For our purposes, an important limitation of the implicit causality concept is that it takes as
given some causal background knowledge (e.g., that mothers punish daughters when they
admit guilt) and asks how people use this knowledge to make inferences about linguistic refer-
ents. Our goal in this paper is to flip this around: what happens when people know the refer-
ents but not the causal background knowledge? This situation is commonly encountered when
people are reading newspaper headlines about scientific discoveries: if scientists report that
eating ice cream increases the risk for cancer, a natural question is whether ice cream causes
cancer. Careful scientists and journalists can expunge causal language from correlation studies,
but can they expunge causal representations from the mental models of readers? To answer
this question, we undertook a series of studies that assess what kinds of causal inferences peo-
ple draw from correlational statements.
Results
We conducted three studies to examine the inference of causality from association statements.
The results of Studies 1 and 2 are summarized in Fig 1, and the results of Study 3 are shown in
Fig 2. In Study 1, participants were presented with statements of the form “X is associated with
Y” and asked to judge whether X caused Y, or Y caused X. In Study 2, participants were pre-
sented with statements of the form “X is associated with an increased probability of Y”, and
asked to make the similar causal judgments. In both studies, we ran versions with nonsense
names designed to sound similar to medical terminology (e.g., “Themaglin” or “Pneuben”) or
arbitrary letter symbols (see Methods for details).
We analyzed the data from Study 1 as follows. If participants chose the first variable as caus-
ing the second variable after being presented with the sentence “[X] is associated with [Y]”,
this was coded as 1, and if they chose the second variable as causing the first, this was coded as
0. All responses within a study were averaged together (288 responses total in the ‘nonsense
names’ condition, 291 responses total in the ‘symbols’ condition). If people were responding
randomly, we would expect the average value to be 0.5. Note that a strategy such as ‘just pick
the first answer’ is negated by the randomization of the variable order in both questions and
answers. However, the mean response for both studies was significantly below chance, by a
two-sided proportion z-test using Holm-Bonferroni correction for multiple comparisons
(‘nonsense names’ condition: M = 0.23, Z = −11.14, SE = 0.025, p < 10
−28
; ‘symbols’ condition:
M = 0.38, SE = 0.029, Z = −4.29, p < 10
−4
).
These results suggest that when given a simple association statement between two variables,
participants inferred that the second variable causes the first. Put plainly, when presented with
a sentence such as ‘Themaglin is associated with Pneuben’, or ‘X is associated with Y’, partici-
pants took this to imply ‘Pneuben causes Themaglin’, and ‘Y causes X’.
The analysis of data from Study 2 followed that of Study 1. If participants chose the first var-
iable as causing the second variable after being presented with the sentence “[X] is associated
with [RELATIONSHIP] [Y]”, this was coded as 1, otherwise the response was coded as 0. All
responses within each relationship and within each study were averaged together. Again, if
people were responding randomly, we would expect the average value to be 0.5.
We found that the addition of context drives all responses to be significantly above chance,
by a two-sided proportion z-test using Holm-Bonferroni correction for multiple comparisons
(‘nonsense names’ condition: M
risk increase
= 0.87, SE = 0.03, Z = 10.58, p < 10
−25
, M
risk decrease
=
0.94, SE = 0.02, Z = 17.91, p < 10
−71
, M
probability increase
= 0.88, SE = 0.03, Z = 11.25, p < 10
−28
,
M
probability decrease
= 0.89, SE = 0.03, Z = 12.00, p < 10
−32
; ‘symbols’ condition: M
risk increase
=
0.84, SE = 0.04, Z = 9.14, p < 10
−19
, M
risk decrease
= 0.87, SE = 0.03, Z = 10.96, p < 10
−27
, M
prob-
ability increase
= 0.86, SE = 0.04, Z = 10.30, p < 10
−24
, M
probability decrease
= 0.82, SE = 0.04, Z = 8.16,
Causal implicatures from correlational statements
PLOS ONE | https://doi.org/10.1371/journal.pone.0286067 May 18, 2023 2 / 8
additional external funding received for this study.
The funders had no role in study design, data
collection and analysis, decision to publish, or
preparation of the manuscript.
Competing interests: The authors have declared
that no competing interests exist.