1 Parallel enrollments: associations between stress and coping of college students with their performance

College students are a vulnerable subgroup of the general population, and are subject to a variety of unique stressors, such as relocation from home, gaining responsibilities, academic demands, becoming more independent, among others [1]. High levels of perceived stress exceeding their coping capabilities and a feeling of being overwhelmed are reported [2, 3]. Prolonged stress is associated with negative consequences for academic performance [4], campus engagement [5], dropping out, i.e., “withdrawing” [6], and mental disorders [7]. Therefore, coping is important for students to maintain performance [8]. An extensive body of literature has provided insights into stress, coping and preventive measures for college students [9,10,11] as well as student performance predictors, for instance finding gender differences [12, 13]. Previous studies were conducted in a multitude of university settings worldwide, being generalizable and making stress and coping of university students a well-researched field of interest. However, countries with different university structures and rules than what is the “norm” or “average” can impact students with unique stressors. In the case of Austria (Europe), students do not pay tuition fees and can enroll in as many degree programs simultaneously as they want [14]. Stress can be an issue for students in one degree program [4] and is known as impediment to their performance [15]. Being enrolled in more than one program may have different or even stronger effects on student performance. Although Austria is one of the smaller countries in central Europe in terms of population and area, implications of its unique system can be of broader interest to policymakers, university management staff and curriculum designers worldwide and provide perspective for application elsewhere. Therefore, research is needed to better understand the relationship between stress components and college student performance under these unique conditions.

1.1 The Austrian University System and multiple enrollments

While the program types “dual enrollment” and “double degree programs” are internationally implemented, they are not equivalent to the possibility of enrolling in two separate degree programs. Dual enrollment specifies programs addressing high school students, giving them the opportunity to complete university courses before starting college [16]. This program type is known to facilitate the transition from high-school to college and to increase the odds for completing a degree program [17]. Double degree programs, also known as joint degree or combined degree programs, are single programs combining two fields and being studied concomitantly for a longer period of time than a regular degree program [18, 19]. It allows students to graduate faster than doing two degrees consecutively and may involve studying at two universities and in different countries [18, 19]. Austria’s university system, contrastingly, offers both of these programs together with the possibility of enrolling in an unlimited number of degrees without time constraints. Compared to joint degree programs, there is no overall structure connecting two or more programs. Given semester-wise enrollment deadlines, students are allowed to enroll in new programs at any point in their career [14]. In comparison, no studies have addressed how multiple enrollments affect overall time of students until graduation.

Another differentiation needs to be made from double majors and elective curriculum modules. Compared to students in multiple programs being able to get multiple degrees, double majors let students graduate with one degree, while they complete about the same amount of workload of single-program students [20]. By implementing elective modules in curricula [21], students are given the possibility to choose which courses they want to do [22]. This can also mean doing more than what is required to complete a degree program. However, the outcome is still one degree and a workload lower than studying two full curriculums. Similar concepts exist in other European countries, for instance Germany, where students are allowed to enroll in two programs, but have to fulfill the numerus clausus. It also needs to be noted that there are different matriculation laws for each federated state, which means there is no unique university system country-wide [23, 24].

The absence of tuition fees [14] and the freedom to try out different fields of study may be two structural reasons Austrian college students frequently make use of their possibilities, making multiple and parallel enrollments common. Passed exams can be transferred from one degree to another, if both curricula contain the same or a similar course. In a study investigating the motivations of students to enroll in double degree programs, increasing employability and career opportunities, specific skill acquirement or enrichment of the curriculum vitae were among the top reasons of students to choose a double degree program [25]. Since there are no comparable studies concentrating on to their motivations to enroll in multiple programs, an overlap in the motivations can only be assumed.

The Austrian university system adheres to the “European Credit Transfer System” (ECTS), with every course being measured in these credits. One credit is the equivalent of 25 real-time working hours of students [26]. On the level of each enrolled study program, the Austrian university system has introduced two legal regulations: tolerance semesters [14] and the minimum requirement for studying [27]. Although there are no tuition fees, students can continue with their studies in each program until they reach the minimum number of semesters allocated for a degree program, together with a predefined number of semesters specified by curriculum designers and the University for each Program. Usually, this timeframe is set at two semesters for bachelor’s programs. For bachelor degrees with a minimum time of six or eight semesters [28], this means the tolerance timeframe equals eight and ten semesters, respectively. It is only when this border is crossed in a study program that tuition fees are charged if students continue [14]. The second regulation is defined as a minimum credit requirement of 16 ECTS credits, which needs to be fulfilled. If students fail to reach this threshold until the end of their second academic year in a degree program, they are banned from it [14]. Additionally, bachelor’s and diploma programs can have beginning- and orientation phases. They are limited to the first semester of a given program and constitute a package of first semester courses that are mandatory to complete. Otherwise, they cannot continue with the rest of the curriculum [14]. This system offers a lot of freedom in the choices of students, but is regulated via performance- and workload-driven university structures at the same time.

1.2 Student performance, parallel enrollments and stress

Most previous research on the Austrian university system has been conducted on meta-levels, e.g., focusing on university management, governance [29, 30], knowledge transfer and industry [30, 31] or university research in general [32]. On account of the distinctiveness of the Austrian system, a focus on parallel enrollments has not yet been set. Dimensions of stress influencing academic success [33] and their potential negative effects have been studied before [4]. Differences between genders and predictors of student performance also have been identified earlier [12]. However, research has been carried out in other systems underlying other sets of rules. By making student performance central on a program level in Austria and allowing multiple enrollments [14, 27], students with parallel studies must cope with twice the amount of workload what enrollment in one full-time degree program would mean. With respect to obtaining information on how the freedom of choice in this system affects the effects of stress on student performance, understanding the implications of parallel enrollments for students can generate evidence for policymakers and curriculum planners worldwide. As an example, opening up more restrictive systems and adapting to well-implemented structures from other countries may have the potential to increase graduates’ employability; expecting overlapping motivations of students beginning a joint degree program or enrolling in multiple studies [25].

1.3 Expectations

Due to the uniqueness of the Austrian university system, no research exists for this specific context of multiple enrollments. However, a better understanding of the outcomes of giving students more freedom of choice can be relevant for universities worldwide. Since little is known about student performance of those with parallel study programs, an explorative approach has been chosen for this study. It aims to compare the performance of students with one enrollment with students undertaking multiple parallel enrollments in respect of the associations between stress, coping and related dimensions on multiple performance indicators. New evidence will be generated from associations between stress, coping and related variables with academic success. The research question this study wants to address is: which associations between stress, coping and related dimensions with indicators of student performance exist in students with one and students with two or more enrollments? A sub-question is whether there are gender differences in the performance predictors.

2 Methods

2.1 Data background and sample

A larger research project focusing on the effects of student work and parallel enrollments on student performance was the base for the data described in this study. The goal was to merge data from the administrative database of the University of Graz (Austria, Europe) with survey data collected in the project. In order to accomplish this task, at the end of June 2023 all enrolled students received an e-mail with the invitation to take part in the study. No specific compensation was offered for participation. Students could take part in a lottery to win small prizes. The point in time for the survey’s offering was selected due to most exam weeks and finals being scheduled prior to the summer holidays (July–September). By syncing the recruitment of participants to this timeframe, their feelings, opinions and answers on the questionnaire should best reflect the student performance indicators (e.g., grades, ECTS credits) from the internal database used in this study. In addition to these parameters, participants’ sociodemographic information and parallel enrollments were merged with the survey data. The performance measures were accumulated over the last full academic year 2022/23 up until the end of June 2023. Data merging was accomplished via students’ IDs, which were deleted after creating the final dataset. This was done mid-July 2023, which means that almost all of the exam data from June should have been processed, synchronized with the database and available for this study.

Data collection and database queries were done at the University of Graz (Austria, Europe). Per academic year, around 30,000 students have a valid enrollment. Due to the absence of tuition fees and no restrictions in how many parallel enrollments are possible, this leads to students trying out different fields of studies, with many possessing multiple, simultaneous enrollments. From an infrastructural perspective, Graz has a number of different universities located in close range to each other with program cooperation across them, further increasing the possibilities to enroll in more than one program at one or multiple institutions. The study was approved by the ethics committee of the University of Graz (GZ 39/96/63 ex 2022/23).

At the moment of recruitment, 26,622 students had 60,766 valid enrolments in the database. The number of studies did not give any information on how actively they were studied by the students, meaning that some of them only existed on paper. A priori power analysis for a power of 0.80 and moderate effect sizes of R2 = 0.30 in linear regression models with five predictors for the main analyses showed a minimum overall sample size of 49 participants. From all the students in the database, 227 students answered the questionnaire on the first sending of the e-mails, of which 213 cases could be used for analyses due to provision of a student ID, surpassing the minimum required sample size. Considering the small sub-sample of 47 students with more than one enrollment and moderate effects of R2 = 0.30 a power of 0.78 would have been reached. Since the study was sent out during a critical time in the academic year, recruitment of additional participants during the summer holidays was not seen ideal and the sample was considered sufficient due to the minimal deviation from the target value. Table 1 shows the absolute and relative frequencies of demographic sample characteristics as well as the mean age.

Table 1 Sample characteristics
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In terms of representativeness of the sample, descriptive statistics on the administrative database’ data show that between 2012/13 and 2022/23 32% of students had more than one enrollment. This is very similar to 31% of students in this study. Referring to official statistics on all Austrian university students, 54% of students in 2021/22 were female and 46% male, with 68% having an Austrian citizenship [34]. Both characteristics show different ratios in this study. While Austrian citizenships are very common and more females have an enrollment at Austrian universities, the relative frequencies are higher for both in this study. With the exception of Psychology and Computational Social Systems, the program frequencies of the sample composition reflect the situation at the University of Graz, with teacher training and Pedagogy being two large fields of study [34]. The former two fields are overrepresented, which can be explained via the recruiting process. Psychology students need to take part in surveys and experiments as part of their curriculum, while others do not. Students of Computational Social Systems may show a larger interest in taking part in online surveys, since their field is closely related to survey design and related methods.

2.2 Procedure

Students received an e-mail via an official university mailing list commonly used for the distribution of surveys. This service can be utilized once per semester at the university for all kinds of surveys and is hosted by the university’s communication department. After clicking on the link in the e-mail, students were redirected to the landing page of the questionnaire. This site informed them about the data matching procedure, the backgrounds of the study and that their privacy was guaranteed in respect of using their student ID for data matching. In order to go on, informed consent and a data privacy statement had to be confirmed separately from each other, before the student ID had to be filled in. At the beginning of the survey, other project-related questions were asked. This included students’ employment and student work (unemployed), how they are financing their student lives, daily activities, interests and psychosocial dimensions on the satisfaction with their studies and one question on the properties of their learning environment. Three questions were asked, concerned with how much perceived resources of their lives are occupied by their studies, learning and study-related stress. The survey also included six selected items from the German version of the 10-item Perceived Stress Scale [35, 36] and six items from the SCI Stress- and Coping Inventory [37]. In the final part of the survey, students answered two filter questions on possible parallel enrollments. The final question asked students about which of their studies they treated as their main study program or if they treated all of them equally. This was only shown to students who indicated their enrollment in more than one program. If there was only one study program, it was automatically labeled as primary study program.

2.3 Variables

The accumulated student performance measures, i.e., the main outcome variables, were retrieved from the university’s administrative database for the academic year 2022/23. These were the ECTS credits, the number of exams taken, the number of enrolled courses, the average grade of all exams during the academic year and the number of exams that have not been passed, i.e., negative exams. Depending on which study program was treated as the main program, these measures of students with parallel enrollments were spread into two columns, each for one study program. The first one was always treated as their prioritized study program. If the option that all programs were treated equally was selected, prioritization was estimated via the amount of ECTS credits as a measure of workload. The more credits, the higher the ranking. More than the top-2 programs were not included in the analyses, as this would apply to only nine students in the dataset. Descriptive statistics for the outcome variables in the whole dataset can be found in Table 2.

Table 2 Students’ performance indicators as outcome variables for statistical analyses
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Predictor variables for the main analyses were operationalized as resources, coping with stress and well-being. The overall project had more questions and the size of the survey had to be kept to a minimum to ensure a maximized response rate. Thus, the goal was to find a small set of variables to describe the underlying psychometric properties of each questionnaire. The following items of the 10-item Perceived Stress Scale [36] and the SCI Stress- and Coping Inventory [37] were used (both in German). Scales of questions marked with “r” have been reversed in the analyses. They can be found in Appendix A, scale statistics in Appendix B and descriptive statistics for the predictor variables in Table 3.

Table 3 Descriptive statistics for predictor variables of the statistical analyses
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2.4 Apparatus

Data was retrieved from an Oracle® SQL database. The tool to create and conduct the survey was LimeSurvey®. Data merging and data curation were completed using R [38], with the package used for querying the data RODBC [39]. Analyses were performed using IBM SPSS® version 29.

2.5 Statistical analyses

Statistical analyses were done on three different levels: (1) full dataset, (2) students with one enrollment, (3) students with two or more enrollments for the top-2 study programs’ measures. The first level means the unfiltered dataset. Analyses on this level were done for the prioritized program, if there was more than one. The second level was centered on students with one enrollment. Applying analyses both to the prioritized and non-prioritized programs’ measures, level three focused solely on students with more than one program. Multiple regression models were used to obtain information on the predictor variables explaining variance of the performance indicators in these three settings. Multiple regression models were used to find influences on the resources of students. A mixed ANOVA model and two univariate ANOVA models add more information to differences in the predictor variables between genders. Pearson correlations were used to identify correlations between the predictors. A correlation diagram on the unfiltered dataset for all variables is included in Appendix C.

3 Results

3.1 Main results

Multivariate linear regression models were calculated to determine influencing dimensions on student performance indicators. Tables 4, 5, 6, 7 show the results of the regression analyses on the different analysis levels.

On each analysis level, i.e., dataset as a whole, one program, two or more programs, the predictor variables could not explain variance of ECTS credits and grade point average. In the unfiltered dataset (Table 4) significant associations showed that the more resources of students are occupied by learning the higher their number of courses, R2 = 0.06, F(5, 207) = 2.41, p = 0.038. Associations for the number of negative exams were obtained, R2 = 0.10, F(5, 207) = 1.64, p < 0.001, indicating that a high amount of resource occupation by learning is linked to a higher number of failed exams and a higher number of resource occupation by one’s studies to a lower number of failed exams.

Table 4 Multivariate regression models predicting student performance indicators of students in the whole dataset, for their prioritized study program
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Results for students in one study program (Table 5) showed that a high resource occupation from learning is associated with a higher number of exams, R2 = 0.08, F(5, 157) = 2.79, p = 0.019, a higher number of courses in the semester, R2 = 0.07, F(5, 157) = 2.42, p = 0.038, and a higher number of negative exams, R2 = 0.09, F(5, 157) = 3.26, p = 0.008. Similar to the results on the unfiltered dataset (Table 4), resource occupation from one’s studies was also negatively associated with the number of failed exams. Students with more than one enrollment showed the following associations: a higher average well-being is associated with a lower number of exams in their prioritized study program (Table 6), R2 = 0.24, F(5, 44) = 2.79, p = 0.028. No significant influences were obtained for the non-prioritized study programs from the predictor variables (Table 7).

Table 5 Multivariate regression models predicting student performance indicators of students with only one enrollment
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Table 6 Multivariate regression models predicting student performance indicators of students with two or more enrollment, for their prioritized study program
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Table 7 Multivariate regression models predicting student performance indicators of students with two or more enrollments, for their non-prioritized second study program
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3.2 Additional results

A one-factorial mixed ANOVA showed a main effect resources, F(2, 422) = 6.85, p = 0.001, ηp2 = 0.03, and an interaction resources × gender, F(2, 422) = 7.96, p < 0.001, ηp2 = 0.04, in the inner subject effects. Between subject effects showed a significant main effect gender, F(1, 211) = 7.98, p = 0.005, ηp2 = 0.04. On average, the percentage of resources taken up by the studies (M = 51.19, SD = 1.88) is reported to be higher than the resources taken up by learning (M = 44.08, SD = 2.02). There were no differences observed between resource load from studies and study-related stress, p = 0.085, or from learning and study-related stress, p = 0.548. Post hoc Bonferroni adjustment on the interaction revealed the following results: females report more study-related stress (M = 56.09, SD = 2.17) than males (M = 37.67, SD = 3.81), p < 0.001. There are no differences between males and females in how much resources their studies, p = 0.294, and learning take up, p = 0.112.

Two univariate ANOVAs showed no difference in the amount of coping reported by males and females, F(1, 211) = 2.13, p = 0.146, ηp2 = 0.01, but a significant difference in well-being, F(1, 211) = 12.35, p < 0.001, ηp2 = 0.06. Females report more well-being (M = 3.34, SD = 3.10) compared to males (M = 3.10, SD = 0.40). Pearson correlations in the unfiltered dataset showed a positive correlation between average well-being scores and resource load from study-related stress, r = 0.38, p < 0.001 as well as a negative correlation between coping score and resource load from study-related stress, r = -0.17, p = 0.045. No correlation could be obtained for coping and well-being, r = 0.04, p = 0.564.

4 Discussion

4.1 Main results

The purpose of this research was to exploratively obtain information on associations between student performance and well-being, coping and resource occupation in the setting of parallel enrollments. The goal was to find evidence, which associations between stress, coping and related dimensions with student performance exist in students with one and students with two or more enrollments.

Differences between the analysis levels in respect of results from the unfiltered dataset show that the mix of single-study and multiple-study students affected the results. It suggests that they may be treated as different populations performance-wise and in terms of resource occupation. With the only exception of well-being being negatively associated with the number of exams for students in parallel study programs, the predictors coping and well-being had no significant influences in any of the models, along with resource occupation via study-related stress. Compared to this single association, students with one enrollment have associations between the number of exams, courses and negative exams mostly with resources occupied by learning, not with well-being. It is not clear why these differences exist, and this finding requires further research.

Since this study is of correlative nature, definitive causality between predictors and outcomes cannot be determined. It can be assumed that associations between student performance and resource occupation from learning is bidirectional. This means that the number of exams, courses and negative exams influence the resources taken up by learning, and vice versa. Research on students claiming that course load is the major cause of stress has been previously published [40]. A higher number of courses, i.e., higher workload, causes a higher amount of stress for students [41], therefore resource occupation by learning may also be higher. However, this does not explain why well-being and stress coping had no effects in the models.

One explanation for the lack of predictive value from well-being and coping may come from the use of these scales and items. Both the 10-item Perceived Stress Scale [36] and the SCI Stress- and Coping Inventory [37] were shortened for use in this study. This may have affected the validity of the measured constructs. Therefore, they may not have truly measured stress and well-being as well as coping. For instance, the items from the SCI “When I have too much stress, I smoke a cigarette.” and “With stress and pressure, I relax in the evening with a glass of wine or beer.” may trigger different responses from students. Many college students report alcohol consumption and symptoms at a level that meets prescribed standards for abuse or dependence [42]. It is likely that not using the full questionnaires and including these questions changed the overall perception of the questions, producing misleading answers and error that cannot be identified in the dataset. In line with this, the reliability of the SCI scale was not good and could not be improved (Appendix A). Additional analyses on the six items show that item-scale correlations were not positive for all items and generally low (Appendix B). Reversing those and the aforementioned items in different constellations and repeating the analyses did not improve the Cronbach’s alpha. Mean differences of more than a standard deviation of the items could be observed between the first and last three items of the scale. A low construct validity can be assumed, as indicated by the low item-scale correlations. Coping might not be sufficiently measured by the questions used. Additionally, the differences in answering behavior support that there may have been an inconsistency in how questions have been perceived. These factors could have compromised the results of the analyses.

Performance in the non-prioritized studies may not have shown significant associations between predictors and performance outcomes due to very small degrees of freedom in some of the variables (e.g., ECTS and grades). Since not every student took exams in non-prioritized study programs, the available data was small for most outcome variables. This has likely compromised statistical power and possible effects may not show even if they exist in the population.

4.2 Additional results

Checks for gender differences in the predictors revealed that women report a higher study-related stress resource load than men and women report higher well-being scores than men, with no differences in coping. There were no differences in resource occupation for the studies in general and learning. Although the original stress scale was reversed to form the variable well-being, resources taken up by study-related stress had a moderately positive correlation to well-being. Research showed that there are differences in both stress levels and coping for men and women among college students, with women having higher levels of perceived stress and lower levels of coping [43, 44]. Coping, however, was negatively correlated with study-related stress. The negative correlation indicates that better coping means lower scores in perceived resources taken up by study-related stress. A correlation between well-being and coping does not exist. If well-being as the reverse scale of stress would truly measure stress, it should show a correlation to coping. These results in relation to previous research support the assumption that the well-being-score could exhibit impaired validity, therefore skewing the results of the analyses.

4.3 General methodological limitations

The finals- and examination phase for recruitment is difficult as students may not have a high motivation to take part in a research project during the most stressful time of the year. This may be the reason why the sample was rather small compared to all students. From 26,622 students, 227 filled in the questionnaire, meaning around 0.9% of all potential participants. The sample size was rather small, but increasing it by extending the recruitment period was not meaningful. Due to the theoretical construction of this study being based on students during the most stressful time in the academic year, a later recruitment would have meant contacting students during the summer holidays (July–September). Stress levels of students would have been different after this time period [45]. With respect to the predictor variables well-being, coping and resource occupation, two different populations would have been included in this study, negatively affecting the results.

The sample of this study is similar to the general Austrian student body, although some differences in the relative frequencies compared to official numbers could be identified. Some bias in the data may be attributable to a higher proportion of the sample being female and from Austria than over all Austrian universities. Having less students come from foreign countries, student performance may be a bit different, because most courses at the University of Graz are in German. This means that students attend those in a non-native language, which can lead to anxiety and lower academic achievement under certain circumstances [46]. Since anxiety is a correlate of students’ stress [47], both better outcomes for stress and performance can be expected in this sample compared to the real population. This may have masked some of the associations between stress and performance in this study.

ECTS credits were meant to be equivalent to student workload, with one credit point totaling 25 h of real-time work [26, 48]. However, courses with the same ECTS credit count do not always equal the same workload for students and are not always comparable across courses [49]. There is a variability in the connection between ECTS credits and true workload. Research demonstrated that motivation and performance outcomes do not change when a course is worth one more ECTS credit than before [50]. It also needs to be considered that there can be interindividual differences in how much workload one credit means for a person. As an example, students with prior knowledge of the contents of a course show higher achievement than others [51]. This implies that some subgroups of the student population experience a different workload as ECTS credits dictate. Considering these factors contributing to the variability of ECTS credits, they are lower in stability and validity as the other outcome variables used as measures for student performance. In line with this, grades were also shown to vary across disciplines and institutions [52], suggesting more instability compared to other indicators. This may be the reason why no predictor had a significant association with ECTS credits and grade point average.

4.4 Future outlook and implications

This study is a first step towards exploring the implications of giving students the freedom to enroll in multiple degree programs. Differences in the associations between predictors on performance variables could be obtained by implementing different analysis levels. While the non-prioritized study programs of students with two or more enrollments showed no influences in the models, significant effects could be obtained in the prioritized programs and on the other levels. This may suggest that different “rules” apply to second-priority programs of students with more than one enrollment. Since there were only associations between stress variables and student performance in prioritized programs, non-prioritized studies, and the students enrolled in those, may not be treated like single-enrollment students from a university’s governance perspective. Past research showed that targeted support structures are important for student retention and success [53, 54]. This implies that such structures may need to be defined and set up, which should be one focus of future studies. The lack of associations in non-prioritized programs may be directly related to why those programs are not the main priority of students. One implication of this study is that it should be considered that some enrolled studies of students may only exist on paper or as a reason to enrich the curriculum vitae with a few specific courses, having no intention to graduate or pursue those programs the same way they do with their prioritized ones. What this means for students on the job market after finishing their programs is yet to be studied.

Further research is also needed to better understand the differences that exist between students with one and multiple study programs as well as between the study programs of students with parallel enrollments. Since the results were of correlative nature, no causal relationships could be established with the obtained effects. It is likely that the effects in this study are of bidirectional nature, since student performance can influence their perception of stress [40]. In order to make future recommendations for policymakers and university managers, the directions and influences need to be clearer. Also, long-term analyses are warranted to compare the outcomes of studying multiple programs at once compared to studying one program in the same university system.

5 Conclusions

This study showed that students with one study program and students in multiple simultaneous programs may be treated as different populations performance-wise, as different indicators predicted performance per group. Associations between stress variables and performance indicators were found for students with one enrollment and in prioritized programs of students with more than one enrollment, but not in non-prioritized programs. The results suggest that there may be reasons why some programs are prioritized and others are not, which needs further exploration. It also can be implied that students with more enrollments may need different support structures in their studies, due to the differences between the associations of performance indicators and stress. Due to the explorative and correlative nature of this study, only initial insights into influences on student performance could be obtained in this setting. The outcomes and predictors are likely to influence each other, creating a need for further research into causal relationships between these variables.