Estimation and Standardization of Variance Parameters for Planning Cluster-Randomized Trials: A Short Guide for Researchers

Abstract

A review of literature covering the past decade indicates a shortage of cluster-randomized trials (CRTs) in education and psychology in Turkey, the gold standard that is capable of producing high-quality evidence for high-stake decision making when individual randomization is not feasible. Scarcity of CRTs is not only detrimental to collective knowledge on the effectiveness of interventions but also hinders efficient design of such studies as prior information is at best incomplete or unavailable. In this illustration, we demonstrate how to estimate variance parameters from existing data and transform them into standardized forms so that they can be used in planning sufficiently powered CRTs. The illustration uses publicly available software and guides researchers step by step via introducing statistical models, defining parameters, relating them to notations in statistical models and power formulas, and estimating variance parameters. Finally, we provide example statistical power and minimum required sample size calculations.  

Keywords

• cluster-randomized trials,variance estimation,statistical power analysis,minimum required sample size

Abstract

Geçtiğimiz on yılı kapsayan literatür taraması, bireysel seçkisiz atamanın mümkün olmadığı durumlarda, önemli kararlar alınırken etkili kanıt üretebilecek altın standardındaki seçkisiz-küme deneylerinin (SKD) Türkiye'de eğitim ve psikoloji alanlarında yetersiz sayıda olduğunu göstermektedir. SKD sayısının azlığı sadece programın etkililiği konusunda toplam bilgiye zarar vermekle kalmayıp, önceki bilgiler mevcut olmadığından veya en iyi ihtimalle eksik olduğundan bu tür çalışmaların etkili bir şekilde tasarlanmasını da engellemektedir. Bu çalışmada, mevcut verilerden yola çıkarak varyans parametrelerinin nasıl kestirilebileceği, nasıl standart formlara dönüştürülebileceği ve böylece bunların nasıl yeteri kadar güçlü SKD’lerin planlanmasında kullanılabileceği gösterilmiştir. Bu çalışmada belirtilen amacı gerçekleştirmek üzere halka açık yazılım kullanılmıştır.  Burada istatistiksel modelleri tanıtıp, parametreleri tanımlayarak, istatistiksel model ve güç formüllerinde varyans parametrelerini tahmini gösterimlerle (notasyon) ilişkilendirerek araştırmacılara adım adım rehberlik edilmeye çalışılmıştır.     

Keywords

• seçkisiz-küme deneyleri,varyans kestirimi,istatistiksel güç analizi,gerekli en küçük örneklem büyüklüğü

References

1. Bland J. M. (2004). Cluster randomized trials in the medical literature: two bibliometric surveys. BMC Medical Research Methodology, 4(21). DOI: https://doi.org/10.1186/1471-2288-4-21
2. Bloom, H. S. (1995). Minimum detectable effects a simple way to report the statistical power of experimental designs. Evaluation Review, 19(5), 547-556. DOI: https://doi.org/10.1177/0193841X9501900504
3. Bloom, H. S. (2006). The core analytics of randomized experiments for social research. MDRC Working Papers on Research Methodology. New York, NY: MDRC. Retrieved from DOI: https://www.mdrc.org/sites/default/files/full_533.pdf.
4. Bloom, H. S., Bos, J. M., & Lee, S. W. (1999). Using cluster random assignment to measure program impacts statistical implications for the evaluation of education programs. Evaluation Review, 23(4), 445-469. DOI: https://doi.org/10.1177%2F0193841X9902300405
5. Bulus, M., Dong, N., Kelcey, B., & Spybrook, J. (2019). PowerUpR: Power Analysis Tools for Multilevel Randomized Experiments. R package version 1.0.4. DOI: https://CRAN.R-project.org/package=PowerUpR
6. Cameron, A. C., & Miller, d. L. (2015). A practitioner’s guide to cluster-robust inference. Journal of Human Resources, 50, 317-372. DOI: https://doi.org/10.3368/jhr.50.2.317
7. Dong, N., & Maynard, R. (2013). PowerUp!: A Tool for Calculating Minimum Detectable Effect Sizes and Minimum Required Sample Sizes for Experimental and Quasi-experimental Design Studies. Journal of Research on Educational Effectiveness, 6(1), 24-67. DOI: https://doi.org/10.1080/19345747.2012.673143
8. Bates, D., Maechler, M., Bolker, B., & Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1), 1-48. DOI: https://doi.org/10.18637/jss.v067.i01

9. Hayes, R. J. & Moulton, L. H. (2017). Cluster Randomized Trials (2nd ed.). New York, NY: Chapman and Hall/CRC Press. DOI: https://doi.org/10.4324/9781315370286
10. Hedberg, E. C. (2016). Academic and behavioral design parameters for cluster randomized trials in kindergarten: an analysis of the Early Childhood Longitudinal Study 2011 Kindergarten Cohort (ECLS-K 2011). Evaluation Review, 40(4), 279-313. DOI: https://doi.org/10.1177/0193841X16655657
11. Hedberg, E. C., & Hedges, L. V. (2014). Reference values of within-district intraclass correlations of academic achievement by district characteristics: Results from a meta-analysis of district-specific values. Evaluation Review, 38(6), 546-582. DOI: https://doi.org/10.1177/0193841X14554212
12. Hedges, L. V., & Hedberg, E. C. (2013). Intraclass correlations and covariate outcome correlations for planning two-and three-level cluster-randomized experiments in education. Evaluation Review, 37(6), 445-489. DOI: https://doi.org/10.1177/0193841X14529126
13. Hedges, L. V., & Rhoads, C. (2010). Statistical Power Analysis in Education Research (NCSER 2010-3006). Washington, DC: National Center for Special Education Research, Institute of Education Sciences, U.S. Department of Education. Retrieved from https://files.eric.ed.gov/fulltext/ED509387.pdf
14. Konstantopoulos, S. (2009a). Using power tables to compute statistical power in multilevel experimental designs. Practical Assessment, Research & Evaluation, 14(10).
15. Konstantopoulos, S. (2009b). Incorporating Cost in Power Analysis for Three-Level Cluster-Randomized Designs. Evaluation Review, 33(4), 335-357. DOI: https://doi.org/10.1177/0193841X09337991
16. Moerbeek, M., & Safarkhani, M. (2018). The design of cluster randomized trials with random cross-classifications. Journal of Educational and Behavioral Statistics, 43(2), 159-181. DOI: https://doi.org/10.3102/1076998617730303
17. Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods (2nd ed.). Thousand Oaks, CA: Sage Publications.
18. R Core Team (2019). R: A language and environment for statistical computing. R Foundation for Statistical Computing [Computer software]. Vienna, Austria. Retrieved from https://www.R-project.org.
19. Spybrook, J., Shi, R., & Kelcey, B. (2016). Progress in the past decade: an examination of the precision of cluster randomized trials funded by the U.S. Institute of Education Sciences. International Journal of Research & Method in Education, 39(3), 255-267. DOI: https://doi.org/10.1080/1743727X.2016.1150454
20. Spybrook, J., Westine, C. D., & Taylor, J. A. (2016). Design parameters for impact research in science education: A multistate analysis. AERA Open, 2(1). DOI: https://doi.org/10.1177/2332858415625975
21. Westine, C. D. (2016). Finding Efficiency in the Design of Large Multisite Evaluations: Estimating Variances for Science Achievement Studies. American Journal of Evaluation, 37(3), 311-325. DOI: https://doi.org/10.1177/1098214015624014
22. Westine, C. D., Spybrook, J., & Taylor, J. A. (2013). An empirical investigation of variance design parameters for planning cluster-randomized trials of science achievement. Evaluation Review, 37(6), 490-519. DOI: https://doi.org/10.1177/0193841X14531584
23. Zopluoglu, C. (2012). A cross-national comparison of intra-class correlation coefficient in educational achievement outcomes. Eğitimde ve Psikolojide Ölçme ve Değerlendirme Dergisi, 3(1), 242-278.