In part I of “It could be culture,” I looked at the association between mixed race identity and NAEP math and reading scores. Generally, I found that mixed race identity, as indexed a number of ways, was associated with scores intermediate to the parental populations. I was able to rule out a complete monoracial-sampling explanation for this. We are not simply dealing with heterogeneous populations comprised of monoracial Blacks and Whites. As I commented:
“The finding that [self-identifying B/W mixed race individuals who are school identified as Black] over-perform Blacks and that [self-identifying B/W mixed race individuals who are school identified as White] underperform Whites is somewhat informative. It could be that [self-identifying B/W mixed race individuals, in general] include a number of true Black and true White monoracials (i.e., monoracial Blacks and Whites who happened to check both “Black” and “White.”) The effect would be that the scores of [self-identifying B/W mixed race individuals, in general] fall in between those of “Whites” and “Blacks,” thus giving the illusion of intermediate mixed race performance. (Though, in reality, if this were the case, one would not expect the scores to fall in the middle, as they do, as monoracial Whites are 4 times as numerous as monoracial Blacks. As a result, in the above scenario, we would expect 4 times as many monoracial Whites to (mis)check both the “Black” and “White” box as monoracial Blacks and, so, expect the average scores to be skewed to the White end.) Such a “sampling” explanation, though, cannot explain the findings [above] since [self-identifying B/W mixed race individuals who are school identified as Black] presumably excludes monoracial Whites and [self-identifying B/W mixed race individuals who are school identified as White] presumably excludes monoracial Blacks (via school identification in both cases).”
I concluded that either a cultural explanation (being X, identifying as Y) or genetic explanation (being X and Y) could explain the results. I tested the latter and found that a cultural hypothesis was wanting. The results were odd, though, from the perspective of a genetic hypothesis. I noted:
“The most reliable method for identifying mixed race students is that which uses both student and school report. 4th grade mixed race students identified thusly do not behave in accordance with a hereditarian model. 8th grade students do. The results are odd, since we are dealing with overlapping populations. The 2003, 2005, and 2007 4th grade sample is supposedly a representative sample of the same population from which, respectively, the 2007, 2009, and 2011 8th grade sample came from. The mixed race 4th grade increase, relative to Whites, between 2005 and 2007 should have show up as an 8th grade increase, relative to Whites, between 2009 and 2011.”
Further investigation suggested a solution to the paradox found: the correspondence between self-identified and school-identified mixed race status is low. For example, only ½ of 4th grade students who took the NAEP reading test who were school identified as being mixed race, self identify the same way. This would explain why the 4th grade 2005 and 2007 results were at odds with the 8th grade 2009 and 2011 results, even though they were based on samples of mostly the same population. The lack of correspondence between self/school mixed race, of course, does not, in turn, necessarily support a cultural hypothesis, as it’s not clear if self-identified mixed race status is a poor predictor of “true” mixed race status. It could be that both self and school identified mixed race status are fair predictors of “true” status but not of each other.
Whatever the case, the results do call into question the significance of the findings here and elsewhere in context of reducing the hereditarian/environmental uncertainty. It may be that while self identifying “mixed race” individuals perform intermediate to the parental populations, school identified “mixed race” individuals don’t.
To determine if the latter is true, one would need to decompose school identified mixed race results by racial mix. To do this accurately one would need the school level data, which, unfortunately, is not available to us. Nonetheless, we can estimate the scores, if we are willing to make a simple assumption. To estimate the scores, we can cross tab school identified mixed race with self identified race. If we just make the assumption that school identified mixed race individuals who self identified as X are mixed race individual of X and some other parentage, we can estimate these scores based on racial intermarriage rates. (To clarify, we are assuming that a school classified mixed individual who self-classifies as “Black” is “really” Black + something — as opposed to, say, White + Asian.)
For example, in the 4th grade NAEP 2011 Math sample, there were (as estimated from s.e. and SD) about 402 school classified multiracial students who self-classified as Black, 217 who classified as White, 500 who classified as Mixed, and 249 who classified as Mixed Black/White.
And based on the 2000 census, 26% of interracial White marriages were to Blacks and 88% of Black interracial marriages were to Whites. Black/White interracial marriages comprised 25% of the total.
Based on our assumption, we can estimate the school mixed race scores as:
“Self classified B/W” score x sample size”
(Or we could use: Self classified Mixed, School classified Mixed” x sample size x % of Mixed interracial marriages that were B/W. But I am opting to use “Self classified B/W” because those results are less in line with a genetic hypothesis.)
“Self classified White, School classified Mixed” score x sample size x % of White interracial marriages to Blacks.”
“Self classified Black, School classified Mixed” score x sample size x % of Black interracial marriages to Whites.”
We are just creating an N-weighted score based on the probability of admixture.
Doing this for 4th grade Math…Reading, 8th grade Math and Reading, we get:
(To be continued)