The size of the confidence interval is determined by the range it specifies (i.e., a 95% CI is calculated using Z=1.645 or 1.96, one or two tailed). The chart should indicate that they depict a 95% CI or 99% CI or whatever it is.
There are a couple of common problems that I believe should be taught to students, particularly graduate students but also advanced undergraduate methods students. 1) The confusion between interpreting CI and standard error bars. What constitutes a difference between two means with 95% CIs? Many believe that the CI must not overlap, which is not actually the case but does result in a very conservative approach, and when comparing multiple means probably not a bad idea. I was taught, but now question, the idea that so long as the mean of each group is outside the CI of the "other" group there was a difference at the .05 level (assuming 95% CIs). The idea is that the CI around mean A represents the region containing the actual mean of the population with 95% certainty. Thus a mean for group B that falls outside the CI is only likely to represent a sample from population A 5% of the time (ignoring directionality for the time being). BUT... you must also consider the CI around group B, because while the mean for B might not be from population A, you should also check that the mean from A is not from population B and thus you must look at BOTH confidence intervals. This is only a heuristic and not an absolute, I always tell me students that to draw an inference that will be included in the discussion they must perform an inferential test (the CI are for the readers not for the researchers). Standard error bars however require no overlap of the ranges centered on each mean. See Belia et. al (2005) for an interesting study of published authors and their understanding of CI and standard error bars. Belia, S., Fidler, F., Williams, J., & Cumming, G. (2005). Researchers Misunderstand Confidence Intervals and Standard Error Bars. Psychological Methods, 10, 389-396. APA DOI: 10.1037/1082-989X.10.4.389 2) Some programs automatically compute CI based on the entire sample and not for each individual mean (Excel uses only the deviation of the means). The CI for each mean must be computed specifically for that value. CI's can thus vary widely from one mean to another and if all of them look to be the same size around 5 different means there is probably something going on (unless you have a pretty good sized sample - of course at very large sample sizes the CIs are pretty small). Doug Doug Peterson, PhD Associate Professor of Psychology The University of South Dakota Vermillion SD 57069 605.677.5223 ________________________________________ From: Jim Clark [[email protected]] Sent: Thursday, April 19, 2012 9:12 PM To: Teaching in the Psychological Sciences (TIPS) Subject: RE: [tips] confidence intervals Hi But isn't there a p involved in the CI (or rather 1 - p)? I'm not sure how one interprets a CI without some notion of p or its inverse. For example, why do we choose z = 1.645 or 1.96 or 2.333 or whatever to construct the CI? Take care Jim James M. Clark Professor of Psychology 204-786-9757 204-774-4134 Fax [email protected] >>> "Wuensch, Karl L" <[email protected]> 19-Apr-12 9:04 PM >>> I have always introduced estimation, point and interval, prior to Statistical Hypothesis Inference Testing. After introducing hypothesis testing, I note that once one has a confidence interval, e can generally decide whether or not a hypothesis fits well with the observed data or not, no pee necessary. Cheers, [Description: Karl L. Wuensch]<http://core.ecu.edu/psyc/wuenschk/klw.htm> From: Marte Fallshore [mailto:[email protected]] Sent: Tuesday, April 17, 2012 4:55 PM To: Teaching in the Psychological Sciences (TIPS) Subject: [tips] confidence intervals I was at the Rocky Mountain Psychological Association meeting last weekend, and there was a talk on confidence intervals. It got me thinking about teaching about confidence intervals before I get to hypothesis testing and then integrating it with each hypothesis test we do. Has anyone out there done that? How did it go? Have you found a book that may be does something like that? Thanks, Marte ************************************************ Marte Fallshore Department of Psychology Central Washington Univ. 400 E University Way Ellensburg, WA 98926-7575 509/963-3670 509/963-2307 (fax) Room 462, Psychology Building Everyone is entitled to their own opinions, but they are not entitled to their own facts. ~Daniel Patrick Moynihan When I give food to the poor, they call me a saint. When I ask why the poor have no food, they call me a communist. ~Dom Heider Camara I teach for free; they pay me to grade. (anon) ************************************************ --- You are currently subscribed to tips as: [email protected]<mailto:[email protected]>. 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