Drawing Inferences From Multiple Intervals in the Single-Factor Design
Derivations, Clarifications, Extensions, and Representations
Abstract
Although confidence intervals for means are excellent vehicles for making inferences about population values, they are not always efficient and practical for making inferences about the differences among the means. This article reviews and elaborates on methods that modify the calculations and the graphical presentations of confidence intervals in order to make them appropriate for both single value inferences and pairwise comparisons in a single-factor between-subjects design. Extensions of the procedure, as well as potential problems, are also discussed.
References
(2000). Displays for comparing a given state to many others. The American Statistician, 54, 89–93.
. (2009). Publication manual of the American Psychological Association (6th ed.). Washington, DC: Author.
(1980). Graphical display of means. The American Statistician, 34, 195–199.
(1969). Using confidence intervals to test hypotheses. Journal of Quality Technology, 4, 256–258.
(1997). Graphical profiles as an aid to understanding plant breeding experiments. Journal of Statistical Planning and Inference, 57, 93–107.
(1999). Graphical analysis of multiresponse data. Washington, DC: Chapman & Hall/CRC.
(2005). Researchers misunderstand confidence intervals and standard error bars. Psychological Methods, 10, 389–396.
(2002). John W. Tukey’s contributions to multiple comparisons. Annals of Statistics, 30, 1576–1594.
(2004). Analysis of variance via confidence intervals. London, UK: Sage.
(2003). Meta-analysis of raw mean differences. Psychological Methods, 8, 406–418.
(1979). On visual assessment of the significance of a mean difference. Biometrics, 35, 657–665.
(1999). Overlapping confidence intervals. Journal of the American Academy of Dermatology, 41, 1051–1052.
(2009). Confidence intervals: Better answers to better questions. Zeitschrift für Psychologie/Journal of Psychology, 217, 15–26.
(2001). A primer on the understanding, use, and calculation of confidence intervals that are based on central and noncentral distributions. Educational and Psychological Measurement, 61, 532–574.
(2005). Inference by eye: Confidence intervals and how to read pictures of data. American Psychologist, 60, 170–180.
(1991). The use of significance limits in graphical data representations. Experentia, 47, 221–224.
(1997). On the communication of information by displays of standard errors and confidence intervals. Psychonomic Bulletin and Review, 4, 330–341.
(2005). Still much to learn about confidence intervals: Reply to Rouder and Morey (2005). Psychological Science, 16, 494–495.
(1991). SAS system for statistical graphics (1st ed.). Cary, NC: SAS Institute.
(1995). The graphical representation of a collection of means. Journal of the Royal Statistical Society, 158A, 175–177.
(1982). On graphical procedures for multiple comparisons. Journal of the American Statistical Association, 77, 767–772.
(1996). Multiple comparisons: Theory and methods. Boca Raton, FL: Chapman & Hall/CRC.
(2006). Why we don’t really know what statistical significance means: Implications for educators. Journal of Marketing Education, 28, 114–120.
(2004). Design and analysis: A researcher’s handbook (4th ed.). Upper Saddle River, NJ: Prentice Hall.
(2004). Beyond significance testing: Reforming data analysis methods in behavioral research. Washington, DC: American Psychological Association.
(1998). Introduction to statistics and data analysis for the behavioral sciences. New York, NY: W. H. Freeman.
(1994). Using confidence intervals in within-subjects design. Psychonomic Bulletin & Review, 1, 476–490.
(2003). Using confidence intervals for graphically based data interpretation. Canadian Journal of Experimental Psychology, 57, 203–220.
(1997). Goodness of approximation in the linear model. In , What if there were no significance tests? (pp. 199–219). Mahwah, NJ: Erlbaum.
(1978). Variations of box plots. The American Statistician, 32, 12–16.
(2003). Research design and statistical analysis (2nd ed.). Mahwah, NJ: Erlbaum.
(1989). Evaluating overlapping confidence intervals. Journal of Quality Technology, 21, 140–141.
(1983). Analysis of means – a graphical procedure. Journal of Quality Technology, 15, 19–25.
(2003). Overlapping confidence intervals or standard error intervals: What do they mean in terms of statistical significance?. Journal of Insect Science, 3, Retrieved from www.insectscience.org/3.34/Payton_et_al_JIS_3.34_2003.pdf.
(2000). Testing statistical hypotheses using standard error bars and confidence intervals. Communications in Soil Science and Plant Analysis, 31, 547–551.
(2005). Relational and arelational confidence intervals: A comment on Fidler, Thomason, Cumming, Finch, and Leeman (2004). Psychological Science, 16, 77–79.
(2007). JMP start statistics: A guide to statistics and data analysis using JMP (4th ed.). Cary, NC: SAS Institute.
(2003). Basic statistics and the inconsistency of multiple comparison procedures. Canadian Journal of Experimental Psychology, 57, 167–175.
(2001). On judging the significance of differences by examining the overlap between confidence intervals. The American Statistician, 55, 182–186.
(1999). Statistical significance bars (SSB): A way to make graphs more interpretable. Retrieved from www.lrdc.pitt.edu/schunn/SSB/index.html.
(2000). Statistics with confidence. Thousand Oaks, CA: Sage.
(2003). Confidence intervals. Thousand Oaks, CA: Sage.
(1997). Noncentrality interval estimation and the evaluation of statistical models. In , What if there were no significance tests? (pp. 221–257). Mahwah, NJ: Erlbaum.
(1997). Speaking graphically: An introduction to some newer graphing techniques. Canadian Journal of Psychiatry, 42, 388–394.
(2007). Effect sizes, confidence intervals, and confidence intervals for effect sizes. Psychology in the Schools, 44, 423–432.
(2001). Evaluating statistical difference, equivalence, and indeterminacy using inferential confidence intervals: An integrated alternative method of conducting null hypothesis statistical tests. Psychological Methods, 6, 371–386.
(2008). An inferential confidence interval method of establishing statistical equivalence that correct Tryon’s (2001) reduction factor. Psychological Methods, 13, 272–277.
(1990). Data-based graphics: Visual display in the decades to come. Statistical Science, 5, 327–339.
(1991). The philosophy of multiple comparisons. Statistical Science, 6, 100–116.
(1993). Graphic comparisons of several linked aspects: Alternatives and suggested principles. Journal of Computational and Graphical Statistics, 2, 1–33.
(2004). Primer on multiple regression coding: Common forms and the additional case of repeated contrasts. Understanding Statistics, 3, 47–57.
. (1999). Statistical methods in psychology: Guidelines and explanations. American Psychologist, 54, 594–604.
(2002). If we’re so different, why do we keep overlapping? When 1 plus 1 doesn’t make 2. Canadian Medical Association Journal, 166, 65–66.
