Lewandowsky’s recent article, “Role of Conspiracist Ideation” continues Lewandowsky’s pontification on populations of 2, 1 and zero.

As observed here a couple of days ago, there were no respondents in the original survey who simultaneously believed that Diana faked her own death and was murdered. Nonetheless, in L13Role, Lewandowsky not only cited this faux example, but used it as a “hallmark” of conspiracist ideation:

For example, whereas coherence is a hallmark of most scientific theories, the simultaneous belief in mutually contradictory theories—e.g., that Princess Diana was murdered but faked her own death—is a notable aspect of conspiracist ideation [30].

However, this example is hardly an anomaly. The most cursory examination of L13 data shows other equally absurd examples.

One of the more amusing ones pertains to one of Lewandowsky’s signature assertions in Role, in which he claimed, echoing an almost identical assertion in Hoax, that “denial of the link between HIV and AIDS frequently involves conspiracist hypotheses, for example that AIDS was created by the U.S. Government [22–24].”

Lew reported a correlation of -0.111 between CYAIDS and CauseHIV, citing this correlation (together with negative correlations related to smoking and climate change) as follows:

The correlations confirm that rejection of scientific propositions is often accompanied by endorsement of scientific conspiracies pertinent to the proposition being rejected.

However, as with the fake Diana claims, Lewandowsky’s assertions are totally unsupported by his own data.

In the Role survey (1101 respondents), there were 53 who purported to disagree with the proposition that HIV caused AIDS (a vastly higher proportion than in the climate blog survey – a point that I will discuss separately). Of these 53 respondents, only two (3.8% of the 53 and 0.2% of the total) also purported to believe the proposition that the government caused AIDS. It is therefore simply untrue for Lewandowsky to assert, based on this data, that denial of the link between HIV and AIDS was either “frequently” or “often” accompanied by belief in the government AIDS conspiracy. It would be more accurate to say that it was “seldom” accompanied by such belief. Although Lewandowsky did not mention this, both of the two respondents who purported to believe this unlikely juxtaposition also believed that CO2 had caused serious negative damage over the past 50 years.

Lewanowsky’s assertion in Role about a supposed link between denial of a connection between HIV and AIDS and a government AIDS conspiracy had been previously made in Hoax not just once, but twice:

Likewise, rejection of the link between HIV and AIDS has been associated with the conspiratorial belief that HIV was created by the U.S. government to eradicate Black people (e.g., Bogart & Thorburn, 2005; Kalichman, Eaton, & Cherry, 2010)…

Thus, denial of HIV’s connection with AIDS has been linked to the belief that the U.S. gov¬ernment created HIV (Kalichman, 2009)

However, Lewandowsky’s false claim received even less support in the survey of stridently anti-skeptic Planet 3.0 blogs. Even with fraudulent responses, only 16 of 1145 (1.4%) purported to disagree with the proposition that HIV caused AIDS, and of these 16, only 2 (12.5%) also purported to endorse the CYAIDS conspiracy. These two respondents were the two respondents who implausibly purported to believe in every fanciful conspiracy. Even Tom Curtis of SKS argued that these responses were fraudulent. Without these two fraudulent responses, the real proportion in the blog survey is 0. Either way, the data contradicts Lewandowsky’s assertion that disagreement with the HIV-AIDS proposition is “often” or “frequently” accompanied by belief in the government AIDS conspiracy at the climate blogs surveyed by Lewandowsky.

Even though there were even fewer respondents supposedly subscribing to the unlikely propositions in the blog survey, the negative correlation between CYAIDS and CauseHIV propositions was even more extreme: a seemingly significant -0.31, though only the two fake respondents purported to hold the two unlikely propositions.

Update: I’ve added some plots below to illustrate how Lewandowsky’s calculations of correlation go awry.

The contingency table of CauseHIV and CYAIDS for the L13Hoax data is shown below, with the size of each circle proportional to the count in the contingency table. Most of the responses are identical – thus the large circle. Because there are only two respondents purporting to hold the two most unlikely views, this is a very faint dot. A correlation coefficient implies a linear fit and normality of residuals: visually this is obviously not the case. There are a variety of tests that could be applied and the supposed Lewandowsky correlation will fail all of them.

If one goes back to the underlying definition of a correlation coefficent, it is a dot-product of two vectors. In the context of a contingency table, this means that the contribution of each square in the contingency table to the correlation can be separately identified. I’ve done this in the graphic shown below, since the points, while elementary, are not immediately intuitive in these small-population situations. For each square in the contingency table, I’ve calculated the dot-product contribution and multiplied it by the count in the square, thereby giving the contribution to the correlation coefficient (which is the sum of the dot-product contributions.) The area of each circle shows the contribution to the correlation coefficient: pink shows a negative contribution.

There are a few interesting points to observe. In a setup where nearly all the responses are identical and at one extreme, these responses make a positive contribution to the correlation coefficient. Responses in which the respondent strongly disagrees with CYAIDS but only agrees with CauseHIV or in which the respondent strongly agrees with CauseHIV but only disagrees with CYAIDS make a negative contribution to the correlation. Respondents with simple agreement with CauseHIV and simple disagreement with CYAIDS make a strong contribution to the correlation coefficient. The two (fake) respondents make a very large contribution to the correlation coefficent despite only being two responses.



