Tim Erickson, in his PhysLrnR post 17 May 2006 15:20:59-0700,
responded to my post "Re: How Can We Measure Student Learning? -
Response to Statistician
Ling" [Hake (2006)], as follows [bracketed by lines "EEEEEEEE. . .
."]:
EEEEEEEEEEEEEEEEEEEEEEEEEEEEE
On May 17, 2006, at 1:33 PM, Richard Hake. . .[2006]. . . wrote:
Student %post %pre G g
A 95 75 25 0.8
B 50 0 50 0.5
So, pardon my not having everything at my fingertips, but remind us,
would you: is <g> for a class containing just these two students 0.65
((0.8 + 0.5)/2) or 0.56 (70 gained out of a total possible 125)?
I bet it's the former...
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
No, it's the latter: <g> = 0.56.
In "Interactive-engagement vs traditional methods: A
six-thousand-student survey of mechanics test data for introductory
physics courses" [Hake (1998a) - see also Hake (1998b; 2002a,b)], I
calculated the average normalized gain for a course as:
where the angle brackets <. . .> indicate class averages.
For a class consisting of only the two students A and B, Eq. (1) yields:
<g> = 0.56. . . . . . . . . .(2)
As I pointed out in footnote 46 of Hake (1998a), another way to
calculate an average normalized gain for a course would be to average
single student normalized gains:
g-ave = (1/N) S [g (i)] . . . .(3)
where N is the number of students in the class, S stands for
summation from 1 to N, and g(i) is the i-th student's normalized gain.
For a class consisting of just the two students A and B, Eq. (3) yields:
g-ave = 0.65. . . . . . . . .(4)
In response #3 of my post "Re: How Can We Measure Student Learning? -
Response to Statistician Ling" [Hake (2006)], I discuss <g> and g-ave
and repeat the rationale for using <g> rather that g-ave to assess
the effectiveness of a course that was given in "Assessment of
Physics Teaching Methods" [Hake (2002b)].
BTW:
1. It's not hard to show that <g> as expressed in Eq. (1) is equivalent to:
consistent with Tim Ericson's method of calculation.
2. For those analyzing pre/post test results, a valuable website has
been developed by Aaron Titus (2006).
3. As discussed in footnote #46 of Hake (1998a) and also in Hake
(2002b), for a single course with N greater than about 20, the two
normalized gain averages <g> and g-ave are usually within 5%. It can
be shown that this is related to the generally low correlation
between single-student g's and single-student pretest scores, just as
there was a very low correlation r = +0.02 between <g> and <%pre> for
the 62 courses surveyed in Hake (1998a).
Hake, R.R. 1998b. "Interactive-engagement methods in introductory
mechanics courses," online as ref. 25 at
<http://www.physics.indiana.edu/~hake>, or simply click on
<http://www.physics.indiana.edu/~sdi/IEM-2b.pdf> (108 kB). Submitted
on 6/19/98 to the Physics Education Research Supplement (PERS) to Am.
J. Phys. but rejected by its editor on the grounds that the very
transparent Physical Review-type data tables were too complex! A
crucial companion paper to Hake (1998a).
Hake, R.R. 2002a. "Lessons from the physics education reform effort,"
Ecology and Society 5(2): 28; online at
<http://www.ecologyandsociety.org/vol5/iss2/art28/>. Ecology and
Society (formerly Conservation Ecology) is a free online
"peer-reviewed
journal of integrative science and fundamental policy research" with about
11,000 subscribers in about 108 countries.
Hake, R.R. 2006. Re: How Can We Measure Student Learning? - Response
to Statistician Ling, online at
<http://listserv.nd.edu/cgi-bin/wa?A2=ind0605&L=pod&O=D&P=10103>.
Post of 17 May to AERA-D, AERA-L, ASSESS, EdStat, EvalTalk, IFETS,
ITFORUM (abstract only), PhysLrnR, PsychTeacher (rejected), RUME,
STLHE-L (abstract only), TeachingEdPsych, and TIPS.
Titus, A. 2003. "Assessment Analysis; online at
<http://linus.highpoint.edu/~atitus/assess/>: "a web-based program
(CGI script) that helps teachers analyze test results. . . .
STATISTICAL ANALYSIS [of] pre and post test data [t Test, normalized
gain (Individual and Class), Effect Size, Max, Min, Mean, Median,
Standard Deviation, KR-20, item difficulty, point biserial
coefficient]; CORRELATION ANALYSIS; and FACTOR ANALYSIS.