Mike Palij suggests: " As a class project I would suggest students find figures, especially in Tier 1 journals, that use truncated figures and determine (a) does the truncation facilitate understanding or (b) mislead the reader. I predict: (1) There number of truncated figures found will be >> 1.00 and (2) the number of misleading truncated figures will be significantly less than 100%"
Try this out and get back to us. There are exceptions to most rules if you think about it long enough (many are discussed below) and the key here is just to realize that the rule is designed to help graph designers focus on an element that may produce a graph that can be easily misinterpreted. If you understand the purpose of the rule, you will be able to determine when the violation of the rule makes more sense than following it. Speaking of class projects, I have seen more than I would care to remember which have included a non-significant result accompanied by a graph with a truncated y-axis that makes it appear as if the effect size is huge. It isn't as obvious but just as misleading when such a graph accompanies a significant result, in that, it still overstates the effect size but will not be as easily recognized because it fits with the significance of the results. Mike notes: "The "uncorrected" figure shows that there is a very slow increase over time (going from 0% to 4%) while this is obscured in the "corrected" figure. Indeed, the "uncorrected" figure has 0.5% units on the y-axis as the basic units while the "corrected" figure has 20% units (in both cases, horizontal lines are used to show the y-axis landmark values). Looking at the "corrected" figure can anyone determine what the actual percentage is? No, because the y-axis units are too coarse/broad. Seems to me that the "corrected" figure is misleading or at the very least obscures what is happening. The additional detail in the "uncorrected" figure serves to reduce misunderstanding (unless, of course, one isn't paying attention)." It is true that if you are paying close attention to the points in the y-axis you will realize the reason for the apparent inconsistency between the statement that progress in removing the glass ceiling is moving very slowly and the very steep increase in the percentage of female CEOS on the graph is due to the fact that the only part of the scale we are seeing is in the percentages from 0 to 4. But certainly that is an entirely arbitrary choice to present the current percentage as the completion of the graph (the graph suggests that no more progress is even graphable). I would suggest that the uncorrected graph could be purposely used by those who wanted to overestimate the progress women CEO's are making (which looks very impressive in the uncorrected graph and seems like an almost inconsequential flat line in the corrected graph). The corrected graph better makes the graphic point that not much progress has been made in the big picture. My thought is that the corrected graph may somewhat overstate the case, in that, it suggests that the goal of parity would require 100% when in fact it would only require 50%. This has to do with the unstated assumptions people bring to reading graphs. I would say that such reasoning is less arbitrary than using the current percentage as the top point on the graph (which is particularly confusing and counter-productive if you are trying to make the point that there is more progress to be made). Another unstated assumption graph readers have is that the numbers on the y-axis represent ratio data with a true zero point so that if one point on the x-axis is twice as high as another, then that point has twice as much of the graphed property. There are clearly cases where 0 would not be an appropriate base of the graph because the property on the y-axis is not measured in ratio data. It would be misleading, for example, to use a true zero point when plotting scores obtained on a scale from 1 to 7, SAT scores, or IQs as they clearly don't have a true zero (representing absence of the property). So clearly there are cases when it would not be appropriate to include a zero point on the y-axis. The concern is for those times when it would be appropriate to include a true zero and the truncation overstates the effect size. The more general rule might be that the labeling of the y-axis should be based on knowledge of the measurement characteristics of the variable and the effect it will have on the interpretation of the effect size. But that is not very pithy either as a rule or a heuristic. Rick Dr. Rick Froman, Chair Division of Humanities and Social Sciences Professor of Psychology Box 3519 John Brown University 2000 W. University Siloam Springs, AR 72761 [email protected] (479) 524-7295 http://bit.ly/DrFroman --- You are currently subscribed to tips as: [email protected]. To unsubscribe click here: http://fsulist.frostburg.edu/u?id=13090.68da6e6e5325aa33287ff385b70df5d5&n=T&l=tips&o=32723 or send a blank email to leave-32723-13090.68da6e6e5325aa33287ff385b70df...@fsulist.frostburg.edu
