In the "Introducing Statistics" section of Intuitive Biostatistics, the author explains how probability and statistical thinking are not, in fact, intuitive. As humans, our brains are hardwired to look for patterns, even in data that was actually randomly generated. As an example of this, the author points out that coincidences are actually much more common than we realize because "it is almost certain that some seemingly astonishing set of unspecified events will happen often, since we notice so many things each day" (p. 5).
I have often noticed that soon after I learn a new word, I will repeatedly hear that word used over the next several days, even though I could never remember hearing it before in my life. This happened to me a lot when we learned SAT vocab in high school English, I remember repeatedly hearing and reading the word "gregarious" outside of class after first learning what it meant. Apparently this is a common enough phenomenon that it has a name; it's called the "Frequency Illusion" (or the "Baader-Meinhof Phenomenon"). Basically, learning a new word primes the brain to pay more attention when that word is heard again. I probably heard "gregarious" no more often during my sophomore year of high school than in the previous fifteen years of my life, but because my brain was more aware of this word right after I learned it, it seemed like I was hearing it all the time.
This example illustrates how pattern-seeking and unconscious biases can influence our perceptions, even in the most mundane of situations. Because scientists are also human, our interpretation of our findings can also be affected by these cognitive biases. Statistics and rigorous experimental design are imperative to prevent our biases from clouding our scientific judgement, causing us to seek results where no pattern actually exists.