## Ownership Diversity and Innovation: A Novel Framework for Increased Research Transparency### AbstractA split sample/dual method research protocol is demonstrated to enhance transparency while lowering the likelihood of false discovery. We apply the protocol to examine whether diversity in ownership teams boosts or reduces a company's likelihood of reporting a new innovation using data from the 2018 United States Census Bureau's Annual Business Survey. Transparency is enhanced in three ways: (1) all specification testing and identification of potentially productive models are conducted on an exploratory subsample that (2) maintains the validity of hypothesis test statistics from de novo estimation in the holdout confirmatory sample, and (3) all findings are publicly reported in an earlier registered report and this journal publication. Bayesian estimation procedures that incorporate information from the exploratory stage in the confirmatory stage estimation replace conventional frequentist null hypothesis significance testing. In addition to increasing statistical power by using information from the entire sample, Bayesian methods directly estimate a probability distribution for the magnitude of an effect, enabling much more nuanced inference. Estimated magnitudes of diversity along academic discipline, race, ethnicity, and foreign-born status dimensions are positively associated with innovation. A maximally diverse ownership team on these dimensions would be approximately six times more likely to report a new-to-market innovation than a homophilic team.### IntroductionThe credibility crisis in applied research extends far beyond science, eroding the quality of public debate on contentious issues like climate change, public health, and the value or triviality of fostering diversity in a liberal democracy. The admonition to "trust science" rings hollow when findings cannot be replicated, fail to replicate in similar studies, and are not entirely transparent about their derivation or testing of competing hypotheses [1]. Increasing transparency and replicability is something that applied researchers can proactively integrate into their research designs.This article aims to provide proof of concept for a split sample/dual method research design applied to a highly contentious topic: the connection between ownership diversity and business innovation. The protocol addresses two major factors that contribute to the fragility of findings: (1) by dividing the dataset into an exploratory sample for specification testing and a confirmatory sample for hypothesis testing, the validity of statistics that assume de novo tests is preserved; and (2) through false discovery rate and family-wise error rate corrections, the validity of comparing multiple alternatives is preserved [2]. Additionally, we significantly reduce the researcher's degrees of freedom in selecting a diversity measure by mandating that the chosen index adhere to four axioms applicable to the analysis of diversity in small teams.The novel contribution of our protocol is the use of Bayesian methods in the confirmatory stage of the analysis, replacing frequentist methods. This modification leverages information gathered during the exploratory stage and incorporates these estimates as weakly informative priors in the confirmatory phase. The discrete steps of the protocol are outlined in S1 File. In addition to narrowing the credible interval of estimates, the method also raises the informational value of the estimates for inference. Frequentist and Bayesian confirmatory findings are presented together to evaluate the potential advantages of methodological pluralism.The proof-of-concept also demonstrates a viable solution to the data-dependent analysis problem that plagues research using observational or secondary data [3]. The data-dependent analysis problem, where unreported repeated specification testing results in fragile, often unreplicable findings, has long been recognized [4]. Preregistration has since been broadly accepted for randomized control trials, but "it is unclear how to apply preregistration to the analysis of existing data, which account for the vast majority of social science. Researchers need to develop practices applicable to existing data—whether historical or contemporary, quantitative or qualitative—as a priority" [5]. There have been some suggested solutions, but no institutional mechanism for implementation exists [6, 7]. This problem could be resolved by the growing number of researchers utilizing confidential data within the Census Bureau's Federal Statistical Research Data Centers (FSRDCs). Access to data is stringently regulated, so it would be possible to release confirmatory samples to researchers only after the publication of a pre-analysis plan, along with the full set of findings estimated from an exploratory sample used to arrive at the plan. The use of confidential data is becoming common in economics. In 2022, 44 of 94 articles published in the American Economic Review were exempted from data sharing due to confidentiality restrictions [8].### Diversity Findings Vulnerable to False DiscoveryThe empirical problem that demonstrates the proposed protocol assesses how diversity within ownership teams relates to a higher or lower likelihood of reporting new-to-market innovation. The data used are from the 2018 Annual Business Survey (ABS) produced jointly by the United States (U.S.) Census Bureau and the National Center for Science and Engineering Statistics within the U.S. National Science Foundation. The ABS replaced the Survey of Business Owners for companies with employers, added the innovation module from the former Business R&D and Innovation Survey, and an R&D module for microbusinesses with less than ten employees. Information on demographics and the backgrounds of up to four owners for each firm is collected.The hypothesis that diversity in ownership teams fosters innovation stems from a combinatorial view of innovation: the convergence of seemingly unrelated ideas [9]. For instance, business owners from various academic backgrounds could be expected to combine ideas from different domains. Less evident is whether business owners from very different life experiences mediated by, for example, race or country of birth, might also generate more original ideas [10]. The notion that areas with greater diversity are also more inventive than the counterclaim that regional homophily encourages innovation dominates the literature [11\u201313]. Putnam's highly cited study, which provides evidence that diversity is negatively correlated with social capital, trust, and altruism at the regional level, recognizes the overwhelming evidence of a beneficial relationship with creativity and innovation [14].Findings at the firm level on whether diversity or homophily is more likely to drive innovation are conflicting. The theory that diversity hinders innovation arises from the role that homophily may play in facilitating the exchange of information [15, 16]. The two competing effects of diversity on information exchange include affective conflicts—where one group's attitudes or emotions are incompatible with others—and cognitive conflicts—where a divergence of ideas due to differing experiences can resolve as performance-enhancing synthesis [17].Cognitive conflicts are the theoretical foundation of the seminal explanation of diversity's advantage over homophily in problem-solving [18]. Empirical approaches to better isolate cognitive conflicts from affective conflicts include creating a measure of "unusualness" that compares the nationalities of firms to the cultural diversity of a region to capture differences in cognitive approaches [17]. Management studies have demonstrated the benefits of homophily in startups or research partnerships for innovation [16, 19] and firm survival [19]. Given the potential for both affective and cognitive conflicts to influence the effect of diversity on innovation, the direction of influence remains an empirical question.The possible confounding factor of discrimination that might hinder successful innovation from diverse ownership teams is neutralized in the present analysis by the positive measure of innovation available in ABS that is used in this study: substantial change from what was done before and novelty are the essential criteria.In addition to being a widely contested topic with implications for judgments about diversity training, affirmative action, and immigration policy, it is also highly susceptible to false discovery. There are numerous ways to quantify diversity. Nijkamp and Poot [20] consider more than 20 such metrics. Measures typically merge relevant attributes such as race, ethnicity, gender, or foreign-born status to represent diversity. The proliferation of these tools creates a research environment ripe for cherry-picking and prone to false discovery and a multiple comparison problem.The initial step in decreasing the number of estimates is to choose a single measure that satisfies the following axioms discussed below [21]. A single measure lessens the dimensionality of the multiple comparison problem. It eliminates inductive research for measures that complement the researchers' priors. While the axiomatic approach does not guarantee an optimal measure, it does render the selection process transparent.The axioms that the diversity measurement is needed to satisfy include:1. Homophily Axiom: All owners belonging to the same group should produce the lowest diversity measure value.2. Fractionalization Axiom: Increasing the number of groups should increase the diversity measure value.3. Team Size Axiom: Larger ownership teams, in the absence of homophily, should increase the diversity measure value in comparison to smaller ownership teams.4. Concentration of Ownership Axiom: Ownership centralized in one team member should reduce the diversity measure value in comparison to ownership that is more equally dispersed among team members.The homophily axiom demands that the diversity measure value be the lowest for ownership teams that lack diversity in the dimension of interest. This feature raises the issue of how to deal with single-owner firms for which diversity along any dimension or across many dimensions is impossible. The strategy used in the exploratory analysis that is followed here is to exclude single-owner firms from the analysis. This exclusion allows for a comparison of the association of homophilic and heterophilic collaboration with innovation that is not confounded by the impact of no-owner collaboration on innovation.The fractionalization axiom requires the diversity measure to increase with the number of distinct groups in any ownership team dimension. The seven dimensions used to assess the relationship between diversity and innovation are age, educational level, ethnicity, sex, education specialization, race, and foreign-born status. The maximum number of distinct groups in any dimension is four, corresponding to each owner in a four-owner firm belonging to a different group. Ownership team size limits the number of distinct groups in any dimension. However, two distinct groups characterize dimensions as binary in the 2018 ABS, namely sex or foreign-born status. Table 1 provides details on the distinct groups in each dimension.The team size axiom is at odds with the assumption that diversity is a function of