Exploring factors influence student’s development of Portuguese students

Introduction

The data were obtained in a survey of students taking math courses in a Portuguese secondary school[1]. The data set contains 395 observations (students) and 33 variables that tell information about the students, including their gender, family, study, and alcohol consumption. Among all attributes, we find the following:

• Variables such as school, gender, home address, family size, parent’s cohabitation status, whether being provided with extra-educational support from the school, whether being provided with extra-educational support from their family, whether they are taking extra paid classes, whether there are extra-curricular activities, whether they attend nursery school, whether they want to continue higher education, whether they have internet access at home, and whether they are in a romantic relationship are presented as binary variables.

• Variables such as father’s job, mother’s job, the reason to choose the school, and guardianship are categorical (nominal) variables.

• Variables such as mother’s education level, father’s education level, travel time between home and school, weekly study times, quality of the family relationship, free time after school, the frequency of going out with friends, workday alcohol consumption level, weekend alcohol consumption level, and current health status are coded as quantitative ordinal variables.

• Variables such as age, number of past class failures, grade from the first and second periods, and the final grade are quantitative numerical variables.

In this project, we will study and perform analysis on students’ development in terms of their alcohol consumption, grade in school, health status, and family relationships. We do so by trying to answer four research questions:

• Is students’ alcohol consumption level related to their family relationship quality and romantic relationship?
• How do extracurricular activities and the quality of family relationships associate with students’ current health conditions?
• Does parents’ job and education level relate to students’ grades? If so, in which way.
• Which variables are correlated with students’ relationship with their family most? How are these variables related to family relationships?

More Data Description

Since our project focuses on the four research questions specifically, only part of the variables is used in the project. To make the interpretation easier, here is a more detailed guide on the variables we used and how they are represented:

• famrel: quality of family relationship (numeric: from 1-very bad to 5-excellent)
• romantic: whether the student is involved in a romantic relationship (binary: yes or no)
• Dalc: workday alcohol consumption (numeric: from 1-very low to 5-very high)
• Walc: weekend alcohol consumption (numeric: from 1-very low to 5-very high)
• health: current health status (numeric: from 1-very bad to 5-very good)
• activities: extra-curricular activities (binary: yes or no)
• Fjob: father’s job (nominal: ‘teacher’, ‘health’ care related, civil ‘services’ (e.g. administrative or police), ‘at_home’ or ‘other’)
• Mjob: mother’s job (nominal: ‘teacher’, ‘health’ care related, civil ‘services’ (e.g. administrative or police), ‘at_home’ or ‘other’)
• Fedu: father’s education (numeric: 0 - none, 1 - primary education (4th grade), 2 – 5th to 9th grade, 3 – secondary education or 4 – higher education)
• Medu: mother’s education (numeric: 0 - none, 1 - primary education (4th grade), 2 – 5th to 9th grade, 3 – secondary education, or 4 – higher education)

Question 1: Is students’ alcohol consumption level related to their family relationship and romantic relationship?

Psychological research on Alcohol Use Disorder(AUD) Recovery for adults shows that “AUD and family functioning are inextricably bound…family members’ actions may exacerbate problematic drinking…Research also has demonstrated a reciprocal relationship between drinking, AUD, and the quality of intimate relationships” [2]. These studies inspire us to propose our research question. We, therefore, are interested in how the quality of students’ family relationships and the students’ romantic relationship status relates to the amount of workday and weekend alcohol consumption.

To discover this relationship, we generate two sets of side-by-side facetted bar plots. In our first facetted plot, our explanatory variable is romantic. In our second facetted plot, our explanatory variable is famrel. Both plots use Dalc and Walc as response variables.

From the facetted plot above, we observe that for both weekday and weekend alcohol consumption, the distribution of alcohol consumption for students who are in a romantic relationship is highly similar to that for students who are not in a relationship. Based on this observation, we believe that romantic may not play a significant role in students’ alcohol consumption levels. Thus, we explore the relationship between famrel and alcohol consumption by generating the second set of the facetted plot.

For the plot with weekday alcohol consumption as a response, we observed that the largest proportion of students consume low levels of alcohol (level = 1). As the quality of family relationships increases (from 2 to 5), we observed a monotonic increase in the percentage of students who consume level = 1 alcohol and a monotonic decrease in the percentage of students who consume level = 2 alcohol. Interestingly, we observed that the highest proportion of high alcohol consumption (level = 5) occurs in students who rated the quality of their family relationship as 1 (very poor family relationship). As family relationship quality improves, the proportion of students who have level = 5 alcohol consumption decreases almost monotonically. These observations imply that for weekdays, there seems to be a weak and negative correlation between family relationships and alcohol consumption levels. We speculate that the better the family relationship quality, the less unhealthy alcohol consumption.

For the plot with weekend alcohol consumption as a response, we observed that the proportion of students who has alcohol consumption level = 5 monotonically decreases as we have better family relationship quality. We also observe a monotonic decreasing trend for alcohol consumption level = 4 students (whose family relationship quality ranges from 2 to 5). There is also an obvious monotonic increasing trend for students on alcohol consumption level = 1 (whose family relationship quality ranges from 3 to 5). These observations all indicate that we possibly have a weak and negative correlation between family relationship quality and alcohol consumption on weekends as well.

To verify our speculation on the negative correlation between family relationships and alcohol consumption on both weekdays and weekends, we calculate the correlations between famrel and our two response variables (Dalc and Walc) respectively.

## 
##  Pearson's product-moment correlation
## 
## data:  data$Dalc and data$famrel
## t = -1.5429, df = 393, p-value = 0.1237
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.17492610  0.02123928
## sample estimates:
##         cor 
## -0.07759436

## 
##  Pearson's product-moment correlation
## 
## data:  data$Walc and data$famrel
## t = -2.2626, df = 393, p-value = 0.02421
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
##  -0.20972175 -0.01489292
## sample estimates:
##        cor 
## -0.1133973

Based on the Pearson’s product-moment correlation test, we observed a p-value of 0.1237 using weekdays alcohol consumption as a response. This means that our negative correlation of -0.0776 between family relationships and weekdays alcohol consumption is not significant. We observe a p-value of 0.02421 (<0.05) using weekend alcohol consumption as a response. This indicates that our negative correlation of -0.1134 between family relationships and weekend alcohol consumption is significant: we are 95% confident that we can reject the null hypothesis that the true correlation is zero.

In summary, based on our observations from the two side-by-side facetted bar plots and our correlation test results, we make the following conclusions:

• Whether the student is in a romantic relationship or not doesn’t play a significant role in alcohol consumption.

• While there is a negative yet insignificant correlation between family relationships and weekday alcohol consumption levels, there is a negative and significant correlation between family relationship quality and weekend alcohol consumption. That said, it could be that no matter what the romantic relationship status of a subject is, the better the family relationship quality, the lower the alcohol consumption level during weekends.

Question 2: How do extracurricular activities and the quality of family relationships associate with students’ current health conditions?

Much existing research shows that the involvement in extra-curricular activities and the quality of family relationships can be factors that influence people’s health. Some researchers state that “family relationships are enduring and consequential for well-being across the life course”[4]; while some researchers claim that “teens who participate in extracurriculars have better mental health”[3]. These studies motivate us to find out whether extra-curricular activities and/or quality of family relationships are associated with health conditions for students, and if so, how.

For this research question, we use health as our response variable and use famrel and activities as our two explanatory variables. To get a basic idea of the relationship between the response and explanatory variables, we use the side-by-side facetted boxplot to find the distribution of health given family relationship facetted by whether the students have extra-curricular activities or not.

Based on our facetted side-by-side boxplot, we observe some degree of association between the students’ family relationship and health level. The subjects with very bad family relationship qualities (famrel=1) tend to have worse health conditions since the mean health level for famrel=1 tends to be lower than that for the other famrel values. Subjects with better family relationships tend to have higher health conditions since the purple and blue boxes(representing famrel=4 and famrel=5) have a higher mean health level. However, whether or not the student involved in extra-curricular activity is associated with students’ health level is difficult to be seen, since there is no obvious pattern in the distribution of health given activity in the plot. Thus, we cannot determine a precise enough relationship between activities and health based on this boxplot.

Therefore, to have a clearer and deeper understanding of their associations, we use a mosaic plot to see if we can support the following claims with statistical evidence:

• Student’s health is independent of their family relationship.
• Student’s health is independent of whether or not they involve in extra-curricular activities.

From the left mosaic plot on Health vs. Family Relationship, it appears that there are significantly more students with a very poor health condition (health = 1) than we would expect under the null hypothesis of independence when the students have a very poor family relationship (famrel = 1). Therefore, this observation suggests that we should reject the null hypothesis that students’ health level is independent of their family relationships.

The right mosaic plot on Health vs. Extra-curricular Activities doesn’t indicate any substantially large Pearson residual, thereby not providing any evidence to reject the null hypothesis of independence between extra-curricular activities and health conditions for this dataset.

To sum up, we reach the following conclusions:

• Students’ health and family relationships are dependent.
• Students’ health and extracurricular are independent of each other.

Question 3: Does parents’ job and education level relate to students’ grade? If so, in what way.

Whether or not parents’ educational background and profession are associated with a student’s academic performance has been an ongoing controversial topic. Motivated by this discussion, we want to explore whether a parent’s job and education level have correlations with the student’s grades in this dataset. To answer this research question, we use Fjob, Mjob, Fedu, and Medu as explanatory variables and G3 as a response variable.

Before diving into exploring our question, we observed that the distribution of our quantitative response variable G3 is almost normally distributed, with some outliers on the left. This indicates that we do not need to perform a transformation to this variable.

We start by making four side-by-side boxplots that display the marginal distribution of the final grade by the categorical variables Fjob, Mjob, Fedu, and Medu respectively. Note that for the variables Fedu and Medu, the higher the value, the higher the education level.

From the above boxplot, we observe that students whose father’s profession is a teacher tend to have the highest grades, while those whose mother is a housewife tend to have lower grades than other students. We also observe that students whose father has a low educational level (level = 0) tend to score highest. Similarly, students whose mother has a low education level (level = 0) tend to score as high as those whose mother’s educational level is high (level = 4).

To better understand how the father or mother’s education and job as a whole relate to a student’s final grade, we visualize the variables by making a side-by-side boxplot of G3 by father’s job and education and another by mother’s job and education.

From the above boxplot, we observe that the students with the highest grades are those whose father has teaching as their profession or whose mother works in the health industry. We also notice a weak but monotonically increasing trend in final grades as parents’ (both mother and father) educational level increases. In other words, we think that there appears to be a positive correlation between parents’ education level (ranging from level = 2 to 5) and the student’s final grade: the higher the parent’s educational level, the better the student’s grades are. Despite these observations, we have to admit that our dataset is limited: we don’t have data present for certain job and education category combinations. In addition, we also need to take into account of the high correlation between professions and education levels when we arrive at our conclusions.

To take a closer look at how our four explanatory variables correlate to G3, we performed four Bartlett tests of homogeneity of variances.

## 
##  One-way analysis of means
## 
## data:  G3 and Fjob
## F = 1.3029, num df = 4, denom df = 390, p-value = 0.2683

## 
##  One-way analysis of means
## 
## data:  G3 and Mjob
## F = 3.7545, num df = 4, denom df = 390, p-value = 0.005195

## 
##  One-way analysis of means
## 
## data:  G3 and Fedu
## F = 2.8906, num df = 4, denom df = 390, p-value = 0.0222

## 
##  One-way analysis of means
## 
## data:  G3 and Medu
## F = 6.0884, num df = 4, denom df = 390, p-value = 9.242e-05

We observe p-values of 0.005195, 0.0222, and 9.242e-05 for Mjob, Fedu, and Medu respectively. Since these p-values are less than 0.05, we are 95% confident to reject the null hypothesis that they are not correlated to a student’s final grade. In other words, we conclude that Mjob, Fedu, and Medu have significant correlations with G3. Yet, since we have a p-value of 0.2683 for Fjob, we cannot conclude that we observed a correlation between the father’s job and the student’s final grade.

In a word, we make the following conclusions:

• There are certain professions of parents that could be a factor in influencing a student’s grades: students whose father is a teacher or mother works in the health industry tend to have better academic performances.

• A student’s mother’s job and education, as well as father’s education, have statistically significant correlations with G3.

• Though we observed a seemly increasing trend in students’ grades as the mother’s or father’s educational level increases, it does not apply to students whose parents have the lowest level of education. Those students tend to score as high as those whose parents are very well-educated.

Question 4: Which variables are correlated with students’ relationship with their family most? How are these variables related to family relationship?

We want to examine which variables among all 33 variables could correlate to students’ family relationships. To answer the question, we first exclude some variables that have no apparent relationship with our response variable, family relationship, such as school, the reason why students pick the school, etc. After this process, there are 13 candidate variables left, including gender, age, family size (famsize), parents’ cohabitation status (Pstatus), parent’s education level (Medu and Fedu), parent’s job fields(Mjob and Fjob), guardianship (guardian), whether or not students want to continue with higher education (higher), whether students are involved in a romantic relationship (romantic), health condition (health), and school grade (G3).

We want to see if these 13 variables can be used to cluster students into various family relationship groups (family relationships from 1-the worst to 5-the best), so we created a dendrogram. We encode the categorical variables into numerical values. We then generate the distance matrix of Euclidean distance amongst the 13 candidate variables, standardize it, and create a complete linkage hierarchical clustering with k=5 colors, as well as tree leaves color labeled by students’ family relationship. We label famrel=1 in blue, famrel=2 in green, famrel=3 in yellow,famrel=4 in red, and famrel=5 in purple.

In addition, we use a PCA biplot to identify the existence of any clusters and whether the response variable is related to any of the exploratory variables we mentioned above.

Since our data set is dominated by data with famrel >=3 (the leaf nodes are mostly colored in yellow, red, and purple), it’s easier to focus on whether students with poor family relationships (famrel = 1 or famrel = 2) are being clustered. From the dendrogram, we observe that students with poor family relationships are scattered among all five clusters, or equivalently, all five clusters seem to be heterogeneous with all family relationship types.

From our PCA biplot, we observe that the same problem as before such that the graph is dominated by the data points with famrel >=3 with no obvious clusters. This problem makes it hard to draw any meaningful conclusion. In addition, we observe that less than 30% of total variations are accounted for by the first two principal components.

So based on the observations and conclusions from these two plots, we come up with the following plots with some optimizations. First, to solve the problem where we have few data points with poor family relationships (famrel < 3), we combine 5 family relationship types into 3 types. More specifically, we combine the famrel = 1 and famrel = 2 as one group and encode the group as the poor family relationship, treat famrel=3 as one group and encode the group as the fair family relationship, and lastly combine famrel=4 and famrel=5 as one group and encode the group as the good family relationship.

Second, we eliminate five variables that correspond to the lowest PCA values, according to the previous PCA summary. This process left us with 8 variables including romantic, guardian, age, sex, higher, Fedu, Medu, and Pstatus. We then perform a similar procedure as described above to generate a dendrogram with k=3 colors and leaf color labeled by family relationship (poor is coded in blue, fair is coded in yellow, and good is coded in red) and a PCA biplots.

From the dendrogram after the optimizations, we see that there is some heterogeneity in each of the three clusters in terms of famrel variables. In particular, we infer that the right-hand cluster tends to have students with good family relationships. There are also a few students with a fair family relationship and one with a poor family relationship. The center clusters tend to have students with a good family relationship with few students with a fair and poor family relationship. The right-left cluster is the most heterogeneous. But it’s worth noticing that the majority of students with a poor relationship in the dataset appear in the right-hand cluster.

Next, we look at the PCA biplot with the optimizations. To interpret the graph easier, we divide this plot into four quadrants: the first quadrant (with a positive x-axis and a positive y-axis), the second quadrant (with a negative x-axis and a positive y-axis), the third quadrant (with a negative x-axis and a negative y-axis), and the fourth quadrant (with a positive x-axis and negative y-axis). We observe that all but one student with a poor family relationship falls in the second quadrant, with the rest of the data with poor family relationships scattered in the first, third, and fourth quadrant. Meanwhile, we observe that variables age, guardian, romantic point towards the direction of the second quadrant, and the variable sex points towards the direction opposite of the second quadrant. Thus, we make the following interpretations:

• The variables that are most correlated to students’ relationship with their family are age, guardian, romantic, and sex.

• We observe that the students with poor family relationships tend to have greater value in sex and less value in age, guardian, and romantic relationships. As we mentioned previously, before we perform PCA, we encode the categorical variables with the numerical values. We encode female with 1 and male with 2. We encode students with mother as guardian with 1, students with father as guardian with 2, and students with people other than parents as guardian with 3. We also encode students that are single with 1 and students that are not single with 2. So to interpret the observation in the context of variables, we have students with poor family relationships are tend to be male students who are single, with younger age, and have mothers as their guardians.

• Despite a 10% increase, the variation accounted for by the first and second principal components in this optimized biplot is still less than 50%, which is considered low. Since we did not see an obvious increase in variation after trying another round of variable elimination (based on PCA value), we decide not to perform another round of optimizations and make our exploration of research question 4 terminated here.

In summary, we infer that students’ relationships with their families are most correlated with their age, sex, romantic relationship, and guardianship. Furthermore, students with poor family relationships tend to be male students who are single, of younger age, and have a mother as their guardian.

Conclusion

We derive the following conclusions based on our research study on students’ development in terms of their alcohol consumption, grade in school, health status, and family relationships. First, we find that whether the student is in a romantic relationship or not doesn’t seem to affect students’ alcohol consumption levels while family relationship plays a larger role: there is a negative and significant correlation between family relationship quality and weekend alcohol consumption. Second, students’ health and family relationship quality are dependent, while we do not find evidence that supports dependency between students’ health and extra-curricular activities. Third, certain professions of parents could play a part in a student’s grades (for instance, when a student’s father is a teacher); a student’s mother’s job and education, as well as father’s educational level, have statistically significant correlations with the student’s final grade. Yet, though we see a positive correlation between parents’ educational level and students’ final grades in general, it does not apply to students whose parents have the lowest level of education. Finally, we find that a student’s family relationship is most strongly correlated with their age, sex, romantic relationship, and guardianship. In particular, we find that younger male students who are single and have a mother as guardian tend to have poorer family relationships.

However, we must admit that there are certain limitations to our study. First, our dataset is biased given that we only sample students from one Portuguese school. Second, when defining grades, we only consider math grades from this dataset. It is contentious whether math grades can be used as the only criteria indicating the academic performance of a student. Third, some variables we used in this study are very subjective, such as the quality of family relationships. Our study can be more accurate if these variables are made out of the same scale or can be measured by objective methods. Fourth, since many of our variables are categorical or ordinal, the way to generate data visualization for our purposes is relatively limited.

We believe that there is much more to explore using this dataset. For example, to better comprehend how a student’s relationship with their family can affect alcohol consumption, we could take into account other latent factors such as family size or parent’s cohabitation status that are present in the dataset. Since family relationship quality is a subjective variable from the student’s perspective, these objective measurements could provide more insight into whether our conclusion regarding the weak and negative correlation between family relationships and weekend alcohol consumption makes sense. Similarly, we could explore how factors other than family relationship quality and extra-curricular activities can affect students’ health. Moreover, we could connect our first three research questions and explore how family relationship quality, alcohol consumption, health, and grades correlate. The exploration of these intriguing questions will give us a more comprehensive understanding of this dataset and its implications for the many factors that influence students’ development.

References

[1] UCI Machine Learning. (2016, October 19). Student Alcohol Consumption. Kaggle. Retrieved December 6, 2021, from https://www.kaggle.com/uciml/student-alcohol-consumption. [2] McCrady, B. S., & Flanagan, J. C. (2021, May 6). The role of the family in alcohol use disorder recovery for adults. Alcohol research : current reviews. Retrieved December 6, 2021, from https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8104924/. [3] University of British Columbia. (2020, November 2). Teens who participate in extracurriculars, get less screen time, have better mental health. ScienceDaily. Retrieved December 5, 2021 from www.sciencedaily.com/releases/2020/11/201102124849.htm [4] Patricia A Thomas, PhD, Hui Liu, PhD, Debra Umberson, PhD, Family Relationships and Well-Being, Innovation in Aging, Volume 1, Issue 3, November 2017, igx025, https://doi.org/10.1093/geroni/igx025