  We show that publishing results using the statistical significance
filter---publishing only when the p-value is less than 0.05---leads to a
vicious cycle of overoptimistic expectation of the replicability of results.
First, we show analytically that when true statistical power is relatively low,
computing power based on statistically significant results will lead to
overestimates of power. Then, we present a case study using 10 experimental
comparisons drawn from a recently published meta-analysis in psycholinguistics
(J\"ager et al., 2017). We show that the statistically significant results
yield an illusion of replicability. This illusion holds even if the researcher
doesn't conduct any formal power analysis but just uses statistical
significance to informally assess robustness (i.e., replicability) of results.
