I'm looking for confirmation on my understanding of a 'statistically significant' effect.
For example, let's say that eating apples has a statistically significant positive effect on health (given that you can quantify health in some way). This does not mean that everyone will benefit from eating apples. Rather, it means the average individual from the population will benefit from eating apples.
This would imply that that the closer a single individual is to the the mean, the more likely they are to benefit from eating apples. The farther away an individual is from the mean, the less probable the tangible benefit from eating apples becomes.
Finally, if the above is true, how can statistically significant effects be applied at the individual level when individual effects require comparison to the mean? For example, the statistically significant result for apples is only relevant insofar that you are near the mean, but we have no idea how far any individual is from the mean without some additional metric. Is there a metric for this?
I suspect this line of thought is related to Stephen Jay Gould's "The Median Isn't the Message".