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## Race and Crime: A Reply to Cernovsky and Litman

(response to Z.Z. Cernovsky and L.C. Litman, Canadian Journal of
Criminology, vol. 35, p. 31, 1993) (Canada)

Summary: The extension of statistical analysis by Cernovsky and Litman was
based on erroneous assumptions about the interpretation of variance and
correlation statistics, and, therefore, their criticism of the results of the
research was unwarranted. There is statistical justification for risk
avoidance behavior that is based on the identification of certain individual
characteristics such as age, sex and other variables.

J. Phillipe Rushton

Canadian Journal of Criminology, Jan 1994 36 n1 p79-82

In a critique of my work, Cernovsky and Litman (1993) reproduced a table
that I constructed from INTERPOL data showing that African and Caribbean
countries reported twice the amount of violent crime (murder, rape, and
serious assault) as European countries and three times that of countries from
the Pacific Rim (Rushton 1990). Summing the crimes and averaging the years
gives figures per 100,000 population, respectively, of 143, 74, and 44. These
proportionate racial differences are similar to those found using official
statistics from within the United States (Wilson and Hernstein 1985).

I used a standard 1-way ANOVA design to test whether these huge
proportionate differences in mean levels of crime were statistically
significant given the variance involved and found that they were. Cernovsky
and Litman (1993) deconstructed these aggregates, first into pair-wise per
crime t-tests, then into point biserial correlations, then into a metric of
variance accounted for, and finally into the non sequitur that the prediction
of crime in individual cases would result in 99.9% false positives!

Cernovsky and Litman's conclusions do not follow from their analyses. The
"percent variance accounted for" argument is statistically correct but
substantively erroneous, as discussed at length by Rosenthal (1984) and Hunter
and Schmidt (1990). The [r.sup.2] (and other indices of percent variance
accounted for) are related in only a very nonlinear way to the magnitude of
effect sizes that determine impact in the real world. Small correlations can
have large impacts.

Rosenthal (1984) and Hunter and Schmidt (1990) provide numerous examples of
how a "small" effect can have major practical consequences. I have transformed
some of their examples from medical procedures and personnel selection into
those concerned with criminal justice. Thus, in selection for parole, a
validity coefficient of 0.40 should not be squared to mean that only 16
percent of the variance of recidivism is accounted for. Instead, using
regression predictions, it means that for every 1 standard deviation increase
in mean score on the selection procedure, a gain of the magnitude of a 0.40
standard deviation will result in outcome success -- a substantial increase
with considerable practical value. An effect size of even 0.10 for a parole
procedure, for example, would increase the chance of success from 50:50 to
55:45.

A relatively small difference at the mean can generate rather large
differences at the tails of the distributions (where most repeat offenders are
to be found). A correlation of .16 for a greater black than white likelihood
to break the law would mean that, at the 95th percentile of the distribution,
about 7 percent of the perpetuators would be black and 4 percent would be
white, a ratio of nearly 2:1. The Asian versus African correlations reported
by Cernovsky and Litman (1993) based on INTERPOL data were double this
([gamma]= .32).

A correlation of 0.32 between a treatment and an effect means that an
effect that accounts for only 10 percent of the variance could reduce the
crime rate by almost 50 percent (Rosenthal 1984: 130). It is, therefore, quite
rational for the public to attempt to reduce their chance of being victimized
by avoiding individuals with perpetrator characteristics (age, sex,
socioeconomic and other variables such as race; Rushton 1990). Thus Cernovsky
and Litman's (1993: 34) chastising me for commenting in the media is
inappropriate.

Levin (1992) has examined some of the resulting philosophical issues about
probable risk assessment and the rights to risk avoidance raised by the
disproportionate differences. Levin holds that the taking of differential
precautions is both logically and morally justified. He cites a parallel with
rational choice theory in economics and rejects the arguments that
differential perceptions of dangerousness are the result of "illusory
stereotypes".

Cernovsky and Litman (1993: 35) cite a number of published critiques for a
"plethora" of technical errors that I am supposed to have made. For example,
they claim that I "erroneously" listed as supportive the large-scale study of
cranial capacity by Beals. Smith, and Dodd (1984). It is Cernovsky and
Litman's interpretation of this study that is in error and I refer the reader
to tables 2 and 5 in Beals et al. (1984) so that they can see for themselves
the hard data and statistically significant population differences in
[cm.sup.3]. Irrespective of interpretation, the rank ordering in this world
review is in accord with my prediction. Cernovsky and Litman also fail to
mention more recent empirical support for my hypotheses (Ellis and Nyborg
1992; Rushton 1992).

References

Beals, K.L., C.L. Smith, and S.M. Dodd 1984 Brain size, cranial morphology,
climate, and time machines. Current Anthropology 25: 301-330.

Cernovsky, Z.Z. and L.C. Litman 1993 Re-analyses of J.P. Rushton's crime
data. Canadian Journal of Criminology 35: 3