Reply to Latina2012 Regarding Racial Differences in College Education

Instead of a conversation, I am using the opportunity in the form of a comment on my previous post on ` College Education: US Racial Groups and Sex in the United States, 2000-2010’ to post another blog entry.  To address the comments adequately, I decided against a rapid two statements reply. First, here is the comment:

“Did you test for the significance of your statistics? I am Hispanic, a woman, and an American. I have a PhD, two Master's degree (sic), and speak 6 foreign languages. I also know other Hispanics like me. I demand to know to what extent your findings are likely to be artifacts of biased sampling

Latina2012”

Dr. Latina2012, your second sentence suggests you doubt the statistical report and summary because you yourself, as a Hispanic, are highly educated (congratulations on your multiple advanced degrees; you did not however, state in what subject/areas. And I wonder from which institutions?)

I too have a PhD (University of Southern California, Department of Sociology). My reply to this specific comment is sociological: one must distinguish individual characteristics from the characteristics of his ecological context, or the sociological category of which he is a member.  You, as an individual, are very highly educated, and may probably be, an outlier in your Census category.


Descriptive statistics are immediately applicable to Sociology because the group is a well defined sample. With this introductory, it should be apparent that the previous blog post was talking about groups of people according to their races (as used by the US Census).  Within this racial category, lots of variation are  present.  A rate of educational attainment, say the percent of those who have college degrees, is a mean, or weighted average of measurements (scores).  Obviously, you have an individual score which is above your category's average. But unless you know millions of other Hispanics who have similar educational attainment such as yours, your group of acquaintances is not likely to be representative of your racial category. In effect, your personally known group of similarly highly educated Hispanics would be a "biased" sample.

I will address the remainder of your comments with reference to what I conceive to be a fact about the enumeration (listing) that the US Census bureau does, and with the little that I know of inferential statistics. A “census “by  definition is supposed to be a complete enumeration, so that, by definition, there would be no need of sampling, and hence, the absence of sampling errors, or bias through sampling. But I am aware that when extensive information is desired, and thus when the number of variables increase, the US Censuses  or for that matter, censuses mounted by most countries, often resort to sampling in order to economize resources. Hence, this sampling operation in lieu of the complete census would admit the possibility of errors.  But these error are likely to be well controlled to a minimum since the sampling design is ultimately random [I don’t want to qualify this into an intensive discussion of stratified, multi-staged random sampling since this blog site also addresses non (statistical) PhDs, and I dont want to alienate them!]

Given that, and in response to your demand, I ran an Analysis of Variance using Minitab, for all the groups from White males to Hispanic females (c2 to C9, see below), and found significant differences between them.  By examining the averages for the 11 year period and their spatial positions locating their 95 percent confidence intervals, you can see that my inferences to the total population of the racial groups are statistically sound: far to the right, separated by large distance are the CIs of the Asian population, as also between their males and females.  To a lesser degree, but still higher than the other racial groups, are the CIs of the Whites, with the distance between their males and females lesser in comparison.  In fact, the only clear overlap, indicating gender equality, but not high educational ranking relative to the other groups, is the Hispanic population.

As shown by the output, the type 1 error associated with such inference is likely to be nil.

One-way ANOVA: C2, C3, C4, C5, C6, C7, C8, C9

Analysis of Variance

Source     DF        SS        MS        F        P

Factor      7  18602.95   2657.56   813.61    0.000

Error      80    261.31      3.27

Total      87  18864.26

                                   Individual 95% CIs For Mean

                                   Based on Pooled StDev

Level       N      Mean     StDev  --+---------+---------+---------+----

C2         11    29.691     0.760                  (*)

C3         11    26.918     2.062                *)

C4         11    16.973     1.002       (*)

C5         11    18.745     1.656         (*)

C6         11    53.382     2.485                                      *)

C7         11    46.473     2.980                                (*)

C8         11    11.727     0.742   (*)

C9         11    12.618     1.398    (*

                                   --+---------+---------+---------+----

Pooled StDev =    1.807             12        24        36        48