Statistics is not the core of psychology, it is the core of having a publishable result. Psychologists want to do just enough statistics that they can claim to

Statistics is not the core of psychology, it is the core of having a publishable result. Psychologists want to do just enough statistics that they can claim to have a p-value<0.05 so they can get it into a journal. They don't care if their assumption of normality is correct, or if their assumption of independence is correct, or if the question they asked on the survey is actually measuring the thing they want to measure (spoiler alert: it usually doesn't, but we have a hard time measuring the brain). So they willfully ignore the assumptions because acknowledging that they were violated would mean that they would have to learn more complicated statistical methods. The current use of stats in psychology is just an attempt to make it look like their research is rigorous, when in reality it is usually broken. The ideas of the scientific method are fine in psychology, but since most studies use WIERD samples, don't be surprised that many of those results don't generalize to other demographics.