Dr. Stat

Dr. Stat is a Statistics Professor. This blog is his opportunity to share ideas and opinions about education (especially math education), politics, and whatever else comes up.

Tuesday, March 07, 2006

L.A. Mayor Links Dropout Rate, Civil Rights

Los Angeles Time, 02 March 2006
TITLE: “L.A. Mayor Sees Dropout Rate as ‘Civil Rights Issue’”

The issue was brought to the fore by a Harvard University study estimating that less than 50 percent of L.A. students graduate in four years. The rate is lowest for Latino students. The school district has disputed the study’s figures, saying the overall graduation rate is closer to 70 percent. But Villaraigosa said neither figure is acceptable. “These are numbers that should put a chill down your spine,” he said.

It occurs to me that we should ask the question, "How many people should graduate from high school?" The way most people talk, it should be 100%. But that would be absurd.

Lewis Terman (1916) developed the IQ classification:
Over 140 - Genius or near genius
120 - 140 - Very superior intelligence
110 - 119 - Superior intelligence
90 - 109 - Normal or average intelligence
80 - 89 - Dullness
70 - 79 - Borderline deficiency
Under 70 - Definite feeble-mindedness
(http://www.wilderdom.com/intelligence/IQWhatScoresMean.html)

Now we can argue about the reliability of IQ scores, we can debate whether or not IQ tests are "fair," etc. ad nauseum. But everybody "knows" that there is something to the concept of IQ, even if we are a bit fuzzy about what it means.

IQ is normally distributed, but the distribution varies from place to place and from group to group (racial, socio-economic, etc.). Still, if we consider the overall distribution of the population,


"Adults in the bottom 5% of the IQ distribution below 75) are very difficult to train and are not competitive for any occupation on the basis of ability. Serious problems in training low-IQ military recruits during World War II led Congress to ban enlistment from the lowest 10% (below 80) of the population, and no civilian occupation in modern economies routinely recruits its workers from that below-80 range. Current military enlistment standards exclude any individual whose IQ is below about 85."
"Persons of average IQ (between 90 and 100) are not competitive for most professional and executive-level work but are easily trained for the bulk of jobs in the American economy."


Linda Gottfredson, "The General Intelligence Factor", Scientific American Presents "Exploring Intelligence", pg. 24, 1999, (reference in http://www.geocities.com/rnseitz/Definition_of_IQ.html)

Now let's be really clear about what that means. Ten percent of the population has IQ scores below 80, and those people were not smart enough to be soldiers in WWII and are not smart enough today to be recruited for any working-class jobs. (I assume this does not mean that they do not hold such jobs, just that employers do not seek them.)

THERE IS NO WAY THAT THE BOTTOM 10% OF THE POPULATION CAN LEGITIMATELY GRADUATE FROM HIGH SCHOOL, not if a high school diploma means anything at all. In fact, I would consider it unreasonable to expect this 10% of the population to graduate from eighth grade, if eighth grade completion means anything at all.

Therefore, we may conclude that high school graduation rates in the general population should by no means exceed 90%. Now let's try to get a better idea about the remaining 90%. According to Gottfredson, "Persons of average IQ (between 90 and 100) are ... easily trained for the bulk of jobs...." This suggests that we can expect people with an IQ of at least 90, which is about 75% of the population, to graduate from high school, though not necessarily in a college prep program. This is further refined by Jensen:

In his book, "Straight Talk About Mental Tests", The Free Press, A Division of the Macmillan Publishing Co., Inc., New York, 1981, pg. 12, Dr. Arthur Jensen cites the following four IQ thresholds:
(1) An IQ of 50 or below. This is the threshold below which most adults cannot cope outside of an institution. They can typically be taught to read at a 3rd or 4th grade level. However, they cannot normally function in the customary classroom setting, and they require special training programs.
(2) An IQ between 50 and 75. At this level of intelligence, they generally cannot complete elementary school. Most adults will need smarter help in coping with the world.
(3) An IQ between 75 and 105. Children in this IQ range are not generally able to complete a college prep course in high school.
(4) An IQ between 105 and 115. May graduate from college but generally, not with grades that would qualify them for graduate school.
(5) An IQ above 115. No restrictions.

(reference in http://www.geocities.com/rnseitz/Definition_of_IQ.html)


About 63% of the population is below the 105 mark in IQ, and thus not capable of completing a true college prep high school curriculum, according to Jensen.

So we now have the following breakdown:

below 75: Cannot complete 8th grade (5%)
75-80: 8th grade but not high school (5%)
80-90: High school uncertain (15%)
90-105: High school but not college prep (38%)
above 105: High school--college prep (37%)

Thus we can say that reasonable high school graduation rates, in an average community, are between 75% and 90%, no less, no more. That 15% span might be considered negotiable, and is mainly dependent on the rigor (or "dumbing down") of the high school curriculum.

Now, as I said earlier, IQ varies by group, and not all communities have the same IQ distribution. Therefore, if the distribution of a community is lower, the graduation rates should be lower as well. This is a very important point. WE CANNOT HAVE EQUAL GRADUATION RATES, with equal expectations, IN THE PRESENCE OF UNEQUAL IQ DISTRIBUTIONS.

I have long been an advocate of bringing back the eighth grade diploma, once the standard of education in the US, as a baseline level of education. I also advocate an intermediate diploma, say at the 10th grade level, which would give people who otherwise "drop out" a reasonable and achievable goal, and remove from them the stigma of being classified a "drop out" when there are jobs they are perfectly capable of doing. What is so magical about 12 years of school? For some people, 8 is enough, for others, 10 would be enough. Doing this would stem the tide of dumbing down the high school curriculum in order to get more and more people, who are not intellectually qualified, through 12 years of school. Furthermore, I advocate giving these intermediate diplomas other names, that do not relate to the years of school--so that some people may take more time and some take less to complete the requirements. Calling them, say, Basic Education Diploma, and Intermediate Education Diploma would be fine. The high school diploma should also not be rigidly connected with 12 years of school, as I believe there are students capable of attaining that level in considerably less time.

Economic and social correlates of IQ

IQ<7575–9090–110110–125>125
US population distribution52050205
Married by age 307281817267
Out of labor force more than 1 month out of year (men)2219151410
Unemployed more than 1 month out of year (men)1210772
Divorced in 5 years212223159
% of children w/ IQ in bottom decile (mothers)391767-
Had an illegitimate baby (mothers)3217842
Lives in poverty3016632
Ever incarcerated (men)77310
Chronic welfare recipient (mothers)3117820
High school dropout553560.40
Values are the percentage of each IQ sub-population fitting each descriptor. Compiled by Gottfredson (1997) from Herrnstein & Murray (1994) pp. 171, 158, 163, 174, 230, 180, 132, 194, 247–248, 194, 146 respectively.

(From http://en.wikipedia.org/wiki/IQ)

What about the correlation between low SES (socio-economic status) and the drop-out rate? We are frequently told that we need to increase the graduation rate because people who drop out are more likely to live in poverty. Of course, people who live in poverty are also more likely to drop out. Is there a cause-and-effect relationshiop? Is it cyclical? I believe that the conventional wisdom is incorrect in this area. Low SES and lack of a high school education are both related to two factors, namely low IQ and cultural attitudes about goal-setting (work ethic). Poverty, itself, is not a predicter of failure in school or in life. Next time you go to your local medical clinic, do an informal survey and find out how many of the doctors grew up in poverty. The results may surprise you. I, myself, grew up in poverty--we did not have an indoor toilet, TV, or built-in bathtub until 1973. Yet, today I hold a Ph.D. in statistics. But many who are more "succesful" than I have come from equally depressed childhoods, or worse ones. Poverty does not cause low IQ, or failure in school or life. Unfortunately in our society, low IQ is a powerful predictor of low SES, which can only be overcome by a strong work ethic. For low SES communities, it is there, and only there, that progress is possible. Students must be taught to work hard and strive for goals, so that they too can lead dignified lives.