Quantitative Methods in the Assessment of Undergraduate Research, Scholarship, and Creative Inquiry

Recommended Citation: Lopatto, David. 2023. Quantitative Methods in the Assessment of Undergraduate Research, Scholarship, and Creative Inquiry. Scholarship and Practice of Undergraduate Research 7 (2): 5-12. https://doi.org/10.18833/spur/7/2/3

SPUR represents the philosophy of the Council on Undergraduate Research (CUR) to support and promote high-quality mentored undergraduate research, scholarship, and creative inquiry. Readers of SPUR approach the journal hoping to find model programs, good ideas, and the characteristics or causes of successful undergraduate research programs. The dual goals of SPUR, according to LaPlant (2017), are to “stimulate the rigorous assessment of undergraduate research initiatives and programs” and “that SPUR will encourage best practices and models of undergraduate research” (3) Consideration of these goals leads to two views of the use of quantitative methods. Whereas rigorous assessment evokes ideas concerning statistical comparison and control of confounding variables to clarify a theory of undergraduate research, scholarship, and creative inquiry (URSCI) and its effects on student behavior, finding model programs suggests that programs may be emulated across institutions by educators who are free to change support factors to facilitate the program’s success. In the first case the goal is generalizability; in the second the goal is transferability.

The focus of this commentary is on the use of quantitative research methods in the understanding and assessment of undergraduate research, scholarship, and creative inquiry. The Council on Undergraduate Research has a broad definition of undergraduate research (a mentored investigation or creative inquiry conducted by undergraduates that seeks to make a scholarly or artistic contribution to knowledge), meant to include all scholarly disciplines and interdisciplines. It is necessary to acknowledge that disciplinary pluralism implies epistemological pluralism. The assessment of some undergraduate research programs may rely on the qualitative methods suitable for the nature of the program. For example, Naepi and Airini (2019) described the Knowledge Makers program used to mentor Indigenous researchers and evaluated the impact of the program through e-portfolios and student reflections without the use of quantitative data. Zhen (2020) described a program for teaching chefs to be researchers and presented a summary of successful projects as well as a sample of visual evidence (a photograph) in support of the program’s effectiveness. The observations regarding quantitative methods that follow are not intended to privilege quantitative methods over other epistemologies.

Finding model (exemplary) programs suggests that the authors of many of this journal’s reports are advocating causes (the URSCI mission) as well as investigating causes. CUR’s mission attracts the interest of teacher-scholars whose strategic aim is not one of complete disinterest or impartiality. They want the promise of undergraduate research to succeed. SPUR reports are often composed by mentors, instructors, and program directors who have a stake in the success of their program and the broader mission of CUR. The challenge is to practice impartiality when analyzing undergraduate research programs, and it is in this endeavor that quantitative methods may help. Quantitative methodology comprises conventions for best practices that enhance credibility, such as rules applying to the size and scope of an adequate sample and decision rules for what constitutes “statistical significance.” The promise of quantitative methods is that they permit tactics for evaluation that are objective employed by teacher-scholars who have objectives.

Although textbooks about quantitative methods suggest that a research plan should precede the selection of appropriate measures, it appears that educational researchers rely on available measures of program effectiveness such as student grade point average (GPA), graduation rates, or completion rates. The advantages and disadvantages of these measures are familiar. Institutional measures such as the GPA are routinely collected, and archives are readily available. Although most researchers recognize that grade point averages comprise a heterogeneous mix of course selection, degree of difficulty, and other confounds, the archive continues to be employed in assessment and evaluation (Brown et al. 2020; Nicols-Grinenko et al. 2017; Sell, Naginey, and Stanton 2018). In this selection of a measure, familiarity breeds contentment. Reliance on one imperfect measure is a risky method; however, there is a remedy. The methodology of multioperationalism (Cook and Campbell 1979; Webb et al. 1981) suggests that multiple measures may align to support the argument for the benefits of an URSCI program. Therefore analyzing the GPA and another measure such as student survey responses may strengthen the argument for program effectiveness.

Research Questions

The dual targets of CUR’s mission suggest dual research goals. Consistent with the rigorous assessment of undergraduate research initiatives, Haeger et al. (2020) suggest that the key research question for the study of URSCI is to explicate the causal relationship between URSCI and the various outcomes that have been attributed to the experience (e.g., Lopatto 2004). Haeger et al. observe that quantifying the effects of URSCI has been a challenge, writing that “the majority of research measuring the impact of undergraduate research relies on indirect measures or correlations between outcomes and participation” (67) SPUR also promotes the sharing of models of undergraduate research, inviting the transfer of a model program to new settings even though the underlying causal model is not known. Causal models and model programs are not the same and may afford different sorts of quantitative analysis.

Simplicity

When deploying quantitative methods for purposes of describing or evaluating URSCI, it is tempting to bring to bear the full persuasive impact of sophisticated methods used to uncover latent variables, account for more multiple factors and their interactions, and seek an elusive generalizability of the pedagogy’s effects. There is value in choosing a more modest approach. Experienced researchers caution us that “less is more.” Cohen (1990), writing about psychology, advocated simplicity in research designs, citing the problems that accompany complexity, including poor statistical power (the probability of finding an effect if it exists) and the increase in misleading conclusions of statistical significance when the number of tests increases. Kass et al. (2016) included “keep it simple” in their advice regarding effective statistical practice in computational biology. They wrote, “the principle of parsimony can be a trusted guide: start with simple approaches and only add complexity as needed, and then only add as little as seems essential” (4) Abelson (1995) wrote, “Data analysis should not be pointlessly formal. It should make an interesting claim . . . and do so by intelligent interpretation of appropriate evidence from empirical measurements or observations.” In support of interesting claims authors often use familiar quantitative methods even if the disciplinary focus of the undergraduate research program is complex. For example, the SPUR issue for summer 2019 highlighted programs that featured undergraduate research experiences using big data (large databases and data visualization). None of the featured programs employed big data techniques to evaluate the program’s outcomes. Some reports favored descriptive statistics (Killion, Page, and Yu 2019; Lukes et al. 2019). Others favored descriptions of the program’s development or evolution without quantitative evaluation (Nelson, Yusef, and Cooper 2019). It may be that even as URSCI programs grow to embrace contemporary topics such as machine learning, digital humanities, and artificial intelligence the quantitative methods by which the programs are assessed remain relatively simple. Simple analyses include the t test, which was intended for samples smaller than 30 when comparing a treatment group to a comparison group; as well there is a version for pretest-posttest comparisons. Some reports (e.g., McLaughlin, Patel, and Slee 2020) employ nonparametric statistics that do not demand normally distributed data. Faced with small samples of less than 30, some reports acknowledge the difficulty of inferential comparisons and report only descriptive statistics (Dillon 2020; Spronken-Smith et al. 2018). For these small groups visual representation of data is helpful. If a cohort of students engaging in program is very small, then it may be important to note the reasons for any student who fails to benefit or who drops out of the program. These reasons may be exogenous to the program, such as illness, family crises, etc., and so may not influence the argument for the program’s effectiveness.

Description

Quantitative data are the most common form of reporting the results of programs described in SPUR and other journals; however, the reliance on data does not compel inferential testing or model building. Instead, numerical data can be used as “mere description” (Gerring 2012), providing a more precise account of outcomes than qualitative summaries. If a study reports that student program participants average grades of 3.7, most readers know implicitly that the common GPA scale ranges from 0 to 4, and that 3.7 is a successful grade. Deming (1953) distinguished between surveys that were enumerative (asking how much) and surveys that were analytic (asking why). Enumerative surveys may be adequate for evaluating the effectiveness of a program by reporting graduation rates or attrition rates, vouching for the success of the program but falling short of specifying the specific cause of the success (Cartwright 2007). In some studies mere description is adequate for illustrating an effect. For example, Grindle et al. (2021) used descriptive counts and percentages to illustrate the result of in a study of passive research involvement.

Cohen (1990) noted that simplicity of describing data suggests the use of graphs and diagrams that may aid in presenting a program outcome. The use of figures may efficiently represent descriptive data, and is a common practice in this journal (Barney 2017; Brooks et al. 2019; Garrett et al. 2021; Gold, Atkins, and McNeal 2021; Kuan and Sedlacek 2022; Szecsi et al. 2019). Tufte (1983) outlined the characteristics of graphical excellence, including graphs that serve the clear purpose of description, which encourage the viewer to think about substance, and encourage comparisons between different pieces of data.

Validity

Readers expect the assessment of an URSCI program to be valid. There are many adjectives to be placed before validity, and inevitably three types occur. The first is the validity of the instruments employed to measure outcomes. The second has to do with the internal logic of the program and how that program produces results (internal validity). Finally, the question of the generalizability or transferability of the program arises (external validity).

We expect the creators of instruments to present some evidence of the instrument’s validity by showing that the instrument is in agreement with other methods used to measure the same outcome (Campbell and Fiske 1959). Once the instrument’s trustworthiness is established, the use of the instrument by subsequent researchers often relies on the reputation of the instrument’s original validation. There is often not enough data or time to revisit techniques for validation of the instrument in every study. This trust in the instrument is normal; work proceeds slowly if the research instrument has to be revalidated each time. The concern arises when the new users of the instrument invoke a “mutatis mutandis” approach, that is, making necessary changes in the original instrument so that it fits the new project without affecting the main constructs measured by the instrument. The presumption is that the original instrument is robust, preserving its validity despite alterations. A perusal of the reports published in SPUR suggests that authors often use research instruments created by other researchers. Examples include the SURE survey (Survey of Undergraduate Research Experiences; Lopatto 2004); URSSA (Undergraduate Research Student Self-Assessment; Hunter et al. 2009); and the OSCAR Student Survey (Foster and Usher 2018). Items from these established surveys are occasionally revised to suit the context. Are there credible procedures for changing an instrument while claiming that it retains its essential meaning? The credibility of the instrument can be supported by response process validity, which involves the review of the survey items by subject matter experts, and cognitive interviewing of potential respondents to determine if respondents understood the intended meaning of the survey items. These procedures may or may not lend themselves to quantitative analysis, but they improve the validity of the modified instrument.

The effectiveness of the program, called internal validity, is “the degree to which an experiment is methodologically sound and confound-free” (Goodwin and Goodwin 2017, 148). The validity question reduces to the confidence we have that the URSCI program causes the changes in the students’ behaviors. Traditionally, the gold standard for causal assertions is the true experiment, or randomized controlled trial. Randomized controlled trials are rare in studies of undergraduate research and creativity. Randomized controlled trials rely on the researcher’s control of participant assignment to treatment and comparison groups as the basis for making a causal assertion that the program caused changes in the participant’s behavior. In the absence of randomized controlled trials design features for a causal assertion, researchers use a variety of tactics. Some involve the creation of a nonequivalent comparison group that serves as a proxy for a genuine control group. Nicols-Grinenko et al. (2017) utilized their institution’s undergraduate population as a comparison group for students who participated in undergraduate research. After describing an initiative to build a culture of undergraduate research at their institution, they tracked undergraduate research participants and compared the participants graduation rates and grade point averages to all undergraduate contemporaries. They found higher graduation rates and grade point averages for undergraduate research participants compared to the general student population. Several researchers use a pretest as the comparison group for posttest data. Beer et al. (2019) used both between-groups and pretest-posttest data to argue for the effectiveness of a peer research consultant program. The results showed increments in desirable skills from pretest to posttest based on t tests. Ashcroft et al. (2021) employed pre- and post-ratings of gains in the understanding of research and related items and found several significant Wilcoxon test results in the favorable direction. Tian et al. (2022) reported on the success of inquiry-based learning in China. They found significant gains on self-report items from the SURE survey (Lopatto 2004), although the choice of inferential test was unclear. Several of these reports chose to analyze items on a survey separately, leading to the concern that piecemeal testing may result in false positives (type 1 errors).

Matching and pretest-posttest designs are efforts to preserve the internal validity of the assessment in the absence of experimental control. The objective is a generalizable result. The most ambitious attempts to substitute statistical control for experimental control involve forms of multiple regression models.

Models

The term model can be used to describe a “particular aspect of a given theory” (Fried 2020) or a program to be emulated. In the model as theory, the undergraduate research program is described for replication with adherence to the original method, that is, the program is generalizable. The model as theory suggests that the reader will see a SPUR report that describes an outcome for a sample (usually of undergraduate students) that will generalize to a population. Because URSCI programs seldom follow the formula for assertions of generalization, namely, randomly selecting student participants from the student population and randomly assigning students to treatment and control groups (see Haeger et al. 2020), researchers exploring the nature of undergraduate research employ various statistical methods as a substitute for randomization. The goal is to estimate the main effects of the program to build a theory of URSCI. Student participants in these programs tend to be diverse and so confound the main effects of the program. How do researchers attempt to account for student differences? Some analyses of undergraduate research (UR) include attempts at matching non–randomly assigned program participants with nonparticipants. These analyses employ a range of techniques from simple matching to advanced regression analysis to examine whether student characteristics moderated the program outcome. Rodenbusch et al. (2016), for example, reported that regression analysis of race/ethnicity, gender, and first-generation undergraduate status yielded no significant relation to program success. Galli and Bahamonde (2018) matched UR students and comparison groups on grade point average at time of program admission. Whittinghill et al. (2019) reported an analysis of 10 years of data concerning the effect of UR on graduate rates, grade point average, and entrance into graduate programs. They used propensity matching (Rosenbaum and Rubin 1983) to create a quasi-control group for comparison with the outcomes for UR researchers. Brouhle and Graham (2022) employed a probit regression model to account for possible confounding variables affecting undergraduate research students and a comparison group of nonresearchers. The technique allowed the researchers to argue that differential outcomes, such as the superior grade point averages of the undergraduate research students, were not based on a confounding variable. Sell, Naginey, and Stanton (2018) compared the grade point averages of students with research experience with those who did not, for both contemporary students and graduates. For graduates, propensity matching was used to form a matched comparison group to the undergraduate research group. The analysis, which matched the groups on eight variables including gender and first-generation undergraduate status, found significantly higher grade point averages for research students.

Large-scale programs, or programs that consolidate data over several years, recognize that the student is a heterogenous variable, that is, within the student sample there are many subsamples. These subsamples may be classified by race, ethnicity, gender, or culture. Large-scale programs intend to benefit all students, so quantitative methods are employed to show how well the program results in a general main effect. Some large-scale programs test for differences between student subsamples on a quantitative measure and simply report that no differences were found (Shaffer et al. 2014). Others use sophisticated modeling to eliminate the influence of possible confounds. Hanauer et al. (2017) examined the impact of the SEA-PHAGES undergraduate research program in biology on student success while accounting for a variety of student characteristics. They reported equally positive outcomes for students with diverse economic backgrounds, academic performance, gender, and ethnicity. The intent of these approaches is that they attempt to preserve the idea of the general reference population, that demographic and economic identities of students are confounding variables that may be removed from the analysis statistically, revealing a main effect of URSCI on the general reference population of undergraduate students.

The third use of validity is external validity, usually defined as the degree to which research findings generalize to other populations, settings, or times. The usual argument is that the results drawn from a sample generalize to a reference population. The construct of the reference population to which studies generalize has been questioned by awareness of how WEIRD (Western, educated, industrialized, rich, and democratic) cultural participants in psychological research skew the results away from generalizability (American Psychological Association 2010). Reports published in SPUR seem cognizant of the need to address multiple student populations, an approach sometimes termed culturally responsive assessment (Baker and Henning 2022). Pursuing the goal of generalizability encourages analysts to control confounding variables such as student ethnicity or gender. Pursuing the goal of transferability encourages the consideration of these variables as support factors that are not neutralized but optimized to promote student success. Following Cartwright and Hardie (2012), researchers should be free to optimize support factors rather than to suppress confounding variables. Support factors are “other members of the team of causes” that optimize success. For example, reported successes for undergraduate research in genomics (Lopatto et al. 2008) originated at an institution known for high student selectivity and good financial resources. Reported success of the same program at community colleges (Croonquist et al. 2023) required the recognition that many support factors of the community college programs differed from those in the early reports. Further examples of diverse yet effective programs may be found in the SPUR special issue published in summer 2018, which highlighted culturally relevant programs (Boudreau et al. 2018; Puniwai-Ganoot et al. 2018) that reported effectiveness without claiming to be replications of a standard method. Each program deployed a package of support factors to optimize the program’s success. Whereas studies in pursuit of generalizable results set aside variables such as gender, ethnicity, and socioeconomic status, culturally relevant programs foreground these variables and employ the necessary support factors to facilitate the program’s, and the student’s, success. SPUR reports often suggest model programs that may be emulated (Dickter et al. 2018; Follmer et al. 2017; Foster and Usher 2018; Gilbertson et al. 2021; Gould 2018). The approach makes sense, given that SPUR is a trading post of ideas across academic disciplines and interdisciplines.

SPUR and its parent organization CUR value diversity and equity. Equity is typically taken to mean that different students need adjustments to correct for imbalances and obstacles to success. Equity is a support factor. Equity adjustments imply that students are not replicates of each other. The challenge, then, is to find measures of program effectiveness that includes the individual differences of student participants. For this purpose, it is necessary to reimagine a common distinction in assessment research between direct and indirect measures of student behavior. Direct measures of student learning are said to include tests of knowledge such as exams and quizzes. Indirect measures of student learning include quantitative self-reports found in surveys. Although the multioperational approach to assessment (Cook and Campbell 1979) recommends the use of both measures rather than relying on one, direct measures have been enshrined as superior to student self-reported measures. Within URSCI programs the privileged status of direct measures needs to be interrogated, given that many programs encourage students to create unique products, artifacts, or scholarly reports. The interrogation may proceed in this way: Indirect measure of student behavior, that is, self-reported quantitative ratings, seem to cast the student as an audience to some instructional performance. The self-report is often anonymous, preventing the appreciation of the role of the student’s identity in their experience. In undergraduate research, scholarship, and creative inquiry the student is an active participant (but see Grindle et al. 2021). Their experience is necessarily interpreted through the lens of their personal identity. URSCI experiences may modify or enlarge the student’s identity with respect to professionalism or joining a community of scholars (Palmer et al. 2018). Rigorous statistical modeling treats aspects of identity as confounding variables that need to be partitioned from the main effect of URSCI so that a generalizable treatment effect may be uncovered. Standard quantitative methods such as analysis of variance or multiple linear regression treat the interaction of the independent variable and the student’s identity as an isolatable, additive, and linear component of the experience. If the goal of the assessment is not, however, a generalization from the student sample to a unitary reference population, then we may become interested in the student’s identity as a support factor for the program’s success. The joint effect of a program and the student’s identity is not an interaction but an intersection. The individual differences of the students become a focus of assessment, and the student’s survey data evolves from indirect measure to direct measure. Self-report becomes self-disclosure. Self-disclosure offers the most direct measure of the student’s URSCI experience. The challenge going forward is to optimize the use of quantitative methods to find precise descriptors of student outcomes while preserving the individual differences in student success.

The continuing challenge for faculty and staff who administer undergraduate research programs will be the nearly compulsory assessment of student learning and attitude. The work may seem challenging to program faculty and staff who do not regularly employ quantitative methods. Consulting the myriad online courses, websites, and videos concerning statistics may be off-putting. A less abrasive introduction to quantitative methods may be sources such as Statistics Done Wrong (Reinhart 2015) or Statistics As Principled Argument (Abelson 1995), books that address common problems of quantitative decision-making without elaborate formulas. Similarly, The Craft of Research (Booth et al. 2016), although it does not cover statistical analysis, has a useful chapter on communicating evidence visually. For readers wishing to tutor themselves in statistical techniques there are Statistics Unplugged (Caldwell 2013) and Statistics for the Terrified (Kranzler 2003). For issues concerning quasi-experimental design and threats to validity, Cook and Campbell (1979) remains a standard text.

Encouraging best practices includes encouraging the practitioner. The ongoing explorations in programs for undergraduate research, scholarship, and creative inquiry will best be sustained if they are beneficial to the student and the mentor. Quantitative methods may provide a perspective through which the benefits may be discerned. The construction of this perspective and the picture that emerges provide a shared journey for all participants.

Conflict of Interest

The author has no conflict of interest.

IRB Statement

Not applicable.

Data Availability

Not applicable.

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David Lopatto
Grinnell College
lopatto@grinnell.edu

David Lopatto is a professor of psychology and the Samuel R. and Marie-Louise Rosenthal Professor of Natural Science and Mathematics at Grinnell College. He is the former director of the Grinnell College Center for Teaching, Learning, and Assessment. He has been studying the features and benefits of undergraduate research experiences for many years, creating instruments, including the Survey of Undergraduate Research Experiences (SURE) and the Survey of Classroom Undergraduate Research Experiences (CURE), which may be found at https://sure.sites.grinnell.edu.