The fair-share interpretation may provide some basis for using means to
compare groups. One could think of the mean in the 1998 NAEP data as the reading
score that all students sampled that year would have if reading ability were divided
evenly among all the students sampled. Based on this reasoning, one might
reasonably conclude that the 1998 group had a higher reading score than the 1994
group. Cortina, Saldanha, and Thompson (1999) explored the use of this notion by
seventh- and eighth-grade students and concluded that these students could use the
idea of fair share to derive and compare means of unequal groups. However, we
would guess that many students would regard such reasoning skeptically unless it
were physically possible to reallocate quantities in the real-world situation. If, for
example, we were thinking about the number of boxes of cookies sold by different
scout troops (as in the study by Cortina et al.), redistributing the cookie boxes
evenly makes some sense. In contrast, if we were reasoning about mean weight,
height, or IQ of a number of individuals, we would have to think of these pounds,
inches, or IQ points being shared metaphorically.
The fair-share interpretation may provide some basis for using means tocompare groups. One could think of the mean in the 1998 NAEP data as the readingscore that all students sampled that year would have if reading ability were dividedevenly among all the students sampled. Based on this reasoning, one mightreasonably conclude that the 1998 group had a higher reading score than the 1994group. Cortina, Saldanha, and Thompson (1999) explored the use of this notion byseventh- and eighth-grade students and concluded that these students could use theidea of fair share to derive and compare means of unequal groups. However, wewould guess that many students would regard such reasoning skeptically unless itwere physically possible to reallocate quantities in the real-world situation. If, forexample, we were thinking about the number of boxes of cookies sold by differentscout troops (as in the study by Cortina et al.), redistributing the cookie boxesevenly makes some sense. In contrast, if we were reasoning about mean weight,height, or IQ of a number of individuals, we would have to think of these pounds,inches, or IQ points being shared metaphorically.
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The fair-share interpretation may provide some basis for using means to
compare groups. One could think of the mean in the 1998 NAEP data as the reading
score that all students sampled that year would have if reading ability were divided
evenly among all the students sampled. Based on this reasoning, one might
reasonably conclude that the 1998 group had a higher reading score than the 1994
group. Cortina, Saldanha, and Thompson (1999) explored the use of this notion by
seventh- and eighth-grade students and concluded that these students could use the
idea of fair share to derive and compare means of unequal groups. However, we
would guess that many students would regard such reasoning skeptically unless it
were physically possible to reallocate quantities in the real-world situation. If, for
example, we were thinking about the number of boxes of cookies sold by different
scout troops (as in the study by Cortina et al.), redistributing the cookie boxes
evenly makes some sense. In contrast, if we were reasoning about mean weight,
height, or IQ of a number of individuals, we would have to think of these pounds,
inches, or IQ points being shared metaphorically.
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