This is the study the article mentions.
Does the study have those conclusions?
Not really. The experimental results could equally be explained by a simpler conclusion, that people are less likely to ask others out when they feel disappointed, deflated or embarrassed by something (in this case, the public revelation of a poor test result). The researchers acknowledge that such an explanation is potentially valid and supported by prior research on "affective experience", and acknowledge this as a limitation.
It's also just one study, on about 100 U.S. psychology undergraduates, with a systemic bias excluding more intelligent students. It therefore can't be generalized without being replicated on other populations.
Here's an example of the kind of target used by the study:
Seventy-three male undergraduates (Mage = 18.95) participated in a “Study of Interpersonal Attitudes” in exchange for psychology course credit.
Age, field of study and personal maturity are confounding factors on psychological behavior. As such, the news reporting by "The Independent" is incorrect and misleading.
Is the study reputable/reliable?
While the study is "serious science", is being peer-reviewed (or is in pre-print) and is quite interesting, the methodology has systematic bias against intelligent men, and the conclusions are not supported by the experiment set-up: the study merely shows that embarrassing or diminishing people in front of a potential date makes them feel a bit more antagonistic towards her. Likewise, it shows that flattering people in front of a potential date makes them feel more sympathetic and likely to ask them out. As reported, it does not measure anything else.
Systematic bias
The study in question consists in letting participants take a math test, and then be told that their result was average.
After a few minutes, the experimenter returned with the
“graded” tests and announced their scores while handing
back the tests. Participants always got 12/20 questions
correct
At the end of the experiment, they were asked whether they believed the results and were discarded if they did not. This is a clear systematic bias because it excludes all candidates that are smart enough to expect a nearly perfect score and know that they can't possibly have an average result.
[P]articipants
responded to the following questions in written form: “What
do you think this experiment was about? Was there anything
odd or suspicious about this experiment? If yes, what?”
Responses were later coded for whether participants
mentioned (a) that their partner was not real or part of the
study or (b) thought their test score was fake. Participants
who reported suspicion on one or more of these items were
excluded from analyses.
In fact, it excluded 10% of the participants.
Participants and Procedure
Ninety male undergraduates participated in a “Study of
Interpersonal Attitudes” in exchange for psychology course
credit. Nine participants were excluded because they were
suspicious of the confederate or did not believe the test
feedback; the final sample consisted of 81 participants
(Mage = 18.81).
Validity
First an experiment is set up where the fake results are given in a separate room from the potential date. In this case, performing worse than the date predicts more likelihood to ask the partner out or find them attractive.
Secondly another experiment is set up so that the fake results are given in front of the potential date. In this case, performing better than the date predicts more likelihood to ask the partner out or find them attractive.
I don't see how that supports that "men are threatened by intelligent women". It simply shows the obvious result that when someone's ego is boosted by good results they are more optimistic and when their ego is deflated they become timid.
The authors themselves admit to that, although they simply dismiss this as a "limitation".
Previous research suggests that when people interact with
a potential partner in a live context (e.g., spatially near
context), they rely primarily on their affective experience—
positive or negative—to determine their attraction toward
the target (Eastwick et al., 2014). In addition, research on
SEM suggests that people experience negative feelings
(e.g., jealousy) when they are outperformed in a self-
relevant domain (Salovey & Rodin, 1984). Together, these
two strands of research suggest that men who interacted with
a female confederate in the near condition may have felt
badly when they were outperformed in a self-relevant domain
such as intelligence, and these feelings shaped their evaluations of the confederate. Although we did not measure feelings of jealousy in the present studies, we did assess self-rated
masculinity, which produced mixed results.