Data Matters with Fathom! Dynamic Statistics™ software

Activity 7.2

If you had only the sample means available, could you figure out the standard deviation of the population they came from?

To get you started, here is the relationship between the standard deviation of sample means (the standard error) and the standard deviation of the population from which the observations were drawn.

It would seem that you could multiply both sides by the square root of the sample size and get

To put it the other way,

Does that work? If you have only the sample size and some sample means, can you accurately estimate the population standard deviation?

To find out, you will take two random samples of the representative U.S. sample. Find their means and the standard deviation of the sample means. Multiply what you get by the square root of your sample size. Then check if you got a good estimate of the population standard deviation.

Open the Rep US Sample. Select Analyze, Sample Cases. Get the Collection Inspector for the sample collection, set the sample size as you want it, and add a measure. Set the formula to calculate the mean of the variable you find most interesting. (Use mean().) Click on the sample collection, then select Analyze, Collection Measures. Drag a case table onto the workspace to see the sample means. Select Analyze, Estimate Parameters, Empty Estimate, Estimate mean and drag the name of the sample means onto Variable (continuous): <unassigned>.

That gives you the standard deviation of the sample means, which is an estimation of the standard error. Multiply that by the square root of the sample size to estimate the population standard deviation.

To get its standard deviation, drag an attribute from the case table for the Collection onto the Estimate Parameter window.

How did you do? Was your estimate a good estimate?

Does it matter what the sample size is? Does it matter how many samples you work with?

What if different samples had different sizes? Could you use this equation if different samples had different sizes?