Sample size, effect size and power.

[ernie_aka]

Hi all,
I have a question I haven't been able to answer. I hope you can help me .

I use G power to estimate sample size. In my case, the estimated sample size for my desired effect size = 0.25 and power = 0,95, is 400. But the estimated sample size for an effect size = 0.5 and power = 0,95, is 107!

As far as I understand, larger effect sizes and greater power are indicators of better statistical estimates (or reduce the probability of type-I and type-II errors). Also, the larger the sample, the more accurate to the "reality". Therefore, why do I need fewer subjects when I aim for more strict parameters?

Thanks!

 

[Navaak]

Hi ernie_aka,

The larger the effect size, the easier it is to detect it. Therefore, it makes sense that you need a larger sample size to detect an effect size of 0.25, as compared to a fairly larger effect size of 0.5.
As a rough example, imagine an experiment where you use 2 different fertilizers and try to determine if there is a difference in a plant's growth. It would be easier to detect a difference in growth of, say, 2 cm than it would be to detect a difference of 1 cm.

Hope this helps!

 

[obh]

Another example:

Trying to determine which person is higher?

If you watch from a far distance (low power) you will not be able to distinguish between 178cm and 180cm (low effect)
But you will be able to distinguish between 110cm and 180 cm (high effect)

If you watch from a close distance (hight power) you will probably be able to distinguish between 176cm and 178cm.

If the people are doing squats (high standard deviation) it will be more difficult to choose which one is higher.
If they just stand with minimal moving (low standard deviation) it will be easier.

Cheers

 

[ernie_aka]

Thank you both for your time. It makes all the sense (gosh am i dumb ).