6.99 Practical significance and sample size. 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. Consider the study of elite female Canadian athletes in Exercise 6.74 (page 382). Female athletes were consuming an average of 2403.7 kcal/d with a standard deviation of 880 kcal/d. Suppose that a nutritionist is brought in to implement a new health program for these athletes. This program should increase mean caloric intake but not change the standard deviation. Given the standard deviation and how calorie deficient these athletes are, a change in the mean of 50 kcal/d to 2453.7 is of little importance. However, with a large enough sample, this change can be significant. To see this, calculate the P-value for the test of
H0: μ = 2403.7
Ha: μ > 2403.7
in each of the following situations:
(a) A sample of 100 athletes; their average caloric intake is .
(b) A sample of 500 athletes; their average caloric intake is .
(c) A sample of 2500 athletes; their average caloric intake is .