A Novel Association and Ranking Approach Identifies Factors Affecting Educational Outcomes of STEM Majors

Data Description and Collection

The data analyzed here were obtained from the institutional research offices at the relevant institutions, following IRB approval of the project. Data were obtained for first-time full-time undergraduate students (“FT” students) at two private four-year institutions in the northeastern United States (“School A” and “School B”), who entered between fall 2010 and fall 2014 and who had an initial or last major or a bachelor’s degree in STEM. These two institutions had very small numbers of part-time undergraduates, so only full-time undergraduates were included in our analysis. These cohorts were chosen to enable us to determine six-year graduation rates and to avoid possible effects of the COVID pandemic on student trajectories and outcomes. Both institutions are midsized (5,000–15,000 students), selective (undergraduate admission rate 60%–75%), and offer degrees in liberal arts and sciences and in professions. STEM majors were defined as follows: biological sciences (except medicine and other clinical fields); physical sciences (including physics, chemistry, astronomy, and materials science); mathematical sciences; computer and information sciences; geosciences; engineering; and technology fields associated with the above fields (e.g., biotechnology, chemical technology, engineering technology, information technology). Because of considerable differences in the patterns of graduation between first-time and transfer students, we focused here only on first-time students and will present our analysis of transfer student characteristics elsewhere.

Similarly, given the differences between the paths of students who start at four-year institutions and those who start at two-year institutions, we focused here only on students at four-year institutions, and plan to extend our analysis to students at two-year institutions in a later study. Data obtained for each student included general demographic characteristics (gender, race/ethnicity, and eligibility for Pell grants, a measure of family financial status), overall performance attributes (GPA at the end of the first and second semesters, final GPA, retention from year 1 to 2, number of credits attempted and completed, and degree and year completed), and key STEM class information (the first math class taken and grades in the first math class, introductory biology 1 and 2, general chemistry 1 and 2, and organic chemistry 1). A summary of demographic, major, and GPA information about the students in the dataset is given in Table 1.

Many students started at one of the institutions and later transferred. To track these students’ outcomes, data from the National Student Clearinghouse (www.studentclearinghouse.org), consisting of students’ degree, date of graduation, and major field of degree, were obtained. These data enabled the generation of an accurate and comprehensive view of student success and thereby contributed to informed conclusions about factors influencing students’ STEM degree completion. Our study is similar to that of Voorhen et al. (2022) who followed students’ moves from high school to college using longitudinal data. Our data do not enable us to track students who start with a non-STEM major and leave their original institution, then change to a STEM major but never graduate.

Note. Only students who had an initial or latest (final) major in a STEM discipline are included.

Data Analysis

In this work we analyzed the data using the D-basis algorithm, which is based on Formal Concept Analysis (Ganter & Wille, 1999). The algorithm, applied to a binary table, extracts a set of association rules called implications that hold universally in the dataset. Frequency analysis is then applied to sets of implications to rank attributes of the table in relation to a chosen target attribute. Specifically, the D-basis algorithm identifies how frequently particular attributes occur in students who had a particular outcome (d, the “target”) versus how frequently these same attributes occur in students who had an opposite outcome (¬d, the “counter-target”). For example, the most general test with the data had the target d = “cumulative graduation” and the counter-target ¬d = “never graduated.” The ratio of these two frequencies we call the “relevance” of a particular attribute with respect to the target and counter-target outcomes. This ratio is compared to a “relevance threshold,” defined as the ratio of the number of students with the target attribute present to the number of students with the target attribute absent. Relevance values above the relevance threshold are considered to reflect an association between the attribute and the target attribute that is stronger than predicted by chance. In the next processing step, the attributes were ordered according to their relevance. A more detailed description of the D-basis method is given in the Appendix, A.2 and A.3.

Pathways of FT Student Retention, Majors, and Outcomes

The students in our dataset took many paths through higher education, beginning with their initial majors in their original institutions through diverse eventual outcomes. We defined successful outcomes as those in which students received bachelor’s degrees at any institution, which National Student Clearinghouse data enabled us to track for the many students who pursued degrees elsewhere after leaving their initial institution.

Students’ paths from entry through the transition from the first year to the second year and then to the last available undergraduate outcome were visualized using alluvial plots (Figure 2). After one year, the majority of each cohort was retained at the original institution but 21.5% (School A) or 16% (School B) were not retained (Table 1). Almost half of all students in the group of students not retained after one year were those who started as STEM majors and who ended up not transferring to other colleges and never graduating. At School A they made up about half of those who stayed with STEM and never graduated. At School B the proportion of majors not retained after one year was smaller, and these non-retained students made up a smaller percentage of all non-graduates compared to School A. The two orange streams on the alluvial plots represent the largest loss of STEM majors in these two institutions.

Most of the students who graduated in STEM had also chosen to major in STEM initially, but close to one-fifth of these STEM graduates had an initial non-STEM major (which included those who were undecided; purple streams in the plots).

The blue stream represents initial STEM majors who changed to non-STEM by graduation at their original institution. The proportion of initial STEM majors who changed from STEM to non-STEM was larger at School A than at School B. Possible reasons for this difference include the presence of engineering majors and a medical school at School A, neither of which is true of School B. These factors could affect, for example, advising approaches and faculty grading policies. At both schools many more students changed from STEM to non-STEM majors than from non-STEM (mostly undecided) to STEM majors. Detailed analysis (to be described in a later section) showed that changing majors was strongly associated with graduation outcomes.

The green streams represent non-retained students who successfully graduated at other institutions, either staying in STEM or changing from non-STEM into STEM. One subgroup of them was retained after one year, which indicates that many still transferred after the second year from both schools. Finally, the red stream represents non-retained students who changed their major and graduated as non-STEM majors. Again, a smaller proportion of them was retained after one year.

D-basis Ranking of Attributes Associated With Educational Outcomes

Detailed Analysis of Academic Attributes Associated With Graduation

Analysis of Demographic Factors

Past analyses from many studies indicated that historically disadvantaged minorities, female, first generation, and economically challenged students have more barriers to success compared to students who are White or Asian, male, continuing generation, or economically advantaged (Banerjee, 2016; Bottia et al., 2021; Campbell-Montalvo et al., 2022; Dika & D’Amico, 2016; Reyes, 2011). Surprisingly, D-basis ranking analysis that compared bachelor’s degree graduation anywhere inclusive of any time (> 6 years) to those who never graduated (Figure 3) showed that the usual demographic factors were not highly associated with graduation for either school examined. The D-basis analysis was followed up with detailed analysis of students in different demographic groups and their various outcomes. The results of this analysis (Figure 7) are presented as deviations from the mean values for all students, i.e., a positive value indicates that the indicated outcome occurred more often for the specified group of students than average. The trends and proportions of the analyzed outcomes were very similar between School A and School B and also similar for all STEM majors and biology majors only, so we present only the results for all STEM majors.

Importance of Changing Majors

A first key finding from this study is that changing majors is important for some students to have a successful outcome, namely graduation with any bachelor’s degree even if not with a STEM degree. Although one recent study at a single institution found that students who changed majors more often had lower overall GPAs (Xu & de Silva, 2024), most of the relatively few studies on this topic found, like ours, that changing majors can help improve outcomes (Foraker, 2012; Liu et al., 2021; Micceri, 2001; Seymour & Hunter, 2019; Wolter et al., 2014). We hypothesize that some students feel pressure to enter college with a STEM major and to stay in these majors despite performing poorly in STEM classes, leading them to eventually drop out of college and never graduate (Pitt et al., 2021; Seymour & Hunter, 2019). Encouraging these students to change to other majors may enable them to graduate successfully, even though in different disciplines.

Among students who change majors are also students who enter as undecided. Our data show that undecided students who eventually choose STEM majors have higher rates of success in STEM than those who declare STEM majors initially. This observation suggests that universities should be careful when advising these students and not pressure them to declare a major until the students have tried introductory courses in their prospective STEM major. If they are not successful in these courses they might choose alternative majors in which their likelihood of success is higher. Thus, institutions might be able to improve student outcomes by revising their policies around changing majors to promote exploration of majors through course selection and to enable flexibility in changing majors.

Importance of the First Mathematics Class

There were two main findings about the first mathematics class and student outcomes: First, STEM majors whose first mathematics class is calculus I or higher had improved graduation rates compared to those whose first mathematics class was precalculus or lower. This observation is consistent with other studies (Bowen et al., 2019; Budny et al., 1998; Kopparla, 2019). Second, an institution where many STEM majors started with a less rigorous first mathematics class (statistics, School B) had higher graduation rates for some STEM majors than an institution with traditional math requirements (School A). These observations are not unprecedented (Wilkins et al., 2021) and align with others’ findings that changes to math requirements can improve student success. In one example, a calculus course designed specifically for life sciences students significantly reduced the DFW rate (Eaton & Highlander, 2017). In another example, a contextualized two semester mathematics curriculum for chemistry, life sciences, and physics students improved both learning and interest in the subject matter (O’Leary et al., 2021).

As an alternative to customized calculus courses for specific majors, schools could consider adding statistics as their first mathematics requirement for many STEM majors. Students may be more likely to succeed in statistics as their first math class, thus generating academic momentum and giving them the opportunity to adjust to the challenges of college-level academic work in STEM before tackling more difficult classes. This suggestion is supported by results from a community college-based randomized controlled study of students who needed mathematics remediation. Results showed that students who were assigned to a statistics course with workshops had better outcomes, including graduation with associate and bachelor’s degrees, than students assigned to a traditional algebra course (Douglas et al., 2022). However, most of the students in this population were not planning to be STEM majors, thus this study may not be directly comparable to ours. We recommend that additional studies be carried out to see if starting with statistics in STEM majors leads to better student outcomes in varied institutional contexts.

Another approach could be the implementation of new supporting classes that can be opened mid-semester for those students who are in danger of failing in a precalculus or calculus course. This allows students who are struggling in calculus I to withdraw from the course and still earn credits and maintain full-time status. Hofstra University on Long Island has improved student success in math by directing students who place into precalculus or who are doing poorly in calculus I to take specific computer-aided modules (a program called CAMCLE; Hofstra University Department of Mathematics, 2024). Students work semi-independently to practice both precalculus and early calculus skills before reattempting calculus the following semester. Among the 137 students who took calculus I after CAMCLE (which not all students do), 80% passed in their first attempt and 86% had passed by their second attempt, compared to about a 60% pass rate in calculus I overall (David Wayne, personal communication, November 2024).

Importance of Introductory Courses in Biology and Chemistry

Success in initial biology and chemistry courses was consistently highly ranked as relevant to graduation success of biology majors and of STEM majors in general. This result is consistent with previous findings (Flanders, 2017; Hatfield et al., 2022; Weston et al., 2019) and emphasizes that departments should pay attention to biology and chemistry classes, in addition to required mathematics classes, when working to improve student retention and graduation rates. These classes are taken in the first two years of college, for biology and chemistry majors, and typically there is little possibility to delay them. There are several strategies that could be adopted to attempt to improve success rates in introductory biology and chemistry courses. One change would be to expand a two-semester course sequence to three semesters in order to reduce the amount of course content in each course (Muñiz et al., 2022). Some schools add a pre-course requirement for those who are not college ready (Bonner, 2009). However, these changes are often not adopted because they result in increasing the number of credits and/or time needed to graduate.

Alternatively, various course redesigns have been proposed for introductory biology and chemistry courses without changing the number of course credits. These include instituting student-centered redesigns which was shown to decrease DFW rates (Ueckert et al., 2011) and focusing on core concepts (“Big Ideas”; Roche Allred et al., 2022) in biology to reduce course content and enable increased active learning (Freeman et al., 2014; Sebesta & Bray Speth, 2017; Stanton et al., 2021). Another proposal is to combine two introductory biology and two chemistry courses into four integrated courses (Beers et al., 2021). Finally, some schools have created learning centers focused on STEM courses (Redd, 2016). Results on the efficacy of many of these approaches have not yet been published. Other approaches that have shown encouraging (although generally small) effects include “wise interventions” (Walton, 2014) that increase students’ sense of social belonging (Walton et al., 2023), the value they perceive in class topics (Asher et al., 2023), or the growth mindset messages they receive from the instructor (Canning et al., 2024).

Surprising Lack of Importance of Demographic Factors

For the most part, demographic factors were not associated with graduation success or on-time graduation. Identifying as Asian was strongly associated with graduation in 4 years versus longer at both schools and at graduation anywhere versus never graduating at School A. Female gender was associated with earlier graduation at both schools (Figure 7). The very small numbers of records with certain attribute combinations may have made it difficult to find true associations or resulted in artificially inflated rankings for certain attributes.

Connection with Framework Theory

Astin’s (1993) Input–Environment–Outcome framework theorizes that student success arises from three intertwined domains: the attributes students bring with them (Inputs), the college experiences they encounter (Environment), and the results they achieve (Outcomes). In our D-basis analysis, Inputs—the demographic characteristics (gender, race/ethnicity), and socioeconomic status (Pell eligibility)—offered only a modest signal of who would graduate. By contrast, Environment factors, such as the choice of initial STEM courses (first mathematics, biology, and chemistry sequences) and the timing of the change of majors, were far stronger predictors of persistence. Finally, our Outcomes, STEM versus non-STEM degree completion, on-time graduation within four years, and degree attainment at the original institution or after transfer, underscore Astin’s central claim that well-targeted environmental interventions can amplify or mitigate the influence of incoming student attributes on ultimate degree attainment.

Limitations

While this study provides valuable insights into factors associated with STEM student success, several limitations should be noted. The analysis focused on two private, four-year institutions in the northeastern United States that are similar in size and selectivity and therefore do not reflect the full diversity of higher education contexts. As such, the generalizability of these findings to other institutional types (such as community colleges, large public universities, or minority-serving institutions) remains to be tested. Expanding the application of D-basis analysis to a wider range of institutions in future research will help determine the extent to which the observed associations hold across different educational settings.

The dataset examined students who entered college between 2010 and 2014. This period was intentionally chosen to capture complete six-year outcomes and to avoid disruptions related to the COVID-19 pandemic. However, more recent cohorts may experience different academic and institutional conditions, including shifts in advising practices, course delivery, and student support structures (Charytanowicz et al., 2024). Future studies could extend this work by examining more recent cohorts and exploring whether evolving institutional environments continue to show similar relationships among gateway course performance, changing majors, and graduation outcomes.

Finally, the present analysis was limited to institutional and academic variables and did not include individual characteristics such as high school preparation, motivation, or psychosocial factors that are known to affect persistence (Zhao & Perez-Felkner, 2022). In addition, although we analyzed demographic factors such as gender, race, and financial need separately, we were not able to examine how these characteristics might combine to influence student outcomes. For example, future studies could explore whether students who share multiple characteristics, such as being both first-generation and from an underrepresented racial or ethnic group, differ in their outcomes. The potential impact of these intersecting identities could lead to different patterns of success in STEM (Jabbari et al., 2023; Ovink et al., 2024). Including such analyses, along with information about students’ high school preparation and motivation, would help create a more complete understanding of the factors that shape STEM achievement. Building on this work, future studies might integrate D-basis analysis with complementary quantitative or qualitative methods to capture an even more detailed view of student experiences and outcomes across varied educational settings.

Availability of data and materials

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request. The D-basis code is developed and made publicly available in github: https://gitlab.com/npar/dbasis/-/tree/master. Additional files and code for this project are located in the branch: https://gitlab.com/npar/dbasis/-/tree/stem-work/analysis.

Ethics approval and consent to participate

The work on the data was approved in IRB 20210126-BIO-HCL-SAN-1 [School A]. Only aggregate results are presented in the paper and consent to participate was not applicable.

Competing interests

The authors declare that they have no competing interests.

Funding

This report is based upon work supported by the National Science Foundation under Grant Nos. 1919614 and 2121495. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Authors’ contributions

K. A., J. T. B., G. Z. E., L. H., and J. V. K. conceived and designed the study, acquired, analyzed, and interpreted the data, and drafted and revised the work. S. H. contributed to the data analysis and drafting of the text. M. K. and S. S. contributed to the data analysis. R. K. N. contributed to data analysis and drafting and revision of the work. O. S. created new software used in the work and contributed to data analysis.

Acknowledgments

We thank the staff of the Institutional Research Offices at Schools A and B for providing student data. We thank Wenxian Yu for her contributions to early data analysis. We thank the (STEM)² Network (led by Dr. Jessica Santangelo, Hofstra University, and Dr. Alison Hyslop, St. John’s University) for their support and for inspiring this STEM higher education community partnership. We thank Dr. Nathalia Holzmann (Queens College) for her contributions in the early stages of this project and Dr. Anne Vazquez (St. John’s University) and two anonymous reviewers for helpful comments on the paper.

A.1 Full Results of D-basis Analysis

Full lists of results for the analyses shown in Figure 3 (Attributes for Graduation vs. Non-Graduation in Order of Decreasing Relevance by D-basis Analysis) are available at the following links: https://gitlab.com/npar/dbasis/-/blob/stem-work/results/SchoolA_FTFT_STEM-ByRelevance_col11-col13-FullNames.csv and https://gitlab.com/npar/dbasis/-/blob/stem-work/results/SchoolB_FTFT_STEM-ByRelevance_col11-col13-FullNames.csv

A.2 Introduction to the D-basis Algorithm

D-basis belongs to the family of algorithms that are based on an analysis of association rules. The mathematical background of the algorithm is presented in Adaricheva and Nation (2017). The algorithm retrieves the implications (association rules of confidence = 1) S → d in a table with entries 0 and 1. Here S is a subset of attributes/columns and d is another column (say, an indicator of student graduation in 4 years since entering higher education). The rows of the table represent students included in the study, and the presence of any attribute is indicated by entry of 1 in the column representing the attribute.

The rule S → d holds in the table, if all entries of 1 for the set of attributes S imply an entry of 1 in column d, for each row of the table (a student in our case). If all entries in S ∪{d} are 1 in one particular row, then we say that rule S → d is validated in that row. Set U of all rows validating this rule is called a support of the rule.

Unlike most approaches in mining association rules, in which some rules are selected based on techniques measuring the rules themselves, we are looking at the measurement of relevance of all attributes appearing in the rules with the same target attribute.

In particular, we measure the frequency of any other attribute, say, a as it appears in the antecedents of the rules S → d, together with other attributes. Our parameter of the relevance, which appeared first in Adaricheva et al. (2015) when applying the D-basis to the medical data, requires the computation of the rules not only on target d but also on its complement ¬d, which may or may not appear in the original data.

Another advantage of our approach is that we do not shy away from having a large number of retrieved rules because they provide better representation of all attributes and allow better comparison of attributes related to a given target. The top attributes were identified through testing with variations of the minimal support, which refers to the number of observations validating the rules connecting attributes and a target. In our testing the number of rows (students) in the test data ran from several hundred to several thousand, and we ran the test on minimal support = 10, which would represent between 0.01%–1% of entries of the table.

A.3 Computation of the Relevance of D-basis Output

Here we describe a parameter useful for evaluating data from D-basis which we call “relevance” (Adaricheva et al., 2015). For a fixed column d and any other column a, one can compute the total support of all rules S → d such that a is in S. This parameter shows the frequency that a appears in implications targeting d. The algorithm can also compute a similar frequency of a when targeting ¬d, i.e., an additional column where all entries in d are switched. The ratio of the two frequencies gives the relevance of attribute a to d and is denoted rel_d(a).

The higher rel_d(a), the more frequently attribute a appears in set S for rules S → d compared to rules S → ¬d. All attributes different from d, therefore, may be ranked by the relevance with respect to d. Our method could investigate the attributes with highest ranks with respect to d = “graduation in 4 years” or with respect to d = “student retained from year 1 to 2.” Then all attributes of the table can be ranked in their relevance to a fixed attribute d.

Let us give more precise definition how the relevance of attribute a with respect to target attribute d is computed. Denote X the set of all attributes. For each attribute a ∈ X \ d, the important parameter of relevance of this attribute to d ∈ X is the parameter of total support, computed with respect to any set of rules/basis β of association rules describing the table (in our case, it is the portion of the D-basis which only includes rules of requested minimum-support at least δ):

Thus tsup_d(a) shows the frequency of parameter a appearing together with some other attributes in implications S → d of the basis β. The contribution of each implication S → d, where a ∈ S, into the computation of total support of a is higher when the support of S is higher, i.e., column a is marked by 1 in more rows of the table together with other attributes from S, but also when S has fewer other attributes besides a.

Note that the high frequency of some attribute in implications when targeting attribute d does not mean that same attribute will appear less frequently when targeting the negation of d. This is why the second test is done when targeting ¬d, which may or may not appear in the data. When such attribute is absent in the data, the complementary attribute can be generated from d. Thus, tsup_¬d(a) could also be computed.

Define now the parameter of relevance of attribute a ∈ X \ d to attribute d, with respect to basis β:

The highest relevance of a is achieved by a combination of high total support of a in implications S → d and low total support in implications U → ¬d. This parameter provides the ranking of all parameters a ∈ X \ d.

Typically, we use a threshold to separate the attributes that are positively relevant to d, i.e., rel_d(a) ≥ t, from the rest of attributes.

A.4 Attributes Among Students Who Started or Finished With a STEM Major

A.5 Analysis of Graduation in 4 Years Versus Later Graduation

An additional part of our analysis looked at factors correlated with shorter vs. longer graduation times. We compared those FT STEM students who graduated in 4 years or less and those who graduated in more than 4 years, regardless of whether they graduated from their original institution or from somewhere else or whether they graduated with STEM or non-STEM degrees (although they must have had a STEM major at some point to be included in our analysis). The top 30 attributes by relevance for the two schools are displayed in Figure A1.

At both School A and School B, the following attributes were highly associated with d = “graduation within 4 years” and ¬d = “graduation more than 4 years”:

• • High overall GPA (3.3 or above).
• • High GPA (3.6 or above) during the first two semesters.
• • Good grades in introductory biology courses.

At the same time, the following attributes were highly associated with ¬d = “graduation in more than 4 years” (not shown):

• • Low GPA (2.0 or less), both in the first 2 semesters and overall.
• • More than 14 credits attempted but not earned.
• • 39 or fewer credits attempted or 79 or fewer total credits.
• • Not being retained between year 1 and 2.

Besides these shared trends across both schools when targeting graduation in four years, there were also some differences between School A and School B.

• • Chemistry grades: At School A high grades in organic chemistry were associated with graduating in four years. At School B, earning a B in chemistry 1, 2, and organic chemistry were above the threshold.
• • Major: At School A an initial or final major in chemistry, biochemistry, math, or physics were above the threshold. At School B, the majors associated with graduating in four years were biology and neuroscience.
• • Math class: At School B, taking statistics as the first math class was ranked second out of all attributes and earning an A or B in the first math class both ranked in the top thirty attributes. At School A, having calculus II as the first math class ranked seventh. Math grades at School A were not associated with graduation in 4 years here.

Across both schools, when we test alternate outcome and target graduation in more than 4 years, only about 30 attributes were found above the relevance threshold, indicating that students who graduate in more than 4 years are a less uniform group in their attributes than those who graduate in 4 years or less. The high ranking of GPA factors for both schools suggests that doing poorly in first-year classes is a consistent predictor of delayed graduation, if a student graduates at all. Additionally, transferring to a different university and receiving a bachelor’s degree elsewhere were highly ranked factors for delayed graduation. This observation aligns with the factors outlined above: Students who failed out of their first year but still graduated likely managed to do so because they transferred to another institution that was a better fit for them.

A more detailed analysis of FT STEM students who graduate (Table A2) shows a clear trend: As the time to graduation increases, the percentage of those who graduate somewhere else also increases. It may be surprising, therefore, that while not in the top 30, still above the threshold, out of 218 attributes for graduation on 4 years versus later the rankings of relevance for changing major at School A were STEM-to-STEM at rank 41 and STEM-to-non-STEM ranked 53, while no change of major had rank 59. At School B the picture was different: No change of major had rank 44 and STEM-to-STEM had rank 96. None of the change of major attributes showed relevance to later graduation at either school.

Looking at the percent of students in each path of major graduating at a particular time, we observe that at School A, changing major was correlated with faster graduation (Table A3). STEM students who did not change their major represent a higher proportion of graduates at longer times to graduation (Table A3, 2nd row). Confirming this, the highest percentage of students changing from STEM to non-STEM was among 4-year graduates (Table A3, 3rd row), and the percentage diminished among those who took longer to graduate. Weaker but similar trends were found for those who change between STEM majors and for those who change from non-STEM (usually undecided) to STEM (Table A3, 4th and 5th rows). For those who graduated in 4 years, 56% of these students did not change their major at School B but only 35% at School A kept the same major. For the students at School A who graduated from their original institution, the percentage of those who did not change majors is even smaller. In contrast, for students who started at School A and graduated in 4 years from other institutions, about 70% did not change their major. The percentage of such students is comparable at School B; however, the number of such students is much smaller. For students graduating between 4 and 6 years, at both schools students who did not change their major now accounted for about 40%, with the other students fairly evenly divided between changing from STEM, or into STEM. Thus, it seems a larger subgroup of students in School A change their major early and graduates in the same school, while in School B the majority of students graduating in 4 years stay with their original major. The observation at School A does not support the interpretation that a change of majors always causes a longer path to graduation, at least for students who had a STEM major at some time in college. Instead, successful students who changed from STEM to a non-STEM major must have made this change early in their collegiate career in order to graduate within 4 years.