d = d = = = 0.097 Question 4 What size sample would be needed to detect a mean difference in SAT writing scores of d = .097 when alpha = .01 power = .90 and df = 1 (as usual for two-group t-tests) Answer Total n = 6,329 so 6,329 / 2 = 3,164.5 or 3,165 participants per group. Large samples are required to detect small differences, especially with low Type 1 error rates and high power. Question 5 What happens to n in Question 4 above if we are more willing to increase the Type 1 rate to .05 and reduce power to .80? d = .097 alpha = .05 power = .80 and df = 1 (as usual for two-group t-tests) Answer Total n = 3,339 so 3,339 / 2 = 1,669.5 or 1,670 participants per group. Example: Mathematics SAT d What is ES d for the female vs male comparison of math SAT scores? Female Male Mean 499 531 Standard Deviation 114 121 n (number of participants) 883,955 776,092 Pooled SD = = 113.41 Effect size d can now be calculated using this SD: d =
d = d = = = 0.097 Question 4 What size sample would be needed to detect a mean difference in SAT writing scores of d = .097 when alpha = .01 power = .90 and df = 1 (as usual for two-group t-tests) Answer Total n = 6,329 so 6,329 / 2 = 3,164.5 or 3,165 participants per group. Large samples are required to detect small differences, especially with low Type 1 error rates and high power. Question 5 What happens to n in Question 4 above if we are more willing to increase the Type 1 rate to .05 and reduce power to .80? d = .097 alpha = .05 power = .80 and df = 1 (as usual for two-group t-tests) Answer Total n = 3,339 so 3,339 / 2 = 1,669.5 or 1,670 participants per group. Example: Mathematics SAT d What is ES d for the female vs male comparison of math SAT scores? Female Male Mean 499 531 Standard Deviation 114 121 n (number of participants) 883,955 776,092 Pooled SD = = 113.41 Effect size d can now be calculated using this SD: d =