Advanced Statistical Analyses

  • Miguel A. PadillaEmail author


Statistical models offer much flexibility and many fall under several general umbrellas. The linear mixed model is one such model, and it can be specified to answer vastly different research questions. Three such linear mixed model specifications (or methods) are the hierarchical linear models used when there are clustered data structures; generalizability theory used for evaluating the reliability or consistency of a measurement process; and equivalence testing used for investigating the similarity between conditions. Here, each method is presented in the context of healthcare simulation with a worked-out example to highlight its central concepts while technical details are kept to a minimum.


Equivalence testing Equivalence test TOST Hierarchical linear models HLM Multilevel models Longitudinal models Performance assessment Score consistency Reliability Generalizability theory G theory 


  1. 1.
    Muller KE, Stewart PW. Linear model theory: univariate, multivariate, and mixed models. Hoboken: Wiley-Interscience; 2006. xiv, p. 410.Google Scholar
  2. 2.
    Raudenbush SW, Bryk AS. Hierarchical linear models: applications and data analysis methods. 2nd ed. Thousand Oaks: Sage Publications; 2002. xxiv, p. 485.Google Scholar
  3. 3.
    Snijders TAB, Bosker RJ. Multilevel analysis: an introduction to basic and advanced multilevel modeling. 2nd ed. Los Angeles: Sage; 2012. xi, p. 354Google Scholar
  4. 4.
    Gadde KM, Franciscy DM, Wagner HR, Krishnan KRR. Zonisamide for weight loss in obese adults – a randomized controlled trial. Jama-J Am Med Assoc. 2003;289(14):1820–5.CrossRefGoogle Scholar
  5. 5.
    Elobeid MA, Padilla MA, McVie T, Thomas O, Brock DW, Musser B, et al. Missing data in randomized clinical trials for weight loss: scope of the problem, state of the field, and performance of statistical methods. PLoS One. 2009;4(8):e6624.CrossRefGoogle Scholar
  6. 6.
    Brennan RL. Generalizability theory. New York: Springer; 2001. xx, p. 538Google Scholar
  7. 7.
    Padilla MA, Divers J, Newton M. Coefficient Alpha bootstrap confidence interval under nonnormality. Appl Psychol Meas. 2012;36(5):331–48.CrossRefGoogle Scholar
  8. 8.
    Cortina JM. What is coefficient alpha? An examination of theory and applications. J Appl Psychol. 1993;78(1):98–104.CrossRefGoogle Scholar
  9. 9.
    Hogan TP, Benjamin A, Brezinski KL. Reliability methods: a note on the frequency of use of various types. Educ Psychol Meas. 2000;60(4):523–31.CrossRefGoogle Scholar
  10. 10.
    Peterson RA. A meta-analysis of cronbach’s coefficient alpha. J Consum Res. 1994;21(2):381–91.CrossRefGoogle Scholar
  11. 11.
    McBride ME, Waldrop WB, Fehr JJ, Boulet JR, Murray DJ. Simulation in pediatrics: the reliability and validity of a multiscenario assessment. Pediatrics. 2011;128(2):335–43.CrossRefGoogle Scholar
  12. 12.
    Nadkarni LD, Roskind CG, Auerbach MA, Calhoun AW, Adler MD, Kessler DO. The development and validation of a concise instrument for formative assessment of team leader performance during simulated pediatric resuscitations. Simul Healthc. 2018;13(2):77–82.CrossRefGoogle Scholar
  13. 13.
    Hauck WW, Anderson S. A new statistical procedure for testing equivalence in two group comparative bioavailability trials. J Pharmacokinet Biopharm. 1984;12(1):83–91.CrossRefGoogle Scholar
  14. 14.
    Schuirmann DJ. A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability. J Pharmacokinet Biopharm. 1987;15(6):657–80.CrossRefGoogle Scholar
  15. 15.
    Wellek S. Testing statistical hypotheses of equivalence and noninferiority. 2nd ed. Boca Raton: CRC Press; 2010. xvi, p. 415.Google Scholar
  16. 16.
    Anderson-Montoya BL, Scerbo MW, Ramirez DE, Hubbard TW. Running memory for clinical handoffs: a look at active and passive processing. Hum Factors. 2017;59(3):393–406.CrossRefGoogle Scholar
  17. 17.
    Cardinet J, Johnson S, Pini G. Applying generalizability theory using EduG. New York: Routledge; 2010. xviii, p. 215.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of PsychologyOld Dominion UniversityNorfolkUSA

Personalised recommendations