The best sample size is difficult to give a general answer for. There are different types and degrees of autism, you probably want a representative sample from that perspective. You will also need a control group to compare against. There may also be other biases that you should consider, for example selecting a representative sample from different ethnic and social groups etc. If you use a stratified sampling technique, then you might need different sample sizes for different strata etc. The best idea is probably to look at research papers in a similar area and copy their sampling strategy for a start. If possible, make sure that you exceed the minimum amount of samples to reduce the possibility that your experiment is not valid due to factors that are out of your control, such as outliers etc.
Dear Nils, many thanks for your answer. It is very helpful. I have a representative sample of high risk and low risk group. in our country, we have one ethnic group, though social group could be an issue to be considered. appreciate your reply.
Determining the sample sizes involve resource and statistical issues. Usually, researchers regard 100 participants as the minimum sample size when the population is large. However, In most studies the sample size is determined effectively by two factors: (1) the nature of data analysis proposed and (2) estimated response rate.
For example, if you plan to use a linear regression a sample size of 50+ 8K is required, where K is the number of predictors. Some researchers believes it is desirable to have at least 10 respondents for each item being tested in a factor analysis, Further, up to 300 responses is not unusual for Likert scale development according to other researchers.
Another method of calculating the required sample size is using the Power and Sample size program (www.power-analysis.com).