# Finding an appropriate sample size?

• Feb 11th 2013, 02:23 PM
breepi
Finding an appropriate sample size?
Hi, I'd really like some help on the following issue - I've been searching the internet for over two hours now, so I'm either completely oblivious to something really obvious, or maybe I'm looking for the wrong thing?

I'm completing an assignment for my research design class, and I'm being asked to find the appropriate number of participants for a study, given an effect size of one, if I wanted to have a power of .95 in a between-subjects experiment

I know the purpose of this question is to get me to recognize the trends between effect size and number of participants, but I can't find a formula anywhere!

Thanks so much for your help!
• Feb 11th 2013, 04:42 PM
ILikeSerena
Re: Finding an appropriate sample size?
Quote:

Originally Posted by breepi
Hi, I'd really like some help on the following issue - I've been searching the internet for over two hours now, so I'm either completely oblivious to something really obvious, or maybe I'm looking for the wrong thing?

I'm completing an assignment for my research design class, and I'm being asked to find the appropriate number of participants for a study, given an effect size of one, if I wanted to have a power of .95 in a between-subjects experiment

I know the purpose of this question is to get me to recognize the trends between effect size and number of participants, but I can't find a formula anywhere!

Thanks so much for your help!

Hi breepi! :)

Here's a picture.

http://www.animatedsoftware.com/pics/stats/sgalpha.gif

The top distribution represents your H0 hypthothesis.
The bottom distribution represents your H1 hypothesis.

With your effect size, I presume you mean a Cohen's d?
If that is the case, the picture represents your problem properly: the 2 mountains are apart by a distance which is the standard deviation.

To get a power of 95%, your beta must be 5%.
You would also have an alpha of 5%.
To get alpha and beta both 5%, your need mountains that are narrower - so narrow that the situation becomes symmetric.

It means that the area where alpha begins needs to be 1.96 SE from the mean of the left mountain.
And it also means that the area where beta ends needs to bee 1.96 SE from the mean of the right mountain.
In other words, the distance of the mountains (which is sigma), needs to be 2 x 1.96 SE.

In an equation:

$\displaystyle \sigma = 2 \times 1.96 SE = 2 \times 1.96 \frac {\sigma}{\sqrt n}$

Can you solve that for n?