To me, a prime and highly relevant example is the science around SHS. As a non-vaper / smoker, I cared about the science around that topic, but didn't pay much attention to it. Now as a vaper, I pay a lot more attention to it, and it seems corrupted to me at this time. As in SHS has lots of memes widely known and associated with it, but all of which no longer show up as exactly credible to me.
Here's a report and analysis that came out in Cato Institute's 'Regulation' magazine in 1993, shortly after the first EPA ruling on second hand smoke. It showed the truly junk science used - skewing results and using non-standard statistical tools used in order to come to a 'predetermined' results just barely over the statistical significant number needed to go to press release.
http://object.cato.org/sites/cato.org/files/serials/files/regulation/1993/7/v16n3-5.pdf
It's long, but if you want to know exactly what junk science is, this is a good example.
A significant part:
Manipulation of Data
"Is the EPA meta-analysis
** a scientifically valid
manipulation of data? Combining data and undertaking
a meta-analysis are valid procedures under
appropriate circumstances. But in order to make
the outcome value of their meta-analysis "valid"
and "statistically significant," the EPA first had to
adjust the data as originally published in
peer-reviewed literature and, second, they had to
broaden the confidence intervals to a scientifically
unconventional level of 90 percent.
When a number of studies are combined, the
confidence intervals generally are "ratcheted
down," or tightened, to assess significance; the EPA
did just the opposite and in so doing diminished its
report's scientific value. Lowering of statistical
standards to make valid otherwise unmeaningful
results is an unusual and dubious scientific practice.
In the past, the EPA has employed 95 percent
confidence levels as a measure of scientific validity.
Had the EPA done so in this case, or had it not
adjusted the original data, its analysis would not
have had the same outcome. If the EPA had included
all of the available published data, and not just
11 of 13 studies, its outcome assessment also would
have been different. The manipulation of data in
this manner to develop statistical significance permitted
the EPA to declare passive smoking a Group
A carcinogen-the highest rank possible. Without
the recalculations and manipulations, the EPA
would have not met any of the three classic criteria
for establishing risk.
A relative risk of 1.19, even if the data were
not manipulated, is extremely weak. It is of the
same general magnitude as the risk that an
American citizen faces of dying in a bicycling
accident over the course of a lifetime. It is a risk
that is less than that associated with developing
colon cancer by drinking chlorinated water,
which is in most U.S. cities' water supplies. It is
generally accepted in the medical literature that
any time a relative risk is less than 2.0, the distinct
possibility exists that the finding is artifactual
and a consequence of the influence of confounding
factors."
** "meta-analysis"
Instead of just gathering the data from all the epidemiological studies submitted, because doing it that way didn't get their 'desired result', the EPA did a 'meta-analysis' of only 11 cherry picked studies, and then changed the standard statistical 'confidence interval'.