> Even where you can show statistically significant between-group differences, they are almost certain to be swamped by variability between individuals. Example: Women are, on average, slightly older than men (because of higher life expectancy). The p-value here is as close to zero as you'll get in the real world.
> But, given two randomly selected people, one male and one female, knowing the above is close to useless! The probability of the woman being older differs from 0.5 by no more than a fraction of a percentage point.
True, but sometimes it is the edges of the distribution that are really interesting, and there small differences in the mean can have a big impact.
For instance, what is the male/female ratio in nursing homes, or among people older than 100? I don't know, but I'm willing to bet that it's a noticeable difference.
Similarly true with the difference between male/female aggression as it pertains to the prison population.
> But, given two randomly selected people, one male and one female, knowing the above is close to useless! The probability of the woman being older differs from 0.5 by no more than a fraction of a percentage point.
True, but sometimes it is the edges of the distribution that are really interesting, and there small differences in the mean can have a big impact.
For instance, what is the male/female ratio in nursing homes, or among people older than 100? I don't know, but I'm willing to bet that it's a noticeable difference.
Similarly true with the difference between male/female aggression as it pertains to the prison population.