Blog by Emily Oster: “…When we say an effect is “statistically significant at the 5% level,” what this means is that there is less than a 5% chance that we’d see an effect of this size if the true effect were zero. (The “5% level” is a common cutoff, but things can be significant at the 1% or 10% level also.)
The natural follow-up question is: Why would any effect we see occur by chance? The answer lies in the fact that data is “noisy”: it comes with error. To see this a bit more, we can think about what would happen if we studied a setting where we know our true effect is zero.
My fake study
Imagine the following (fake) study. Participants are randomly assigned to eat a package of either blue or green M&Ms, and then they flip a (fair) coin and you see if it is heads. Your analysis will compare the number of heads that people flip after eating blue versus green M&Ms and report whether this is “statistically significant at the 5% level.”…(More)”.
