Hello Hsin-Yuan,

I would urge you to rely on the G*Power approach; it makes far more sense to have a justifiable basis for sample size that is fitted to the needs of your particular study than to rely on generic "rules of thumb," which might or might not apply to your circumstances. For your study, 50 cases might be far too many or far too few (or, like Goldilocks and the Three Bears: "just right"). It depends considerably on how large or small an effect (difference or relationship, depending on the outcome of interest) you and others deem worthy of paying attention to (should it exist in the population).

How many is too many? If data collection costs nothing (in time, money, personnel, or supplies), then, the more the merrier! However, if your study is all about hypothesis testing, too large a sample will result in a situation in which trivially small effects are sufficient to trigger a statistically significant result. The precision of parameter estimates will be better (than with a smaller sample), but you might well discover that the obtained effect is too small to be judged noteworthy in a practical sense.

Good luck with your work!

Your supervisor is likely giving you an upper-bound heuristic to target in-anticipation of losing participants or other distributional challenges that will hinder your n=30 power assumption for detecting effects (e.g., dropout, latent skewness, etc.). Frankly, if you want to contend with your advisor on something, make it something more meaningful (substantive) than N=30 vs N=50.

Hope this helps,

Matt

The sample size depends on the type of your population, is it finite population or infinite population.

In the case of finite population,

use Slovin formula:

n= N / ( 1+ N * e^2 )

But in the case of an infinite population:

The sample size for any study depends on the standard deviation of the variable ( from previous studies ) and the margin of error you decided. The formula:

n= ( Z^2 * S^2) / E^2

where : Z ( 1.96 for 0.05 and 2.58 for 0.01 )

S = standard deviation from previous studies or pilot study

E = significant level

Also, you can use software to calculate sample size ( SPSS , Minitab , G*power )

My advice to use G*Power . G*Power software is effective tool to calculate sample size for many ranges of experiments.

Good Luck

David Morse

Dear Professor Morse,

Thanks for your reply and sorry to reply to you so late. I was busy running experiments recently. Your answer is fabulous. I will re-think the issue based on your perspective. In my research, I used G*Power approach and refer to the previous paradigms of relevant research to justify how many subjects I need to collect (although I found many authors in published journals who do not explain how they decide the sample size). My studies are about hypothesis testing; I did not consider the effect of sample size. I will consider the advantages and disadvantages of different sample sizes.

Best regards,

Chen

Matthew Kerry

Dear Dr Kerry

Thanks for your reply and sorry to reply to you so late. Regarding the upper-bound heuristic to target in-anticipation of losing participants, I am not sure I understand what you mean. Could you clarify what you mean by the upper-bound heuristic in my case? I am interested in it, but I did not figure out it even I read some documentation on the website. Thanks in advance. In addition, concerning the possibility of distributional changelings, I agree with your opinion, and I will try to make it more meaningful on the number of sample sizes.

Best regards,

Chen

Khalid Hassan

Dear Professor Hassan,

Thanks for your reply and sorry to reply to you so late. I supposed my population is a finite population. It is helpful for your explanation on the formula of sample size. I will take consideration of sample sizes based on a standard deviation and significant level of X. Regarding the software for counting sample sizes, I am using G*Power to calculate it.

Best regard,

Chen