thus, it allows for a scale parameter to be added in the formulationto account for overdispersion in a count data (Yehia, 2021). The NB is modelled typically as a
generalization of Poisson model by allowing for unobserved effect into the conditional mean.
This additional parameter allows the conditional variance to be greater than the conditionalmean, which accounts for overdispersion. This can be accomplished by adding an error term
to the conditional mean μ, so that the variance will be greater than the mean (Greene, 2003) as:
ln µi = xi' b + e i = ln li + ln ui ,

(ui = e i )[3]where εi a random error or unobserved variables that is typically assumed in classical regression
model, that is, error is assumed to be uncorrelated with x. The conditional distribution remains
Poisson-like in the sense that the distribution of yi conditioned on xi and ui with conditionalmean (λi) and variance (μi):

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e-liui (li ui ) yif ( yi | xi , ui ) =y!

[4]

Equation 4, is a Poisson variable with mean (λi) and error term (ui=exp(εi)) assumed to follow
a Gamma distribution. The Poisson-Gamma mixture model is assumed to have a mean of 1.0(Hilbe & Greene, 2007). The main idea of Poisson-Gamma mixture is to allow for the varianceto be greater than the mean by adding an error to the mean (λiui) or to technically account for
overdispersion inherent in count data. This means that the unconditional distribution of f (yi |xi, ui) can be derived by integrating ui out of the density (Greene, 2003; Hilbe & Greene, 2007):¥

e-liui (liui ) yif ( yi | xi ) = òg (ui )dui
y!
0

[5]

The error term, ui, defines the choice of distribution and takes the gamma type error
distribution. The g (ui) from equation 5, is a two-parameter gamma distribution (Greene, 2003),
written out as:

g (ui ) =qq
exp(-q ui )uiq -1
G(q )

[6]

where Γ(.) is a gamma function. The unconditional distribution for yi (Greene, 2003) can be
written as:¥

exp(-li ui )(li ui ) yi q q
exp(-q ui )uiq -1dui ,G( yi + 1)
G(q )0

f ( yi | xi ) = ò

yi = 0,1,...
[7]

where the y factorial, y! = Γ(yi + 1). From equation 6, the mean of gamma distribution is ɵ/ɵ
and variance ɵ/ɵ2. Constraining the mean to one implies setting ɵ = ɵ, which results in one
parameter gamma variance, where ɵ/ɵ2=1/ɵ. This expression explains why the variance is aquadratic function of the mean. The term 1/ɵ is the overdispersion parameter of Negative
binomial. The smaller the value of ɵ the higher the overdispersion allowing the mean andvariance to be different, unlike the Poisson model. The negative binomial presents a more
realistic model for estimating and understanding missed assessments by students. Missed
assessments by students are by nature events that are positively correlated by the frequency
occurrences which in turn induces larger variance. Applying properties of gamma’s integral(Greene, 2003) in equation 7, yields:f ( yi | xi ) =q q liy G(q + yi )G( yi + 1)G(q )(li + q )q + y
i

i

[8]

Using the same properties of gamma function, Hilbe & Greene (2007) provided a convenientversion of equation 8, as:qyi

G( yi + q ) æ q ö æ li öf ( yi | xi ) =
ç
÷ ç
÷ ,
G( yi + 1)G(q ) è li + q ø è li + q ø27yi = 0,1,...
[9]

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Dividing equation 9 through by ɵ yields:
q

yi

ö æ
ö
G( yi + q ) æ1
1
f ( yi | xi ) =ç÷ ç1 ÷ ,G( yi + 1)G(q ) è 1 + (li / q ) ø è 1 + (li / q ) ø

yi = 0,1,...
[10]

Redefining the dispersion parameter obtained above as α = 1/ɵ, and plugging it back to equation
10, yields a density that is commonly recognized in the literature (Cameron & Trivedi,1999;
Hilbe & Greene, 2007):
1/ a

G( yi + 1/ a ) æ 1 ö
f ( yi | xi ) =ç÷G( yi + 1)G(1/ a ) è 1 + ali ) øyiæ ali öç÷ ,
è 1 + ali ø

yi = 0,1,...
[11]

Empirical Specification of Model
To examine the effect of internet connectivity and other students’ characteristics on missed
assessments, we adopt equation 12, for estimation. Estimation of the NB model parameters(β,α) is very straight forward using software packages such as, Stata, SAS, etc. The likelihood
function can be set up from equation 11, as:l = exp( xi' b )n ìüæ a exp( xi' b ) ö æ 1 ö1öïææ 1 öï
'L(b , yi , a ) = å í yi ln ç÷ - ç ÷ ln(1 + a exp( xi b ) + ln G ç yi + ÷ - ln G( yi + 1) - ln G ç ÷ ý'aøèè a øþ
i =1 îïï
è 1 + a exp( xi b ) ø è a ø[12]Differentiating equation 12, with respect to coefficients and equating to zero yields likelihood
equations as follows:¶ log L N æ yi - exp( xi' b ) ö= åç÷ xi = 0'¶bi =1 è 1 + a exp( xi b ) ø[13]The likelihood equation of Poisson is similar to NB equation 13, but the estimates differ due
to the denominator term. However, as the parameter (α) gets closer to zero, the NB approaches
Poisson model and provides the best possible explanation why the NB is regarded as a special
form of Poisson (Hilbe & Greene, 2007).

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