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Standard Errors and Sample Sizes for Two-Level Research
Open accessAbstract
The hierarchical linear model approach to a two-level design is considered, some variables at the lower level having fixed and others having random regression coefficients. An approximation is derived to the covariance matrix of the estimators of the fixed regression coefficients (for variables at the lower and the higher level) under the assumption that the sample sizes at either level are large enough. This covariance matrix is expressed as a function of parameters occurring in the model. If a research planner can make a reasonable guess as to these parameters, this approximation can be used as a guide to the choice of sample sizes at either level.
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“Post hoc power analyses using the multilevel power analysis program PinT (Snijders & Bosker, 1993) confirmed that we had sufficient power (>.80) to detect a mediated pathway comprising paths that were of medium effect sizes and to detect a medium effect size for treatment condition as a moderator of the mediated pathways.”
From Respiratory and cognitive mediators of treatment change in panic disorder: Evidence for intervention specificity. (2010) · cites this paper as Snijders & Bosker, 1993
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In the citing paper
“Tyrer et al reported that brief CBT is no more effective than usual care when it comes to preventing repetition of self-harm, 15”
From Cognitive-behavioural intervention for self-harm: Randomised controlled trial (2008) · cites this paper as [15]
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“Furthermore, this study's findings that time-limited CBT decreases self-harm contrasts with the results reported by Tyrer et al . 15”
From Cognitive-behavioural intervention for self-harm: Randomised controlled trial (2008) · cites this paper as [15]
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Gullo, G. L., & Beachum, F. D. (2020) · Teachers College Record The Voice of Scholarship in Education · doi:10.1177/016146812012200309 · Cited by 31
“Most tools typically used in evaluating the power of multilevel models require equal cluster sizes (Snijders & Bosker, 1993), which were not possible in the current study.”
MethodAcute ingestion of beetroot juice increases exhaled nitric oxide in healthy individuals
Kroll, J. L., Werchan, C. A., Rosenfield, D., & Ritz, T. (2018) · PLoS ONE · doi:10.1371/journal.pone.0191030 · Cited by 28
Application of the hierarchical bootstrap to multi-level data in neuroscience
Saravanan, V., Berman, G. J., & Sober, S. J. (2020) · arXiv · doi:10.48550/arxiv.2007.07797 · Cited by 26
“Given the relationship between the number of points within a cluster to the Design Effect (DEFF; seeDesign Effect inMaterials andMethods), we would expect the false positive rate to increase with the number of neurons per subject in the traditional analysis but not using the other methods [30, 36, 1].”
BackgroundMethodRobertson, S. M. C., Short, S. D., Sawyer, L. E., & Sweazy, S. (2020) · Psychology and Health · doi:10.1080/08870446.2020.1827146 · Cited by 32
“The number of level-2 units particularly influence the power to detect effects in multilevel models (Lane & Hennes, 2018; Snijders & Bosker, 1993).”
BackgroundXie, M., & Baumer, E. P. (2018) · Criminology · doi:10.1111/1745-9125.12172 · Cited by 25
ML-DEs: A program for designing efficient multilevel studies
Cools, W., Noortgate, W. V. D., & Onghena, P. (2008) · Behavior Research Methods · doi:10.3758/brm.40.1.236 · Cited by 24
Variance decomposition of the country, industry, firm, and firm-year effects on dividend policy
Erkan-Barlow, A., Fainshmidt, S., & Judge, W. Q. (2016) · International Business Review · doi:10.1016/j.ibusrev.2016.04.003 · Cited by 24
Multilevel models in health outcomes research
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Krull, J. L. (2007) · Developmental Psychology · doi:10.1037/0012-1649.43.3.602 · Cited by 24
Cervical Spine Motion during Transfer and Stabilization Techniques
Shrier, I., Boissy, P., Lebel, K., Boulay, J., Segal, E., Delaney, J. S., Vacon, L. C., & Steele, R. J. (2014) · Prehospital Emergency Care · doi:10.3109/10903127.2014.936634 · Cited by 23
A fluctuating sense of power is associated with reduced well-being
Anicich, E. M., Schaerer, M., Gale, J., & Foulk, T. A. (2020) · Journal of Experimental Social Psychology · doi:10.1016/j.jesp.2020.104057 · Cited by 27
“A post-hoc power calculation using Power in Two Levels (Snijders, 2005; Snijders & Bosker, 1993) based on a multi-level regression model and an achieved effect size of f2 = 0.13 (95% significance level) suggests the achieved statistical power was 98.6%.”
MethodInfluentialMastagli, M., Hoye, A. V., Hainaut, J.-P., & Bolmont, B. (2021) · Journal of Teaching in Physical Education · doi:10.1123/jtpe.2020-0252 · Cited by 34
Nicolas, M., Martinent, G., Palinkas, L., & Suedfeld, P. (2022) · Journal of Environmental Psychology · doi:10.1016/j.jenvp.2022.101853 · Cited by 23
Sample Size Considerations for Multilevel Surveys
Cohen, M. P. (2006) · International Statistical Review · doi:10.1111/j.1751-5823.2005.tb00149.x · Cited by 23
“A key paper is Snijders and Bosker (1993).”
BackgroundSelf-Referential Processing Predicts Social Cognitive Ability
Dinulescu, S., Alvi, T., Rosenfield, D., Sunahara, C. S., Lee, J., & Tabak, B. A. (2020) · Social Psychological and Personality Science · doi:10.1177/1948550620902281 · Cited by 30
“…we conducted a post hoc power analysis using the multilevel modeling (MLM) power analysis program PinT Version 2.12 (power in two-level models; Snijders & Bosker, 1993), which indicated that we had >.80 power to detect a small effect size (d¼ .20) for the effect of individual characteristics…”
MethodInfluentialMultilevel Modeling in Psychosomatic Medicine Research
Myers, N. D., Brincks, A. M., Ames, A. J., Prado, G. J., Penedo, F. J., & Benedict, C. (2012) · Psychosomatic Medicine · doi:10.1097/psy.0b013e3182736971 · Cited by 22
Meng, J., Fulk, J. L., & Yuan, Y. C. (2013) · Communication Research · doi:10.1177/0093650213476294 · Cited by 22
“First, we used the software PinT (Snijders & Bosker, 1993) to estimate standard errors, and then we employed the formula2 to calculate the actual power using the estimated standard error (Snijders, 2005).”
MethodPathak, S., Xavier-Oliveira, E., & Laplume, A. O. (2015) · The Journal of Technology Transfer · doi:10.1007/s10961-015-9423-x · Cited by 22
“…entrepreneurship across countries in general and on technology use in particular, our multi-level study involving just 20 countries poses limitations on the number of higher-level (country-level institutions in our case) predictors that could be used (Mass and Hox 2005; Snijders and Bosker 1993).”
Zhang, H., Chen, K., & Schlegel, R. J. (2018) · Personality and Social Psychology Bulletin · doi:10.1177/0146167218771330 · Cited by 25
“Yet, post hoc power analyses using the software PinT (Snijders & Bosker, 1993) for Studies 1 to 4 and G*Power (Faul, Erdfelder, Lang, & Buchner, 2007) for Study 5 indicated that power to detect the interaction between self-concordance and perceived performance in all the studies was above .80.”
MethodEarly exposure to neighborhood crime and child internalizing and externalizing behaviors
Ramey, D. M., & Harrington, N. (2019) · Health & Place · doi:10.1016/j.healthplace.2019.04.010 · Cited by 22
Longitudinal emotional process among adolescent soccer player in intensive training centre
Saby, Y., Pupier, Y., Guillet‐Descas, E., Nicolas, M., & Martinent, G. (2019) · Journal of Sports Sciences · doi:10.1080/02640414.2019.1662538 · Cited by 28
“A power analysis was performed in using the Power IN Two-level designs software (Snijders & Bosker, 1993).”
MethodCece, V., Duchesne, M., Guillet‐Descas, E., & Martinent, G. (2020) · European Journal of Sport Science · doi:10.1080/17461391.2019.1709562 · Cited by 21
Increases in Exhaled Nitric Oxide After Acute Stress
Ritz, T., Trueba, A. F., Simon, E., & Auchus, R. J. (2014) · Psychosomatic Medicine · doi:10.1097/psy.0000000000000118 · Cited by 21
“Using published standards (51) and the program Power in Two-Level Models (PinT) (52), it can be determined that we had more than 0.”
MethodBiobehavioral Factors in Child Health Outcomes
Clowtis, L., Kang, D.-H., Padhye, N. S., Rozmus, C., & Barratt, M. S. (2016) · Nursing Research · doi:10.1097/nnr.0000000000000172 · Cited by 21
“A Copyright © 2016 Wolters Kluwer H reported correlation of .35 in biological responses (sCORT) between mother and child was used to calculate a design effect of 1.35 (Ruttle et al., 2011; Snijders & Bosker, 1993), resulting in a needed sample size of 46 dyads.”
MethodInfluentialBotchkovar, E. V., Antonaccio, O., & Hughes, L. A. (2017) · The British Journal of Criminology · doi:10.1093/bjc/azx023 · Cited by 22
Flouri, E., Midouhas, E., Ruddy, A., & Moulton, V. (2017) · European Child & Adolescent Psychiatry · doi:10.1007/s00787-017-0940-z · Cited by 21
“We fitted growth curve models [40] to examine the direct ‘effect’ of socio-economic disadvantage, and its mediation via parenting and the home environment, on the level and development of ADHD children’s comorbid emotional and conduct problems at ages 3–11 years.”
MethodLafit, G., Adolf, J., Dejonckheere, E., Myin‐Germeys, I., Viechtbauer, W., & Ceulemans, E. (2020) · PsyArXiv (OSF Preprints) · doi:10.31234/osf.io/dq6ky · Cited by 25
Huhtala, M., Kaptein, M., Muotka, J. S., & Feldt, T. (2021) · Journal of Business Ethics · doi:10.1007/s10551-021-04744-0 · Cited by 20
Cross-classified models in I/O psychology
Claus, A. M., Arend, M. G., Burk, C. L., Kiefer, C., & Wiese, B. S. (2020) · Journal of Vocational Behavior · doi:10.1016/j.jvb.2020.103447 · Cited by 22
Hart, T. M., Berninger, V. M., & Abbott, R. D. (1997) · School Psychology Review · doi:10.1080/02796015.1997.12085866 · Cited by 20
Arch, J. J., Mitchell, J. L., Genung, S. R., Fisher, R., Andorsky, D. J., & Stanton, A. L. (2019) · BMC Cancer · doi:10.1186/s12885-019-5289-x · Cited by 20
“To estimate power for the hypothesized effects and to allow for the possibility of missing data in that estimation, we took a multi-faceted approach involving both existing software for power calculation in longitudinal multilevel linear modeling (PINT; [97, 98]) as well as a cutting-edge simulation approach (see [99,…”
MethodGray, B. R. (2012) · Cambridge University Press eBooks · doi:10.1017/cbo9781139022422.013 · Cited by 19
Ollier, J., Suryapalli, P., Fleisch, E., von Wangenheim, F., Mair, J. L., Salamanca-Sanabria, A., & Kowatsch, T. (2023) · Frontiers in Public Health · doi:10.3389/fpubh.2023.1185702 · Cited by 20
Gutiérrez, G., & Vanderwood, M. L. (2013) · School Psychology Review · doi:10.1080/02796015.2013.12087488 · Cited by 19
“Level 3 analyses were not conducted to assess the nested structure of measures within students within classrooms (or teachers) because the limited number of school sites would not have offered sufficient power to find reliable effects (Snidjers & Bosker, 1993).”
BackgroundDistress Tolerance as a Predictor of Adherence to a Yoga Intervention
Baird, S. O., Hopkins, L. B., Medina, J. L., Rosenfield, D., Powers, M. B., & Smits, J. A. J. (2015) · Behavior Modification · doi:10.1177/0145445515612401 · Cited by 20
“Post hoc power analyses, using the MLM power analysis program PinT 2.12 (Snijders & Bosker, 1993) indicated that we had greater than 0.80 power to detect a large effect size (d ≥ 0.80).”
MethodInfluentialApportioning Variation in Multilevel Models
Leyland, A. H., & Groenewegen, P. (2020) · Springer eBooks · doi:10.1007/978-3-030-34801-4_6 · Cited by 19
Priming Prepositional Phrase Attachment: Evidence from Eye-Tracking and Event-Related Potentials
Boudewyn, M. A., Zirnstein, M., Swaab, T. Y., & Traxler, M. J. (2013) · Quarterly Journal of Experimental Psychology · doi:10.1080/17470218.2013.815237 · Cited by 19
“Unlike repeated measures analysis of variance (ANOVA), HLM does not require that individuals have the same number of observations (Snijders & Bosker, 1993), and it does not require aggregation across trials.”
MethodSheinfil, A. Z., Foley, J. D., Moskal, D., Dalton, M. R., Firkey, M. K., Ramos, J. M., Maisto, S. A., & Woolf‐King, S. E. (2022) · AIDS and Behavior · doi:10.1007/s10461-022-03657-x · Cited by 18
Heatly, M. C., Bachman, H. J., & Votruba‐Drzal, E. (2015) · Journal of Applied Developmental Psychology · doi:10.1016/j.appdev.2015.06.002 · Cited by 18
Korendijk, E. J. H., Moerbeek, M., & Maas, C. J. M. (2010) · Journal of Educational and Behavioral Statistics · doi:10.3102/1076998609360774 · Cited by 18
“…number of subjects per cluster m can be derived from Equations 3 and 4 (e.g., Moerbeek, Van Breukelen, Berger, & Ausems, 2003; Raudenbush, 1997; Snijders & Bosker, 1993): m ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Cc 1 rð Þ Csr s _ ð5Þ Formula 5 shows that the cluster…”
BackgroundWhat Predicts Recovery Orientation in County Departments of Mental Health? A Pilot Study
Brown, T. T., Mahoney, C. B., Adams, N. H., Felton, M., & Pareja, C. (2009) · Administration and Policy in Mental Health and Mental Health Services Research · doi:10.1007/s10488-009-0253-8 · Cited by 18
Mortimer, J. T., Mont’Alvão, A., & Aronson, P. (2019) · Social Forces · doi:10.1093/sf/soz130 · Cited by 20
“…at least fifty groups with five observations per group provides sufficient power for fixed-effects models, other studies indicate that a large number of groups matter more for coefficient accuracy and statistical power than the number of individuals per group (Cohen 1998; Snijders and Bosker 1993).”
BackgroundWhite, C. A., Slater, M. J., Turner, M. J., & Barker, J. B. (2020) · British Journal of Social Psychology · doi:10.1111/bjso.12385 · Cited by 21
“Future researchers should aim to recruit a balanced distribution of participants across the RAF bases (Snijders & Bosker, 1993).”
BackgroundCece, V., Guillet‐Descas, E., Brenas, M., & Martinent, G. (2020) · European Journal of Sport Science · doi:10.1080/17461391.2020.1862304 · Cited by 22
“A priori power analysis was performed using Power IN Two-level designs software to estimate standard errors of regression coefficients in HLM for power calculations (Snijders & Bosker, 1993).”
MethodSweating the big stuff: Arousal and stress as functions of self‐uncertainty and identification
Brown, J. K., Hohman, Z. P., Niedbala, E. M., & Stinnett, A. J. (2021) · Psychophysiology · doi:10.1111/psyp.13836 · Cited by 18
“…are more robust to issues that reduce power in traditional ANOVA techniques (e.g., missing variables, nonindependent variables, heteroscedasticity; see Singer, 1998; Snijders & Bosker, 1993); thus, multilevel models are as effective, if not more so, at detecting hypothesized effects than ANOVA.”
BackgroundMethodInfluentialWho's to blame? The role of power and attributions in susceptibility to match-fixing
O’Shea, D. E., Barkoukis, V., McIntyre, T., Loukovitis, A., Gomez, C., Moritzer, S., Michaelides, M. P., & Theodorou, N. C. (2021) · Psychology of sport and exercise · doi:10.1016/j.psychsport.2021.101955 · Cited by 18
“…not have an option to assess the power for multi-level structures, we also drew on the guidelines for examining power and sample size in multi-level modelling by Snijders (Snijders, 2005; Snijders & Bosker, 2012) and the software programme PINT (Power IN Two-level designs; Snijders & Bosker, 1993).”
MethodCross-National Differences in Managers’ Creativity Promoting Values
Hoegl, M., Parboteeah, K. P., & Muethel, M. (2012) · Management International Review · doi:10.1007/s11575-011-0114-z · Cited by 18
Power and Sample Size in Multilevel Linear Models
Snijders, T. A. B. (2014) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat06584 · Cited by 18
Self-citationRearte, R., Corva, S. G., de la Sota, R. L., Lacau-Mengido, I. M., & Giuliodori, M. J. (2022) · Journal of Dairy Science · doi:10.3168/jds.2021-21504 · Cited by 17
The Los Angeles Family and Neighborhood Survey
Pebley, A. R., & Sastry, N. (2004) · Cited by 17
The Form and Function of Attachment Behavior in the Daily Lives of Young Adults
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Murayama, K., Usami, S., & Sakaki, M. (2020) · doi:10.31219/osf.io/6cer3 · Cited by 17
Usami, S. (2014) · Behavior Research Methods · doi:10.3758/s13428-013-0432-0 · Cited by 16
Day-to-day variability of post-concussion-like symptoms reported over time by a non-concussed cohort
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“It is difficult to do power calculations where repeated measurements (seven occasions) are nested within each individual [28].”
BackgroundBarker, D., Rancourt, D., & Jelalian, E. (2013) · Journal of Pediatric Psychology · doi:10.1093/jpepsy/jst082 · Cited by 16
“There are some off-the-shelf power calculators that can handle structural equation and growth models (e.g., Optimal Design: Raudenbush et al., 2011; PinT: Snijders & Bosker, 1993).”
BackgroundPadovano, H. T., Janssen, T., Sokolovsky, A. W., & Jackson, K. M. (2020) · Psychological Science · doi:10.1177/0956797620959006 · Cited by 18
“The power analyses were conducted using the Power in Two-Level Designs (PINT) program (Snijders & Bosker, 1993) to estimate power for multilevel models predicting alcohol use from two withinperson (random) variables and two fixed variables.”
MethodMultilevel design efficiency in educational effectiveness research
Cools, W., Fraine, B. D., Noortgate, W. V. D., & Onghena, P. (2009) · School Effectiveness and School Improvement · doi:10.1080/09243450902850176 · Cited by 16
“For models with varying slopes, in general, large sample approximations for the standard errors of the regression coefficients in two-level models have been derived as a function of cluster sizes (Snijders & Bosker, 1993 ).”
BackgroundMethodInfluentialGanesha, H. R., & Aithal, P. S. (2022) · International Journal of Applied Engineering and Management Letters · doi:10.47992/ijaeml.2581.7000.0159 · Cited by 15
Auswertung von Längsschnittdaten mit hierarchisch-linearen Modellen
Göllner, R., Gollwitzer, M., Heider, J., Zaby, A., & Schröder, A. (2010) · Zeitschrift für Klinische Psychologie und Psychotherapie · doi:10.1026/1616-3443/a000032 · Cited by 15
Wilson, D. T., Hooper, R., Brown, J., Farrin, A. J., & Walwyn, R. E. (2020) · Statistical Methods in Medical Research · doi:10.1177/0962280220975790 · Cited by 15
“Alternatively, a function that specifies the cost of sampling at the cluster and the patient level could be specified,(46) and the overall cost could be minimised.(47) The latter approach has been suggested for both two-level(48) and three-level hierarchical trial designs.”
BackgroundCece, V., Guillet‐Descas, E., Tessier, D. P., & Martinent, G. (2021) · Journal of Applied Sport Psychology · doi:10.1080/10413200.2021.1941425 · Cited by 18
“Power IN Two-level design software was used to perform a priori power analysis which is designed to estimate standard errors of regression coefficients in hierarchical linear models for power calculations (Snijders & Bosker, 1993) .”
MethodDesign efficiency for imbalanced multilevel data
Cools, W., Noortgate, W. V. D., & Onghena, P. (2009) · Behavior Research Methods · doi:10.3758/brm.41.1.192 · Cited by 15
Does Excluding Some Groups From Research Designs Improve Statistical Power?
Biemann, T., & Heidemeier, H. (2012) · Small Group Research · doi:10.1177/1046496412443088 · Cited by 15
“…focuses on higher level measures, such as group outcomes (for comparable analyses in multilevel designs with outcome measures at the individual level, see, for example, Raudenbush & Liu, 2000; Scherbaum & Ferreter, 2009; Snijders & Bosker, 1993; see also Murray, 1998, for group-randomized trials).”
BackgroundBrocklehurst, P. R., Tickle, M., Birch, S., McDonald, R., Walsh, T., Goodwin, T. L., Hill, H. R., Howarth, E., Donaldson, M., O’Carolan, D., et al. (2020) · Health Services and Delivery Research · doi:10.3310/hsdr08060 · Cited by 15
ESTIMATING TREND PRECISION AND POWER TO DETECT TRENDS ACROSS GROUPED COUNT DATA
Gray, B. R., & Burlew, M. (2007) · Ecology · doi:10.1890/06-1714.1 · Cited by 15
Pété, É., Goisbault, M., Martinent, G., & Doron, J. (2023) · Sport Exercise and Performance Psychology · doi:10.1037/spy0000323 · Cited by 14
The statistical power to detect cross‐scale interactions at macroscales
Wagner, T., Fergus, C. E., Stow, C. A., Cheruvelil, K. S., & Soranno, P. A. (2016) · Ecosphere · doi:10.1002/ecs2.1417 · Cited by 14
“Although factors affecting the statistical power of hierarchical models generally (Scherbaum and Ferreter 2009) and specifically related to detecting CSIs (Snijders and Bosker 1993, Mathieu et al. 2012) have been studied, these investigations have not been in ecological disciplines.”
BackgroundSpybrook, J. K., Hedges, L. V., & Borenstein, M. (2014) · Journal of Research on Educational Effectiveness · doi:10.1080/19345747.2013.848963 · Cited by 14
Tanjasiri, S. P., Weiss, J. W., Santos, L. S., Flores, P., Flores, P., Lacsamana, J. D., Paige, C., Mouttapa, M., Quitugua, L., Taito, P., et al. (2015) · Progress in community health partnerships · doi:10.1353/cpr.2015.0067 · Cited by 14
Stein, A. T., Medina, J. L., Rosenfield, D., Otto, M. W., & Smits, J. A. J. (2018) · Cognitive Behaviour Therapy · doi:10.1080/16506073.2018.1546768 · Cited by 14
“We used the MLM power analysis program PinT 2.12 (Power in Two-Level Models, Snijders & Bosker, 1993) to calculate the power to detect significance for the paths in our mediation models.”
MethodInfluentialMultilevel models in health outcomes research
Lake, E. T. (2006) · Applied Nursing Research · doi:10.1016/j.apnr.2005.10.002 · Cited by 14
ON OPTIMIZING MULTI-LEVEL DESIGNS: POWER UNDER BUDGET CONSTRAINTS
Headrick, T. C., & Zumbo, B. D. (2005) · Australian & New Zealand Journal of Statistics · doi:10.1111/j.1467-842x.2005.00386.x · Cited by 14
“…been a topic of discussion (e.g. Deming, 1953; Brooks, 1955; Overall & Dalal, 1965; Cochran, 1977; Hsieh, 1988; Donner, Brown & Brasher, 1990; Muller et al., 1992; Marcoulides, 1993; Snijders & Bosker, 1993; Raudenbush, 1997; Moerbeek, van Breukelen & Berger, 2000, 2001; Headrick & Zumbo, 2001).”
Latent growth curve analysis with dichotomous items: Comparing four approaches
Ye, F. (2015) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/bmsp.12058 · Cited by 13
Avoiding Boundary Estimates in Linear Mixed Models Through Weakly Informative Priors
Chung, Y., Rabe‐Hesketh, S., Gelman, A., Liu, J., & Dorie, V. (2012) · Collection of Biostatistics Research Archive · Cited by 13
Wang, A. W.-T., Chang, C., & Hsu, W. (2020) · Annals of Behavioral Medicine · doi:10.1093/abm/kaaa060 · Cited by 13
Gardner‐Neblett, N., Marco, A. D., & Sexton, S. (2020) · Early Education and Development · doi:10.1080/10409289.2020.1823769 · Cited by 13
“Nested sources of variability could not be tested given that at least 10 participants per unit is recommended for multilevel modeling (Snijders & Bosker, 1993).”
BackgroundEmotional intelligence training program for adolescents involved in intensive training centers
Cece, V., Guillet‐Descas, E., Nicolas, M., Saby, Y., & Martinent, G. (2023) · Journal of Applied Sport Psychology · doi:10.1080/10413200.2023.2176565 · Cited by 23
“The a priori power analysis was performed using Power IN Two-level designs software which is designed to estimate standard errors of regression coefficients in hierarchical linear models for power calculations (Snijders & Bosker, 1993).”
MethodStatistical techniques for juror and jury research
Wright, D. F. B., Strubler, K., & Vallano, J. (2011) · Legal and Criminological Psychology · doi:10.1348/135532510x487655 · Cited by 15
When at-risk teens are violent toward romantic partners: The role of common stressors.
Rosenfield, D., Jouriles, E. N., Mueller, V., & McDonald, R. (2012) · Psychology of Violence · doi:10.1037/a0031029 · Cited by 13
Not in the Mood? Affective State and Transactive Communication
Neff, J. J., Fulk, J. L., & Yuan, Y. C. (2014) · Journal of Communication · doi:10.1111/jcom.12109 · Cited by 13
Schlier, B., Hennig, T., & Lincoln, T. M. (2017) · Psychiatry Research · doi:10.1016/j.psychres.2017.03.051 · Cited by 13
Łaszkiewicz, E. (2013) · DOAJ (DOAJ: Directory of Open Access Journals) · Cited by 12
Thébault, J.-L., Hector Falcoff, C., Favre, M., Noël, F., & Rigal, L. (2015) · BMC Health Services Research · doi:10.1186/s12913-015-0767-6 · Cited by 12
“Patients generally underestimate their consumptions during questionnaire surveys [24].”
BackgroundZhang, J., Liu, J., Wang, X., & Zou, A. (2017) · International Journal of Offender Therapy and Comparative Criminology · doi:10.1177/0306624x17720182 · Cited by 12
“…power analyses for multilevel models demonstrates that the sample size of Level 2 units has a significant impact on the accuracy of the estimator (Snijders & Bosker, 1993), and Level 2 variations diminish rapidly when the average number of Level 1 units exceeds 10 (Cohen, 1998; Hoffmann &…”
BackgroundWilson, D., Hooper, R., Brown, J., Farrin, A., & Walwyn, R. (2020) · White Rose Research Online (University of Leeds, The University of Sheffield, University of York) · Cited by 12
Predictors of domestically violent men's aggression toward children: A prospective study.
McDonald, R., Jouriles, E. N., Rosenfield, D., & Corbitt‐Shindler, D. (2011) · Journal of Family Psychology · doi:10.1037/a0022449 · Cited by 12
“Using the program Power in Two-Level Models (Snijders & Bosker, 1993), analyses revealed power ≥ .80 to detect an effect ≥ d = .”
MethodPower for T-Test Comparisons of Unbalanced Cluster Exposure Studies
Hoover, D. R. (2002) · Journal of Heredity · doi:10.1093/jurban/79.2.278 · Cited by 12
The Sampling Ratio in Multilevel Structural Equation Models: Considerations to Inform Study Design
Kush, J. M., Konold, T. R., & Bradshaw, C. P. (2021) · Educational and Psychological Measurement · doi:10.1177/00131644211020112 · Cited by 11
“Further analyses indicated RMSE nearly perfectly matched the parameter standard error (r = 0.997), where RMSE values were a function of the L1 sample size (Snijders & Bosker, 1993).”
BackgroundMethodInfluentialColin, C. R., Woodcock, L., Wright, L. Y., Jimenez, E. Y., & Papoutsakis, C. (2023) · Journal of the Academy of Nutrition and Dietetics · doi:10.1016/j.jand.2023.01.002 · Cited by 11
Adaptiveness of emotion regulation flexibility according to long-term implications.
Pruessner, L., & Ortner, C. (2025) · Journal of Affective Disorders · doi:10.1016/j.jad.2025.02.114 · Cited by 13
Specification Search for Identifying the Correct Mean Trajectory in Polynomial Latent Growth Models
Kim, M., Kwok, O., Yoon, M., Willson, V. L., & Lai, M. H. C. (2015) · The Journal of Experimental Education · doi:10.1080/00220973.2014.984831 · Cited by 11
“The residual variances of the measurement waves (i.e., θδ) were all set as 1.00 for both ID and AR(1) structures, which was a common practice in power analysis (Bosker, Snijders, & Guldemond, 2003; Snijders & Bosker, 1993).”
MethodInfluentialIntroduction to Hierarchical Modeling
Degenholtz, H. B., & Bhatnagar, M. (2009) · Journal of Palliative Medicine · doi:10.1089/jpm.2009.9595 · Cited by 11
Elite swimmers’ internal markers trajectories in ecological training conditions
Vacher, P., Martinent, G., Mourot, L., & Nicolas, M. (2018) · Scandinavian Journal of Medicine and Science in Sports · doi:10.1111/sms.13200 · Cited by 11
Heinrichs, N., Kliem, S., & Hahlweg, K. (2017) · Prevention Science · doi:10.1007/s11121-017-0782-4 · Cited by 11
Joo, S., Wang, Y. Q., Ferron, J. M., Beretvas, S. N., Moeyaert, M., & Noortgate, W. V. D. (2021) · Journal of Educational and Behavioral Statistics · doi:10.3102/10769986211035507 · Cited by 10
“…variable is a level-1 variable (i.e., a variable that varies within participants), we expect the asymptotic order of magnitude of the error variance of ĉ W IPD would be inversely related to the total sample size based on the analytic work on mixed linear models of Snijders and Bosker (1993).”
MethodAhmad, B., Ryan, V., Maziak, W., Pless‐Mulloli, T., & White, M. J. (2013) · BMC Public Health · doi:10.1186/1471-2458-13-233 · Cited by 10
“A further limitation of this study is the low statistical power to estimate between neighbourhood variation, mainly as a result of the small number of individuals available within a high proportion of the neighbourhoods [31,38,39].”
BackgroundZhao, Y., & Edland, S. D. (2021) · The International Journal of Biostatistics · doi:10.1515/ijb-2020-0107 · Cited by 10
“Under this assumption, it can be shown (Appendix A) that [(XiV−1 i Xi)]22 = (σ(2)b1 + σ(2)ε/∑(tj − t)2) [8], and Eq.”
Cooper, A. B., Rosenberg, A. A., Stefánsson, G., & Mangel, M. (2004) · Fisheries Research · doi:10.1016/j.fishres.2004.08.006 · Cited by 10
“…on sample size and power calculations for mixed-effects models focuses on the fixed-effects terms, and not on the power of detecting random effects, and is limited to traditional clinical trials study designs (e.g. Snijders and Bosker, 1993; Diggle et al., 1994; Raudenbush and Liu, 2000, 2001).”
BackgroundThe validity of value-added measures in secondary schools
Scherman, V. (2007) · UpSpace Institutional Repository (University of Pretoria) · Cited by 10
Metadata
- Authors
- Snijders, T. A. B., & Bosker, R. J.
- Affiliations
- University of Groningen (NL)
- University of Twente (NL)
- Venue
- Journal of Educational Statistics
- Published
- 1993-09
- Volume
- 18
- Issue
- 3
- Pages
- 237-259
- ISSN
- 0362-9791 (ISSN-L)
- OpenAlex
- W2097507923
- Cited by
- 487
- References
- 17
- Citations by year
- 2026: 11 · 2025: 13 · 2024: 14 · 2023: 14 · 2022: 14 · 2021: 27 · 2020: 26 · 2019: 34 · 2018: 20 · 2017: 28 · 2016: 22 · 2015: 25 · 2014: 24 · 2013: 35 · 2012: 21
- FWCI
- 1.01
- Type
- journal article
- Language
- en
- Open access
- green
- www.jstor.org
- Locations
- Journal of Educational Statistics (publishedVersion)
- University of Twente Research Information (submittedVersion, other-oa)
- RePEc: Research Papers in Economics (submittedVersion)
- University of Groningen research database (University of Groningen / Centre for Information Technology) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Survey Sampling and Estimation Techniques
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Keywords
- two-level designs, multilevel analysis, standard errors, sample size determination, covariance matrix approximation, multilevel data
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