Dr. Paul H. Blackman writes:
But let's get back to the estimates of gun ownership by the cases and
the controls.
OK. Unlike Dr Suter's straw man argument this is a real threat to the
study. If gun ownership of the cases is under-reported more than gun
ownership of the controls is under-reported, the correlation between
guns and homicide is weakened. If gun ownership of the cases is
under-reported LESS than gun ownership of the controls is
under-reported, the correlation between guns and homicide is
strengthened.
The cases were, of course, proxies for them. But the situation was
that a homicide occurred in that home, allowing a certain amount of
searching by law enforcement, esp. if guns were involved.
Kellermann did not use reports from law enforcement to measure gun
ownership. (If he had, the ownership rates for cases would have been
higher.)
In addition,
Kellermann et al. waited about a month after the homicide to contact
the proxies who were hoped to be persons living in the home, certainly
relatives, who almost certainly were going through the remains in the
course of the month, thus allowing more truthful statements than might
otherwise have been the case, with no temptation to lie.
Fair enough, if case proxies found guns that they were unaware of
before the killing, this would weaken the correlation.
Controls: The survey relied upon by Kellermann et al. fails to show
that ordinary people admit gun ownership to strangers. Kleck's
appendix on the topic, and the Bordua et al. survey and other studies
of Illini indicates that people often don't tell authorities about guns
(in the Illinois case, a FOIA card) but will admit it to survey
research,
Kellermann's study did not rely on something like a FOIA card, but
survey research.
and in other instances will lie. Surveys generally show such
a dramatically lower reporting of guns by women than of men --- when
household ownership is the question --- as to suggest a substantial
understatement when asking "controls" such as these.
Controlling for this factor will strengthen the correlation. Consider:
-
Data for the cases was based solely on proxies while about half the
data for controls was obtained from the controls themselves rather
than proxies. -
Cases were mostly male.
-
Controls were matched by sex so were also mostly male.
-
Consequently, proxies were more likely to be female than the controls
-
If women are more likely to under report it follows that this
underreporting would be greater for the cases than for the controls,
thus strengthening the correlation.
This possibility is, however, undercut by one factor that would
weaken the correlation that you did not mention:
the proxies for the controls reported a higher rate of gun ownership
than the controls did. Kellermann implies that the difference was
small, but I would have like to have seen an analysis stratified by
proxy/non-proxy.
It would have
taken about 11 controls falsely denying guns in their homes for the
statistical significance of Kellermann et al.'s crude odds ratio to
disappear.
Or, to put it another way, the difference in the crude odds ratio
would disappear if 35 more controls falsely denied than cases did.
The odds are good there were 20-40 false denials.
This is a pure guess. We do know that at least 8 cases falsely
denied.