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Multiple Inference and Gender Differences in the Effects of Early Intervention: A Reevaluation of the Abecedarian, Perry Preschool, and Early Training Projects
Abstract
The view that the returns to educational investments are highest for early childhood interventions is widely held and stems primarily from several influential randomized trials—Abecedarian, Perry, and the Early Training Project—that point to super-normal returns to early interventions. This article presents a de novo analysis of these experiments, focusing on two core issues that have received limited attention in previous analyses: treatment effect heterogeneity by gender and overrejection of the null hypothesis due to multiple inference. To address the latter issue, a statistical framework that combines summary index tests with familywise error rate and false discovery rate corrections is implemented. The first technique reduces the number of tests conducted; the latter two techniques adjust the p values for multiple inference. The primary finding of the reanalysis is that girls garnered substantial short- and long-term benefits from the interventions, but there were no significant long-term benefits for boys. These conclusions, which have appeared ambiguous when using “naive” estimators that fail to adjust for multiple testing, contribute to a growing literature on the emerging female–male academic achievement gap. They also demonstrate that in complex studies where multiple questions are asked of the same data set, it can be important to declare the family of tests under consideration and to either consolidate measures or report adjusted and unadjusted p values.
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“In the results presented in Extended Data Tables 6 and 7, we also adjusted for the fact that we conducted multiple tests on the same dataset by implementing FDR corrections and report the FDR q values50. We also report the bootstrapped P value51 to account for regressions with a small number of clusters.”
From Last-mile delivery increases vaccine uptake in Sierra Leone (2024) · cites this paper as [50]
In the citing paper
“Finally, we note that our findings are robust to Type I error concerns. 10 We calculate sharpened two-stage q-values in Table 4 (Benjamini et al., 2006b; Anderson, 2008) and the observed impacts remain statistically significant at the 1 percent level.”
From Food Coma is Real: The Effect of Digestive Fatigue on Adolescents' Cognitive Performance (2024) · cites this paper as Anderson, 2008
In the citing paper
“We perform False Discovery Rate (FDR) adjustment using the method described in (77), considering each experiment (Reduced and Increased Exposure) separately and grouping the variables as:”
From Reranking partisan animosity in algorithmic social media feeds alters affective polarization (2025) · cites this paper as [77]
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“The outcomes used to create each index are quite diverse and group a variety of very different outcomes (e.g., crime, employment, education). It is difficult to interpret his indices. Moreover, the components of his indices change with age.”
From Analyzing social experiments as implemented: A reexamination of the evidence from the HighScope Perry Preschool Program (2010) · cites this paper as Anderson (2008)
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High School Majors and Future Earnings
Dahl, G. B., Rooth, D., & Stenberg, A. (2022) · American Economic Journal Applied Economics · doi:10.1257/app.20210292 · Cited by 33
“The findings are further robust to multiple inference adjustments using the False Discovery Rate (FDR) control (see, e.g., Anderson 2008).”
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“Both approaches are increasingly used in economics (Anderson, 2008; Heckman, Moon, Pinto, Savelyev, & Yavitz, 2010; Hoynes, Schanzenbach, & Almond, 2016; Kling, Liebman, & Katz, 2007).”
MethodSpillover Effects of Early-Life Medical Interventions
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Mission Motivation and Public Sector Performance: Experimental Evidence from Pakistan
Khan, M. Y. (2025) · American Economic Review · doi:10.1257/aer.20231247 · Cited by 33
“Since the data are only available for 703 of the 710 workers, I assign the average value of the treatment group to the missing data and use Anderson (2008)’s method to weight each component by the inverse of the variance-covariance matrix to create a summary index of health outcomes.”
InfluentialBoys, Girls, and "Two Cultures" of Child Care
Winer, A. C., & Phillips, D. A. (2012) · Merrill-palmer Quarterly · doi:10.1353/mpq.2012.0004 · Cited by 34
“…that when gender differences in outcomes of child care or early intervention are reported, boys are consistently found to experience more negative consequences and fewer benefits from time spent in these settings (Anderson, 2008; Desai et al., 1989; Howes & Olenick, 1986; Oden et al., 2000).”
BackgroundInfluentialThe Long-Term Effects of Long Terms – Compulsory Schooling Reforms in Sweden
Fischer, M., Karlsson, M., Nilsson, T., & Schwarz, N. (2019) · Journal of the European Economic Association · doi:10.1093/jeea/jvz071 · Cited by 32
Abarcar, P., Barua, R., & Yang, D. (2019) · Economic Development and Cultural Change · doi:10.1086/703045 · Cited by 32
“Ashraf et al. (2015) find in a randomized study among migrants from El Salvador that improving monitoring and control over savings (by providing new types of savings accounts that allowmigrant joint or sole ownership) leads to higher savings in the home country.”
BackgroundElusive Longer-Run Impacts of Head Start: Replications Within and Across Cohorts
Pages, R., Lukes, D. J., Bailey, D. H., & Duncan, G. J. (2020) · Educational Evaluation and Policy Analysis · doi:10.3102/0162373720948884 · Cited by 38
“Finally, consistent with Anderson’s (2008) study of early childhood interventions life”
BackgroundPollution, Ability, and Gender-Specific Investment Responses to Shocks
Molina, T. (2020) · Journal of the European Economic Association · doi:10.1093/jeea/jvaa005 · Cited by 32
“Though this negative cognitive shock affects both men and women, it significantly reduces the probability of high school completion for women only, which is consistent with a number of existing studies that find larger female schooling responses to early-life health shocks or interventions (Bobonis et al., 2006; Maluc…”
ResultExperimental Evidence on the Effectiveness of Nonexperts for Improving Vaccine Demand
Alsan, M. M., & Eichmeyer, S. (2024) · American Economic Journal Economic Policy · doi:10.1257/pol.20210393 · Cited by 32
Aspirations and financial decisions: Experimental evidence from the Philippines
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Blair, R., Curtice, T., Dow, D., & Grossman, G. (2022) · Social Science & Medicine · doi:10.1016/j.socscimed.2022.115045 · Cited by 32
“We measure compliance with a standardized summary index (following Anderson (2008)) comprising seven items, scaled such that larger values indicate greater compliance: 1) number of days spent at home without leaving; 2) number of times attending church or mosque; 3) number of times going to a…”
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Saka, O., Eichengreen, B. J., & Aksoy, C. G. (2022) · Journal of money credit and banking · doi:10.1111/jmcb.12945 · Cited by 32
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Billings, S. B., & Johnson, E. B. (2011) · Journal of Urban Economics · doi:10.1016/j.jue.2011.12.001 · Cited by 32
“Some examples of recent economics papers that adopt FWE corrections include Anderson (2005), Kling et al.”
Can interventions affect commitment demand? A field experiment on food choice
Sadoff, S., & Samek, A. S. (2018) · Journal of Economic Behavior & Organization · doi:10.1016/j.jebo.2018.11.016 · Cited by 32
Lavy, V., Silva, O., & Weinhardt, F. (2009) · National Bureau of Economic Research · doi:10.3386/w15600 · Cited by 32
“However, there is little evidence that these differences are 20 For example, Anderson (2008) shows that three well-known early childhood interventions (namely, Abecedarian, Perry and the Early Training Project) had substantial short- and long-term effects on girls, but no effect on boys.”
Grigorieff, A., Roth, C., & Ubfal, D. J. (2016) · SSRN Electronic Journal · doi:10.2139/ssrn.2768187 · Cited by 35
“32For each family of outcomes, we control for a false discovery rate of 5 percent, i.e. the expected proportion of rejections that are type I errors (Anderson, 2008).”
InfluentialGertler, P., Green, B. S., & Wolfram, C. (2024) · The Quarterly Journal of Economics · doi:10.1093/qje/qjae003 · Cited by 31
In the Eye of the Storm: Hurricanes, Climate Migration, and Climate Attitudes
Arias, S. B., & Blair, C. (2024) · American Political Science Review · doi:10.1017/s0003055424000352 · Cited by 38
“These indices afford several advantages, including mitigating multiple inference concerns (Anderson 2008, 1484).”
Macours, K., Schady, N., & Vakis, R. (2008) · Cited by 31
Policy Deliberation and Voter Persuasion: Experimental Evidence from an Election in the Philippines
López‐Moctezuma, G., Wantchekon, L., Rubenson, D. L., Fujiwara, T., & Lero, C. (2020) · American Journal of Political Science · doi:10.1111/ajps.12566 · Cited by 31
“For the poverty-reducing policy, the survey asks to rank the policy they would like to be implemented the most among a conditional cash transfer program, an anti-corruption policy or an increase in public investment.22 Causal effects are estimated following Anderson (2008).”
BackgroundCarreri, M. (2018) · The Journal of Politics · doi:10.1086/715062 · Cited by 31
Tougher, S., Dutt, V., Pereira, S. K., Haldar, K., Shukla, V., Singh, K., Kumar, P., Goodman, C. A., & Powell‐Jackson, T. (2017) · The Lancet Global Health · doi:10.1016/s2214-109x(17)30454-0 · Cited by 31
Long-Run Effects of Temporary Incentives on Medical Care Productivity
Celhay, P., Gertler, P., Giovagnoli, P., & Vermeersch, C. M. J. (2019) · American Economic Journal Applied Economics · doi:10.1257/app.20170128 · Cited by 30
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Christensen, G., & Miguel, E. A. (2016) · National Bureau of Economic Research · doi:10.3386/w22989 · Cited by 32
Last-mile delivery increases vaccine uptake in Sierra Leone
Meriggi, N. F., Voors, M., Levine, M., Ramakrishna, V., Kangbai, D. M., Rozelle, M., Tyler, E., Kallon, S., Nabieu, J., Cundy, S., et al. (2024) · Nature · doi:10.1038/s41586-024-07158-w · Cited by 36
“31 We also report the bootstrapped p-value 32 to account for regressions with a small number of clusters.”
MethodThe Effects of Promotions on Heart Disease: Evidence from Whitehall
Anderson, M., & Marmot, M. G. (2011) · The Economic Journal · doi:10.1111/j.1468-0297.2011.02472.x · Cited by 31
“Testing a summary index can increase statistical power and correct for multiple inference (Anderson, 2008).”
BackgroundSelf-citationThe health implications of unconventional natural gas development in Pennsylvania
Peng, L., Meyerhoefer, C. D., & Chou, S. (2018) · Health Economics · doi:10.1002/hec.3649 · Cited by 30
Sepsis-Associated 30-Day Risk-Standardized Readmissions: Analysis of a Nationwide Medicare Sample*
Norman, B. C., Cooke, C. R., Ely, E. W., & Graves, J. A. (2017) · Critical Care Medicine · doi:10.1097/ccm.0000000000002476 · Cited by 30
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Gibbons, S., Silva, O., & Weinhardt, F. (2017) · Journal of the European Economic Association · doi:10.1093/jeea/jvw018 · Cited by 30
“…girls respond differently to a number of educational interventions, peer interactions and external circumstances (Cross and Madson 1997; Eagly 1978; Anderson 2008; Lavy et al. 2012), and with evidence suggesting that boys are more negatively affected than girls by neighbourhood changes that might…”
BackgroundAn Experiment in Candidate Selection
Casey, K., Kamara, A. B., & Meriggi, N. F. (2021) · American Economic Review · doi:10.1257/aer.20200125 · Cited by 30
Haas, N., & Khadka, P. (2020) · American Journal of Political Science · doi:10.1111/ajps.12519 · Cited by 30
“MDEs exceed 0.3 for three effects that we report as 12 See for example Mvukiyehe and Samii (2017), who use the Anderson (2008) index presented in this paper, and Matanock, Diaz and Garcia-Sanchez (2018), who conduct an endorsement experiment on peace policies in Colombia.”
MethodInfluentialSelf-help groups, savings and social capital: Evidence from a field experiment in Cambodia
Ban, R., Gilligan, M., & Rieger, M. (2020) · EUR Research Repository (Erasmus University Rotterdam) · doi:10.1016/j.jebo.2020.09.029 · Cited by 30
“Further, we report q-values controlling for the False Discovery Rate (FDR) for each table’s row of estimates as proposed by Anderson (2008) . Finally, each table also shows average, standardized effects following Kling et al. (2004) and Clingingsmith et al. (2009) .”
InfluentialHyperglycemia associated with acute brain injury in neonatal encephalopathy
Tam, E., Kamino, D., Shatil, A. S., Chau, V., Moore, A. M., Brant, R., & Widjaja, E. (2021) · NeuroImage Clinical · doi:10.1016/j.nicl.2021.102835 · Cited by 30
Lohmann, P. M., Gsottbauer, E., You, J., & Kontoleon, A. V. (2020) · Journal of Economic Behavior & Organization · doi:10.1016/j.jebo.2022.12.007 · Cited by 53
Collyer, S. M., Gandhi, J., Garfinkel, I., Ross, S., Waldfogel, J., & Wimer, C. (2022) · Socius Sociological Research for a Dynamic World · doi:10.1177/23780231221141165 · Cited by 31
“To address this possibility, we ran a series of models where we corrected for multiple hypothesis testing by controlling for the false discovery rate and calculating the sharpened q statistics on the basis of the methods outlined by Anderson (2008) (Appendix C, Table C3).”
MethodImproving College Instruction through Incentives
Brownback, A., & Sadoff, S. (2019) · Journal of Political Economy · doi:10.1086/707025 · Cited by 30
“37 The effects of instructor incentives among adjunct instructors are robust to corrections for multiple hypothesis testing using the method described in Anderson (2008).”
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Andrews, R., Jargowsky, P. A., & Kuhne, K. (2012) · National Bureau of Economic Research · doi:10.3386/w18598 · Cited by 30
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“In regression analyses results, we report sharpened False Discovery Rate (FDR) q-values in lieu of p-values to account for multiple hypothesis testing [25].”
MethodStacked linear regression analysis to facilitate testing of hypotheses across OLS regressions
Oberfichtner, M., & Tauchmann, H. (2021) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x211025801 · Cited by 29
“However, independently testing numerous parallel hypotheses without taking multiple-testing issues into account seems to still be common in applied research; see, for instance, the discussions in Anderson (2008) and List, Shaikh, and Xu (2019).”
BackgroundStein, D., Bergemann, R., Lanthorn, H., Kimani, E., Nshakira-Rukundo, E., & Li, Y. (2022) · BMJ Global Health · doi:10.1136/bmjgh-2021-007747 · Cited by 29
“40 We also report results from each index component separately, and related secondary outcomes.”
Jacob, B. A., Pilkauskas, N., Rhodes, E., Richard, K., & Shaefer, H. L. (2022) · National Tax Journal · doi:10.1086/720723 · Cited by 29
“We follow the approach outlined in Anderson (2008) to create composite measures from these individual survey items.”
MethodKindergarten for all: Long run effects of a universal intervention
Drange, N., Havnes, T., & Sandsør, A. M. J. (2016) · Economics of Education Review · doi:10.1016/j.econedurev.2016.04.002 · Cited by 29
“First, girls seem to benefit more than boys, in line with what is often found in the literature on cognitive impact of early childhood interventions (Anderson, 2008).”
ResultPre-registration and Results-Free Review in Observational and Qualitative Research
Jacobs, A. M. (2020) · Cambridge University Press eBooks · doi:10.1017/9781108762519.009 · Cited by 30
The geography of the COVID-19 crisis in England
Davenport, A., Farquharson, C., Imran Rasul, A., Sibieta, L., & Stoye, G. (2020) · doi:10.1920/bn.ifs.2020.bn0294 · Cited by 29
“8 We construct Anderson indices; see Anderson (2008) for details on the methodology.”
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“To address this issue, we used a conservative two-step method proposed by Benjamini et al. (2006) and implemented in Stata by Anderson (2008).”
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“Following Kling et al. (2007), Anderson (2008), and Hoynes et al. (2016), I create indices to aggregate the outcomes for each wave.”
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“In particular, we calculate false discovery rate adjusted “q-values” that limit the expected proportion of rejections within a set of hypotheses that are Type I errors, following Anderson (2008).”
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“…message, and DG with both labor and self-efficacy messages in Panels B and D. Standard errors are clustered at the village level with p-values reported in parentheses and False Discovery Rate p-values (Anderson, 2008), which correct for multiple hypothesis testing (MHT), are reported in brackets.”
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Gender differences in the skill content of jobs
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“…literacy at work combines the indices for reading skills at work and writing skills at work into one measurement using the methodology developed by Anderson (2008) **Information and communication technologies numeracy skill use index can be computed for any respondent who answers at least one of…”
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Short-Term Impacts of a Pay-it-Forward Livestock Transfer and Training Program in Nepal
Janzen, S., Magnan, N., Sharma, S., & Thompson, W. M. (2018) · AEA Papers and Proceedings · doi:10.1257/pandp.20181120 · Cited by 27
“Where no obvious standard index exists in the literature (asset ownership, financial inclusion, physical health, and mental health), we employ Anderson (2008) to create a standardized weighted average of subindicators.”
InfluentialThe Medium-Term Impacts of High-Achieving Charter Schools on Non-Test Score Outcomes
Dobbie, W., & Fryer, R. G. (2013) · National Bureau of Economic Research · doi:10.3386/w19581 · Cited by 27
“alternative mechanisms: (1) non-cognitive skills, (2) social networks, and (3) economic preference parameters.”
InfluentialReducing Crime and Violence: Experimental Evidence on Adult Noncognitive Investments in Liberia
Blattman, C., Jamison, J. C., & Sheridan, M. (2016) · doi:10.1596/1813-9450-7648 · Cited by 27
“Anderson, M. L. (2008). Multiple inference and gender differences in the effects of early intervention: A reevaluation of the Abecedarian, Perry Preschool, and Early Training Projects.”
InfluentialCohen, J., Pascaline Dupas, Y., & Schaner, S. G. (2012) · National Bureau of Economic Research · doi:10.3386/w17943 · Cited by 27
(Successful) Democracies Breed Their Own Support
Acemoğlu, D., Ajzenman, N., Aksoy, C. G., Fiszbein, M., & Molina, C. (2021) · National Bureau of Economic Research · doi:10.3386/w29167 · Cited by 31
“It reports the proportion of variables that are statistically significant using the sharpened False Discovery Rate (FDR) q-values, which follows Anderson (2008) and takes into account the expected fraction of type I errors (for reference, we also report the proportion of variables that are…”
MethodNordic Council of Ministers (2012) · doi:10.6027/tn2012-544 · Cited by 29
On the Persistence of the China ShockPreprint
Autor, D., Dorn, D., & Hanson, G. (2022) · SSRN Electronic Journal · doi:10.2139/ssrn.4114342 · Cited by 28
Pollakowski, H. O., Weinberg, D. H., Andersson, F. W., Haltiwanger, J., Palloni, G. E., & Kutzbach, M. (2022) · American Economic Journal Economic Policy · doi:10.1257/pol.20180144 · Cited by 27
“The false discovery rate controls for the expected proportion of rejections of the null hypothesis that are actually false (see Anderson 2008).”
BackgroundIntrahousehold preference heterogeneity and demand for labor‐saving agricultural technology
Gulati, K., Ward, P. S., Lybbert, T. J., & Spielman, D. J. (2023) · American Journal of Agricultural Economics · doi:10.1111/ajae.12430 · Cited by 26
“The cost of family labor is not included. c Bargaining power index is constructed using a generalized weighting procedure employed in Anderson (2008) and measures the difference in power between men and women as captured by differences between their age, education, the amount of credit they could…”
MethodDube, O., MacArthur, S. J., & Shah, A. (2024) · The Quarterly Journal of Economics · doi:10.1093/qje/qjae039 · Cited by 32
Leonelli, S., Muhn, M., Rauter, T., & Sran, G. S. (2025) · Journal of Accounting and Economics · doi:10.1016/j.jacceco.2025.101811 · Cited by 37
Venkataramani, A. S., Cook, E. E., O’Brien, R., Kawachi, I. I., Jena, A. B., & Tsai, A. C. (2019) · PLoS Medicine · doi:10.1371/journal.pmed.1002821 · Cited by 28
Nakajima, N., Jung, H., Pradhan, M., Hasan, A., Kinnell, A., & Brinkman, S. A. (2019) · Developmental Science · doi:10.1111/desc.12931 · Cited by 26
“…© 2019 The World Bank Developmental Science © 2019 John Wiley & Sons Ltd 1 | INTRODUC TION Research has shown that gender differences in educational achievement emerge in the early years of school (Cobb-Clark & Moschion, 2017) and can persist into adulthood (Anderson, 2008).”
BackgroundUsing household grants to benchmark the cost effectiveness of a USAID workforce readiness program
McIntosh, C., & Zeitlin, A. D. (2022) · Journal of Development Economics · doi:10.1016/j.jdeveco.2022.102875 · Cited by 29
Metadata
- Authors
- Anderson, M. L.
- Affiliations
- University of California, Berkeley (US)
- Corresponding author
- Anderson, Michael L.
- ORCID
- Anderson, Michael L.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2008-12-01
- Volume
- 103
- Issue
- 484
- Pages
- 1481-1495
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2099805722
- Cited by
- 2,410
- References
- 37
- Citations by year
- 2026: 210 · 2025: 258 · 2024: 262 · 2023: 266 · 2022: 258 · 2021: 240 · 2020: 187 · 2019: 147 · 2018: 117 · 2017: 85 · 2016: 93 · 2015: 65 · 2014: 47 · 2013: 68 · 2012: 37
- FWCI
- 99.90
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of the American Statistical Association (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- eScholarship (California Digital Library) (submittedVersion)
- Topics
- Social Sciences › Education › Early Childhood Education and Development
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- gender differences, early childhood intervention, Abecedarian Project, treatment effect heterogeneity, family-wise error rate, false discovery rate, returns to education
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