Every user of statistics should understand the distinction between statistical significance and practical importance. a sufficiently large sample will declare very small effects statistically significant. let us suppose that sat mathematics (sat) scores in the absence of coaching vary normally with mean μ = 500 and σ = 100. suppose further that coaching may change μ but does not change σ. an increase in the sat score from 500 to 503 is of no importance in seeking admission to college, but this unimportant change can be statistically very significant. to see this, calculate the p-value for the test of the given hypotheses in each of the following situations.