HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH I. DEFINITION OF THE AVERAGE NORMALIZED GAIN <g> In Hake (2002b) I wrote (slightly edited):
The half-century old average normalized gain <g> for a treatment has been independently defined [Hovland et al. (1949), Gery (1972), Hake (1998a)] as <g> = Gain/[Gain (maximum possible). In terms of %scores
<g> = (<%post> - <%pre>) / (100% - <%pre>)
Where angle brackets <. . . .> indicate the class average (preferably only for students who have taken both the pre and post tests). HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
Then Dennis asked: ". . .please explain how the term "normalized" is any part of the definition of <g> above."
A similar concern was expressed by Ted Micceri (2002) in his ASSESS post of 8 Apr 2002. Micceri wrote [bracketed by lines "MMMMMMMMMM. . . . . ."]:
MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM First of all, I am offended by the very use of the term "Normalized," when in fact one speaks of "Gaussianized" data. For those who still adhere to the utter fallacy of the mistermed "normal" curve, I recommend reading . . . Micceri (1989). . . " I would have called them Mythical Beasts, except that I am not sure about Unicorns. So the underlying assumptions of the transformation are fallacious to start with, unless they are applied to the gain scores themselves, which causes other problems - more on that below." MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
I responded [Hake (2002c)] (slightly edited):
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH I think there is a physics/psychometric language gap here. To a physicist "to normalize" CAN mean merely "to divide a quantity by some parameter so as to make the 'normalized' quantity useful" (i.e., "reduce it to a norm or standard" in accord with Webster's 3rd unabridged), and does not necessarily have anything to do with the "mistermed 'normal' curve."
For example, a "normalized weight D" of a BODY of weight "W" and volume "V" could be DEFINED as:
D = W/V . . . . . . . . . . . . . . . . . (1)
where D is just the "weight density". Ever since the work of Archimedes (231 + or - 21BC) it's been known by the scientific cognoscente that the density "D" IS A MUCH BETTER INDICATOR OF WHETHER OR NOT A BODY WILL SINK OR FLOAT IN WATER THAN IS THE WEIGHT "W." For example, a BODY of density D will float if D < D(water).
Similarly the [single student] "normalized gain g" for a TREATMENT is DEFINED (Hovland 1949, Gery 1972, Hake 1998a) as:
g = Gain/[Gain(max)] . . . . . . . . . . (2)
Ever since the work of Hovland et al. (1949) it's been know by
pre/post cognoscente (up until about 1998 probably less than 100
people worldwide) that g IS A MUCH BETTER INDICATOR OF THE EXTENT TO
WHICH A TREATMENT IS EFFECTIVE THAN IS EITHER gain OR posttest. For
example, if the TREATMENT yields [a course average] <g> > 0.3 for a mechanics course, then the course is in the "interactive-engagement zone."
Now the normalized gain "g", per se, does not necessarily have anything to do with the "mistermed 'normal' curve." In my own survey (Hake, 1998a,b; 2002a) the <g> (<g> means the average g for a class) distributions for both interactive-engagement (IE) and traditional (T) courses are NOT
Gaussian [see Fig. 2 in Hake (1998a) and Hake (2002a).]
So Micceri and other statistics buffs might feel more comfortable using the name "effectiveness index" (Hovland 1949), "gap closing parameter" (Gery 1972), "Hovland Measure" (Pendelton 1998). . . .[or even the atrocious "fractional gain" of Redish (2003)].
HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH
Richard Hake, Emeritus Professor of Physics, Indiana University 24245 Hatteras Street, Woodland Hills, CA 91367 <[EMAIL PROTECTED]> <http://www.physics.indiana.edu/~hake> <http://www.physics.indiana.edu/~sdi>
REFERENCES Archimedes. 231 + or - 21 BC. "On floating bodies I."
Gery, F.W. 1972. "Does mathematics matter?" in A.Welch, ed., Research papers in economic education. Joint Council on Economic Education. pp. 142-157.
Hake, R.R. 1998a. "Interactive-engagement vs traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses," Am. J. Phys. 66: 64-74; online as ref. 24 at
<http://www.physics.indiana.edu/~hake>. A comparison of the pre- to post-test average normalized gain <g> for 62 introductory high-school, college, and university physics courses enrolling a total 6542 students showed that fourteen "traditional" (T) courses (N = 2084) which made little or no use of interactive-engagement (IE) methods achieved an average gain <g> T-ave = 0.23 � 0.04 (std dev), regardless of the experience, enthusiasm, talents, and motivation of the lecturers. In sharp contrast, forty-eight courses (N = 4458) which made substantial use of IE methods achieved an average gain <g>IE-ave = 0.48 � 0.14 (std dev), almost two standard deviations of <g>IE-ave above that of the traditional courses. For the definition of <g>, and operational definitions of "traditional courses," and "interactive-engagement" courses see the article. More recently, normalized gain differences between T and IE courses that are consistent with the work of Hake have been reported by many other physics education research groups as referenced in Hake (2002a,b).
Hake, R.R. 1998b. "Interactive-engagement methods in introductory mechanics courses," online as ref. 25 at
<http://www.physics.indiana.edu/~hake>. Submitted on 6/19/98 to the Physics Education Research Supplement to AJP (PERS)." In this sadly suppressed (Physics Education Research has no archival journal!) crucial companion paper to Hake (1998b): average pre/post test scores, standard deviations, instructional methods, materials used, institutions, and instructors for each of the survey courses of Hake (1998b) are tabulated and referenced. In addition the paper includes: (a) case histories for the seven IE courses of Hake (1998b) whose effectiveness as gauged by pre-to-post test gains was close to those of T courses, (b) advice for implementing IE methods, and (c) suggestions for further research.
Hake, R.R. 2002a. "Lessons from the physics education reform effort." Conservation Ecology 5(2): 28; online at <http://www.consecol.org/vol5/iss2/art28>. "Conservation Ecology," is a FREE "peer-reviewed journal of integrative science and fundamental policy research" with about 11,000 subscribers in about 108 countries.
Hake, R.R. 2002b. "Assessment of Physics Teaching Methods, Proceedings of the UNESCO-ASPEN Workshop on Active Learning in Physics, Univ. of Peradeniya, Sri Lanka, 2-4 Dec. 2002; also online as ref. 29 at
<http://www.physics.indiana.edu/~hake/>.
Hake, R.R. 2002c. "Re: Normalized Gains, "post of of 11 Apr 2002 20:25:41-0700 to ASSESS, AERA-D, EvalTalk, PhysLrnR, POD; online at
<http://lists.asu.edu/cgi-bin/wa?A2=ind0204&L=aera-d&P=R1481>.
Hake, R.R. 2003. "Re: Normalized Gain (was Inquiry method and motivation)," post of 24 Nov 2003 17:12:05-0800 to EvalTalk, Math-Learn, PhysLrnR, & POD; online at
<http://listserv.nd.edu/cgi-bin/wa?A2=ind0311&L=pod&O=D&P=18573>. Later sent to AERA-D, ASSESS, and Biopi-L; and in abstract form to Chemed-L, Phys-L, Physhare, STLHE-L, EdStat, FYA, and AP-Physics.
Hovland, C. I., A. A. Lumsdaine, and F. D. Sheffield. 1949. "A baseline for measurement of percentage change." In C. I. Hovland, A. A. Lumsdaine, and F. D. Sheffield, eds. 1965. Experiments on mass communication. Wiley (first published in 1949).) Reprinted as pages 77-82 in P. F. Lazarsfeld and M. Rosenberg, eds. 1955. The language of social research: a reader in the methodology of social Research." Free Press.
Micceri, T. 1989. "The unicorn, the normal curve, and other improbable creatures." Psychological Bulletin, 105: 156-166.
Micceri, T. 2002. "Re: Best Predictor of Knowledge Gain is Low Pretest Score?" ASSESS post of 8 Apr 2002 11:09:04-0400; online at <http://lsv.uky.edu/cgi-bin/wa.exe?A2=ind0204&L=assess&F=&S=&P=1736>.
Pendleton, W.W. 1998. "Re: measuring change," AERA-D post of 4 May 1998 12:11:16-0400; online at
<http://lists.asu.edu/cgi-bin/wa?A2=ind9805&L=aera-d&P=R509>.
Redish, E.F. 2003 "Teaching Physics With the Physics Suite." John Wiley.
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