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!

breepi said:

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!

Click to expand...

Have you looked for the Sampling Theorem?

Suppose there is a population distribution with mean \(\displaystyle \mu\) and standard deviation \(\displaystyle \sigma\). The Sampling Theorem says that if you look at the distribution of random samples of size N taken from the population will have the same mean as the population, with standard deviation reduced by a factor \(\displaystyle \sqrt{N}\). That is,
mean of sample means = \(\displaystyle \mu\)
standard deviation of sample means = \(\displaystyle \sigma \ /\sqrt{N}\)
The distribution of sample means will "always" be a normal distribution, so you can work out the 95% confidence limit from tables.

I don't know all the jargon - in particular I don't recognize "effect size of one." If you need more help, post a reply showing all the work you have done, and explaining what the terms mean.

Thanks so much for replying!!

I honestly don't have much work done - I'm just so confused by this whole thing...

The effect size is assumed =1 , but in the previous questions I found it by using (mean of population A - mean of population B)/Standard Deviation

The question just reads "Assume you have an effect size of 1. How many participants would you need to have power of .95 in a between subjects experiment?"

breepi said:

Thanks so much for replying!!

I honestly don't have much work done - I'm just so confused by this whole thing...

The effect size is assumed =1 , but in the previous questions I found it by using (mean of population A - mean of population B)/Standard Deviation

The question just reads "Assume you have an effect size of 1. How many participants would you need to have power of .95 in a between subjects experiment?"

Click to expand...

I find this discussion at
http://www83.homepage.villanova.edu/richard.jacobs/EDU%208603/lessons/stastical%20power.html
"The basic formula to calculate the effect size is to subtract the mean of the control group from that of the experimental group and, then, to divide the numerator by the standard deviation of the scores for the control group. " That corresponds exactly with your statement "(mean of population A - mean of population B)/Standard Deviation." It means there is one standard deviation of difference between the control group and the experimental group.

Are you doing "hypothesis testing," where you set up a null hypothesis and then find a critical statistic to see whether you can reject the null hypothesis?

Perhaps what you need is Student's t-Distribution. The "power" of a test is the probability of detecting a real difference between the means (when there really is a difference). The handbook I use has a table (in the section on the t-Distribution) called "Number of Observations for t-Test of Difference between Two Means." The statistic is
\(\displaystyle \triangle = \dfrac{\mu_1 - \mu_2}{\sigma}\)
which is the "effect size," given to be 1.00. For power = 0.95, the parameter \(\displaystyle \beta\) = 1 - power = 0.05. There is another parameter \(\displaystyle \alpha\) which gives the risk of rejecting when true .. I think you could also make that 0.05. In that case the table gives me 27 for the required number of observations.

If you have never heard of the t-Distribution, then none of that paragraph is very useful. What distributions DO you know about?