Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-25T20:11:03.298Z Has data issue: false hasContentIssue false
  • English
  • Français

Our statistical intuitions may be misleading us: Why we need robust statistics

Published online by Cambridge University Press:  20 May 2011

Jenifer Larson-Hall
Jenifer Larson-Hall*
Affiliation:
Kyushu Sangyo University, Fukuoka, [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Most academics' intuitions about statistics follow those of naive laypeople – that is, we often think that a sample should reflect the population characteristics more closely than it does, and expect less variability in samples than is truly found in them. These intuitions may prevent us from understanding why modern developments in statistics are needed. Another intuition most researchers hold is that it is better to be conservative when performing statistics, and this may involve adjusting p-values for multiple tests, using more conservative post hoc tests, or setting an alpha value lower than .05 when possible. However, the more we try to control against making an error in being overeager to find differences, the stronger the probability that we will make an error in not finding differences that actually exist. These two forces need to be counterbalanced, and this involves increasing the power of our tests. Robust statistics can increase the power of statistical tests to find real differences. I discuss the need for robust techniques to avoid reliance on classical assumptions about the data. Examples of robust analyses with t-tests, correlation, and one-way ANOVA are shown.

Type
Plenary Speeches
Information
Language Teaching , Volume 45 , Issue 4 , October 2012 , pp. 460 - 474
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abrahamsson, N. & Hyltenstam, K. (2008). The robustness of aptitude effects in near-native second language acquisition. Studies in Second Language Acquisition 30, 481–509.CrossRefGoogle Scholar
Fox, J. with contributions from 20 others (2009). Rcmdr: R Commander. R package version 1.5–4. http://CRAN.R-project.org/package=RcmdrGoogle Scholar
Gass, S. (2009). A historical survey of SLA research. In Bhatia, T. K. & Ritchie, W. C. (eds.), The new handbook of second language acquisition. Bingley, UK: Emerald Group Publishing, 3–27.Google Scholar
Gschwandtner, M. & Filzmoser, P. (2009). mvoutlier: Multivariate outlier detection based on robust methods. R package version 1.4. www.statistik.tuwien.ac.at/public/filz/.Google Scholar
Hampel, F. R. (1973). Robust estimation: A condensed partial survey. Zeitschrift fur Wahrscheinlichkeitstheorie und verwandte Gebiete 27, 87–104.CrossRefGoogle Scholar
Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. J. & Stahel, W. A. (1986). Robust statistics: The approach based on influence functions. New York: Wiley.Google Scholar
Howell, D. C. (2010). Statistical methods for psychology (7th edn). Pacific Grove, CA: Duxbury/Thomson Learning.Google Scholar
Huber, P. J. (1981). Robust statistics. New York: John Wiley & Sons.CrossRefGoogle Scholar
Kline, R. (2004). Beyond significance testing: Reforming data analysis methods in behavioral research. Washington, DC: American Psychological Association.CrossRefGoogle Scholar
Krashen, S. D. (1977). The Monitor Model for adult second language performance. In Burt, M. K., Dulay, H. C. & Finocchairo, M. (eds.), Viewpoints on English as a second language. New York: Regents, 152–161.Google Scholar
Larson-Hall, J. (2008). Weighing the benefits of studying a foreign language at a younger starting age in a minimal input situation. Second Language Research 24.1, 35–63.CrossRefGoogle Scholar
Larson-Hall, J. (2010). A guide to doing statistics in second language research using SPSS. New York: Routledge.Google Scholar
Larson-Hall, J. & Herrington, R. (2010). Examining the difference that robust statistics can make to studies in language acquisition. Applied Linguistics 31.3, 368–390.CrossRefGoogle Scholar
Luh, W.-M. & Guo, J.-H. (2001). Using Johnson's transformation and robust estimators with heteroscedastic test statistics: An examination of the effects of non-normality and heterogeneity in the non-orthogonal two-way ANOVA design. British Journal of Mathematical and Statistical Psychology 54, 79–94.CrossRefGoogle ScholarPubMed
Maronna, R. A., Martin, R. D. & Yohai, V. J. (2006). Robust statistics: Theory and methods. Hoboken, NJ: Wiley.CrossRefGoogle Scholar
Nickerson, R. S. (2000). Null hypothesis significance testing: A review of an old and continuing controversy. Psychological Methods 5.2, 241–301.CrossRefGoogle ScholarPubMed
R Development Core Team (2009). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. www.R-project.org.Google Scholar
Tukey, J. W. (1960). A survey of sampling from contaminated distributions. In Olkin, I., Ghwyne, S. G., Hoeffding, W., Madow, W. G. & Mann, H. B. (eds.), Contributions to probability and statistics: Essays in honor of Harold Hotelling. Stanford: Stanford University Press, 448–485.Google Scholar
Tversky, A. & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin 76, 105–110.CrossRefGoogle Scholar
Wilcox, R. (1995). ANOVA: A paradigm for low power and misleading measures of effect size? Review of Educational Research 65.1, 51–77.CrossRefGoogle Scholar
Wilcox, R. (1998). How many discoveries have been lost by ignoring modern statistical methods? American Psychologist 53.3, 300–314.CrossRefGoogle Scholar
Wilcox, R. (2001). Fundamentals of modern statistical methods: Substantially improving power and accuracy. New York: Springer.CrossRefGoogle Scholar
Wilcox, R. (2003). Applying contemporary statistical techniques. San Diego, CA: Elsevier Science.Google Scholar
Wilcox, R. (2005). Introduction to robust estimation and hypothesis testing. Burlington, MA: Elsevier Academic.Google Scholar
Wilcox, R. R. & Schönbrodt, F. D. (2009). The WRS package for robust statistics in R (version 0.11). http://r-forge.r-project.org/projects/wrs/Google Scholar
Yuen, K. K. & Dixon, W. J. (1973). The approximate behaviour and performance of the two-sample trimmed t. Biometrika 60.2, 369–374.CrossRefGoogle Scholar
Supplementary material: File

Larson-Hall Supplementary Material

Larson-Hall Supplementary Material

Download Larson-Hall Supplementary Material(File)
File 69.2 KB