Omega-Squared.txt Dear 6430 students, We have discussed omega-squared as a less biased (than is eta-squared) estimate of the proportion of variance explained by the treatment variable in the population from which our sample data could be considered to be random. Earlier this semester we discussed a very similar statistic, r-squared, and I warned you about how this statistic can be inflated by high levels of extraneous variable control. The same caution applies to eta-squared and omega-squared. Here is a comment I posted to EDSTAT-L on this topic a few years back: ------------------------------------------------------------------------------ Date: Mon, 11 Oct 93 11:27:23 EDT From: "Karl L. Wuensch" To: Multiple recipients of list Subject: Omega-squared (was P Value) Josh, backon@vms.huji.ac.il, noted: >We routinely run omega squared on our data. Omega squared is one of the most >frequently applied methods in estimating the proportion of the dependent >variable accounted for by an independent variable, and is used to confirm the >strength of association between variables in a population. ............ Omega-squared can also be misinterpreted. If the treatment is evaluated in circumstances (the laboratory) where the influence of extraneous variables (other variables that influence the dependent variable) is eliminated, then the omega-squared will be inflated relative to the proportion of the variance in the dependent variable due to the treatment in a (real) population where those extraneous variables are not eliminated. Thus, a treatment that really accounts for a trivial amount of the variance in the dependent variable out there in the real world can produce a large omega-squared when computed from data collected in the laboratory. To a great extent both P and omega-squared measure the extent to which the researcher has been able to eliminate "error variance" when collecting the data (but P is also greatly influenced by sample size). Imagine that all your subjects were clones of one another with identical past histories. All are treated in exactly the same way, except that for half of them you clapped your hands in their presence ten minutes before measuring whatever the dependent variable is. Because the subjects differ only on whether or not you clapped your hands in their presence, if such clapping has any effect at all, no matter how small, it accounts for 100% of the variance in your sample. If the population to which you wish to generalize your results is not one where most extraneous variance has been eliminated, your omega-squared may be a gross overestimate of the magnitude of the effect. Do note that this problem is not unique to omega-squared. Were you to measure the magnitude of the effect as being the between groups difference in means divided by the within groups standard deviation the same potential for inflation of effect would exist. Karl L. Wuensch, Dept. of Psychology, East Carolina Univ. Greenville, NC 27858-4353, phone 919-757-6800, fax 919-757-6283 Bitnet Address: PSWUENSC@ECUVM1 Internet Address: PSWUENSC@ECUVM.CIS.ECU.EDU ======================================================================== Sender: edstat-l@jse.stat.ncsu.edu From: Joe H Ward Karl --- good comment!! My early research days were spent in an R-squared, Omega-squared, Factor Analysis environment. My own observations say: "BEWARE of those correlation-type indicators!!!" --- Joe Joe Ward 167 East Arrowhead Dr. San Antonio, TX 78228-2402 Phone: 210-433-6575 joeward@tenet.edu