I have done some reading about how to make sure I have enough participants for me to gain significant results for a trial I hope to run soon, but I am not sure if I'm heading in the right direction. It is completely possible that I've totally misinterpreted everything and am wrong. I need to work this out before getting further into the proposal for the research, as if I can't get a significant result then I doubt I'll get ethical approval!
I've used the tool G*POWER to determine whether I will be able to get significant results with the small sample size I have to work with: 6-8.
I understand the output from G*POWER to mean that if I intend to test for a difference of one full letter grade (here that difference would be 10%), with both groups being fairly homogeneous (SD of 2.5), I will be able to do so with 3 participants or more per group. If I test for the same difference with double the SD, I will need 7 participants per group.
Is this correct? (output below)
The test: t-test difference between independent groups (2 grps)
A priori: compute required sample size
Estimates:
grp 1 mean: 80 (%, an A grade)
grp 1 SD: 2.5 (quarter of a grade variation)
grp 2 mean: 70 (%, B grade)
grp 2 SD: 2.5 (quarter of a grade variation)
= effect size: 4
Input: Tail(s) = One
Effect size d = 4
α err prob = 0.05
Power (1-β err prob) = 0.95
Allocation ratio N2/N1 = 1
Output: Noncentrality parameter δ = 4.898979
Critical t = 2.131847
Df = 4
Sample size group 1 = 3
Sample size group 2 = 3
Total sample size = 6
Actual power = 0.988811
And with SD of 5 (half grade) for both groups (effect size 2):
Input: Tail(s) = One
Effect size d = 2
α err prob = 0.05
Power (1-β err prob) = 0.95
Allocation ratio N2/N1 = 1
Output: Noncentrality parameter δ = 3.741657
Critical t = 1.782288
Df = 12
Sample size group 1 = 7
Sample size group 2 = 7
Total sample size = 14
Actual power = 0.969582
If someone with experience in this area could please let me know if I am correct?
Thanks
I've used the tool G*POWER to determine whether I will be able to get significant results with the small sample size I have to work with: 6-8.
I understand the output from G*POWER to mean that if I intend to test for a difference of one full letter grade (here that difference would be 10%), with both groups being fairly homogeneous (SD of 2.5), I will be able to do so with 3 participants or more per group. If I test for the same difference with double the SD, I will need 7 participants per group.
Is this correct? (output below)
The test: t-test difference between independent groups (2 grps)
A priori: compute required sample size
Estimates:
grp 1 mean: 80 (%, an A grade)
grp 1 SD: 2.5 (quarter of a grade variation)
grp 2 mean: 70 (%, B grade)
grp 2 SD: 2.5 (quarter of a grade variation)
= effect size: 4
Input: Tail(s) = One
Effect size d = 4
α err prob = 0.05
Power (1-β err prob) = 0.95
Allocation ratio N2/N1 = 1
Output: Noncentrality parameter δ = 4.898979
Critical t = 2.131847
Df = 4
Sample size group 1 = 3
Sample size group 2 = 3
Total sample size = 6
Actual power = 0.988811
And with SD of 5 (half grade) for both groups (effect size 2):
Input: Tail(s) = One
Effect size d = 2
α err prob = 0.05
Power (1-β err prob) = 0.95
Allocation ratio N2/N1 = 1
Output: Noncentrality parameter δ = 3.741657
Critical t = 1.782288
Df = 12
Sample size group 1 = 7
Sample size group 2 = 7
Total sample size = 14
Actual power = 0.969582
If someone with experience in this area could please let me know if I am correct?
Thanks