Measuring "prejudice" in Piston 2010, Hopkins 2019, and Hopkins and Washington 2020
The average eighth grade math score on the 2019 National Assessment of Educational Progress (NAEP) was 310 for Asian/Pacific Islander students, 292 for White students, 268 for Hispanic students, and 260 for Black students. This pattern has been consistent for many years, for fourth grade students (Figure 3), for eighth grade students (Figure 4), and for twelfth grade students (Figure 5).
However, before inferring that Asian/Pacific Islander students are better in math on average than are White students and Hispanic students and Black students, be aware that this inference could be labeled "prejudice" in peer-reviewed research such as Piston 2010 and Hopkins and Washington 2020, which measured "prejudice" as a difference in ratings of groups on stereotype scales for certain characteristics.
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Piston 2010 conceptualized "prejudice" with "an etymological perspective":
An assessment that one racial group possesses a negative attribute relative to another racial group is a "pre-judgment"; it precedes, but may or may not influence, the evaluation of an individual member of that group, such as Barack Obama.
So, if you make a good faith interpretation of NAEP scores and/or SAT scores and infer that Asian/Pacific Islander students are better on average in math than are White students and Hispanic students and Black students, that would be "prejudice" by the analysis in Piston 2010.
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Your responses might not be "prejudice" based on Hopkins 2019:
We define prejudice as a standing, negative predisposition toward a social group held in the face of contradictory information.
Based on this, Hopkins 2019 seems to require evidence that Asian/Pacific Islander students are not better on average in math than are White students and Hispanic students and Black students ("contradictory information") before labeling that belief as "prejudice".
I asked Dan Hopkins in a tweet what "contradictory information" he was referring to for his use of "prejudice", and, perhaps as a consequence, Hopkins and Washington 2020 removed the "held in the face of contradictory information" restriction. From Hopkins and Washington 2020:
'Prejudice' refers to a standing, negative predisposition toward a social group.
So, by Hopkins and Washington 2020, it would be "prejudice" to have a justified standing, negative predisposition toward a hate group that regularly commits terrorism. That might be a proper conceptualization of "prejudice", but I would be interested in seeing Hopkins or Washington use "prejudice" in that way.
Hopkins and Washington 2020 used stereotype scale differences as measures of "prejudice", but it seems possible to perceive that members of one group perform better on average on some measure than members of another group, without having a "standing, negative predisposition" toward either group, especially because nothing in these traditional stereotype scales indicates that the scales measure belief about innate or genetic characteristics.
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From what I can tell, the belief that U.S. Asian/Pacific Islander students are better in math on average than are White students and Hispanic students and Black students would be "prejudice" under the conceptualizations in Piston 2010 and Hopkins and Washington 2020, even though I think that this belief can result from a good faith interpretation of high quality evidence. I thus think that use of the conceptualizations of "prejudice" in Piston 2010 or Hopkins and Washington 2020 has the potential to be misleading and to corrode public discourse.
The potential to mislead is because I think that "prejudice" has a negative connotation in everyday language, and I don't think that a good faith interpretation of high quality evidence should have a label that has a negative connotation. I am not aware of anything that prevents researchers from labeling such stereotype scale responses as "stereotype scale differences" or something similar that would more precisely describe the phenomenon being measured.
The potential to corrode public discourse is the potential that fear of application of the "prejudice" label can make people less likely to express beliefs that have been derived from a good faith interpretation of high quality evidence, and I don't think that, barring some compelling reason otherwise, people should be discouraged from expressing a belief that has been derived from a good faith interpretation of high quality evidence.