Do outliers affect bivariate correlation? I recently found a significant positive correlation for three variables (anxiety, depression, and Fear of Missing Out). FOMO is my variable of interest. 
I did a one sample t-test to measure the scores for FOMO in relation to the cut off score (22-meaning that participants are at risk for FOMO), it showed that participants on average scored less than 22, indicating they do not experience Fear of Missing Out, so I'm really confused as to how there's a positive bivariate correlation yet participants scored significantly less?
I'm wondering if the outliers may have caused the positive correlation among the three variables. 
 A: Yes, even a single outlier in a moderately large bivariate sample can have a marked influence on sample correlation. 
Here is an extreme contrived example:
Variables $X$ and $Y$ are simulated (in R) as independent samples of size $n = 100,$ both from $\mathsf{Norm}(\mu=50,\, \sigma=3).$ The sample correlation is $r = 0.078 \approx 0.$
set.seed(2019)  # for reproducibility
x = rnorm(100, 50, 3);  y = rnorm(100, 50, 3)
cor(x, y)
[1] 0.07750579
plot(x, y, pch=20)


Now I add a far outlier at $(150, 150).$ The sample correlation changes to $r = 0.93.$
x1 = c(x, 150);  y1 = c(y, 150)
cor(x1,y1)
[1] 0.9314391
plot(x1, y1, pch=20)
  points(150,150, col="red")  # emphasize outlier


Note: The default method of computing correlation in R is Pearson's. If you use the argument meth="s" in the function cor, then
R will compute Spearman's rank correlation (Pearson's correlation on the ranks). The outlier
has minimal influence on Spearman's correlation; the outlier has rank 101 for both variables:
cor(x, y);  cor(x, y, meth="s")
[1] 0.07750579  # Pearson without outlier
[1] 0.1491509   # Spearman without outlier
cor(rank(x), rank(y))
[1] 0.1491509   # Spearman (again) w/o outlier

cor(x1, y1);  cor(x1, y1, meth="s")
[1] 0.9314391   # Pearson with outlier
[1] 0.1741759   # Spearman with outlier

