Psychometric sample size requirements

Good afternoon,

What is the guidance for psychometric sample size requirements?

For instance, say I developed a psychometric tool to assess resilience with scores ranging from 0 to 100.
Let’s say, the Los Angeles County Unified School District has agreed to use my tool to assess resilience for High School students.
Before the tool is used to establish a resilience baseline, I want to know how many subjects I need to ensure they are representative of 100,000 High School students in the district.

Please advice.
Regards, Al
You need an idea of how large the standard deviation of your measurement might be.
Then you can use a formula which gives you the standard error for your sample mean,
depending on sample size and standard deviation. The formula is
standard error = standard deviation/square root of sample size.

For example, if resilience has a standard deviation of 30, then the standard error would be
30/square root of 100 = 30/10 = 3 .

Now, with your standard error you can compute a conficence interval for your
sample mean, which gives you an idea how precise your estimates will be.

For the limits of a 95% confidence interval around your mean, you multiply the
standard error with 1.96. This would result in a confidence interval of +/- 5.9 points
around the mean. For a 90% interval, multiply with 1.65.

You can play around with this using e.g.
Mind that the assumed standard deviation is crucial.

Which precision you want to achieve by increasing your sample size, is up to your
judgement, or up to the requirements of your customer.

Just my 2pence

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