  Automatic machine learning-based detectors of various psychological and
social phenomena (e.g., emotion, stress, engagement) have great potential to
advance basic science. However, when a detector $d$ is trained to approximate
an existing measurement tool (e.g., a questionnaire, observation protocol),
then care must be taken when interpreting measurements collected using $d$
since they are one step further removed from the underlying construct. We
examine how the accuracy of $d$, as quantified by the correlation $q$ of $d$'s
outputs with the ground-truth construct $U$, impacts the estimated correlation
between $U$ (e.g., stress) and some other phenomenon $V$ (e.g., academic
performance). In particular: (1) We show that if the true correlation between
$U$ and $V$ is $r$, then the expected sample correlation, over all vectors
$\mathcal{T}^n$ whose correlation with $U$ is $q$, is $qr$. (2) We derive a
formula for the probability that the sample correlation (over $n$ subjects)
using $d$ is positive given that the true correlation is negative (and
vice-versa); this probability can be substantial (around $20-30\%$) for values
of $n$ and $q$ that have been used in recent affective computing studies. %We
also show that this probability decreases monotonically in $n$ and in $q$. (3)
With the goal to reduce the variance of correlations estimated by an automatic
detector, we show that training multiple neural networks
$d^{(1)},\ldots,d^{(m)}$ using different training architectures and
hyperparameters for the same detection task provides only limited ``coverage''
of $\mathcal{T}^n$.
