Question - 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 a study of elite female Canadian athletes that investigated whether elite athletes are deficient in their nutritional intake. A total of n = 201 athletes from eight Canadian sports centers participated in the study. Female athletes were consuming an average of 2403.7 kilocalories per day (kcal/day) with a standard deviation of 880 kcal/day. The recommended amount is 2811.5 kcal/day.
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 caloric deficient these athletes are, a change in the mean of 50 kcal/day 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
Ho: μ = 2403.7
Ha: μ > 2403.7
in each of the following situations:
(a) A sample of 100 athletes; their average caloric intake is x- = 2453.7.
(b) A sample of 500 athletes; their average caloric intake is x = 2453.7.
(c) A sample of 2500 athletes; their average caloric intake is x- = 2453.7.