stdevp( ) appears to be mislabeled

[Mike Elzinga]

(05-28-2016 06:08 PM)parisse Wrote:  By the way, it should not be that essential. I mean sqrt(n/n-1) is 1.017... for n=30, in other words your confidence interval will be almost the same for a reasonable sample size (interval length will increase by less than 2%). If you make a poll of size n=1000 we are talking of less than 0.05% change. Insisting too much on the unbiaised vs biaised stddev estimate difference might miss more important comprehension.

This is precisely what my little app is demonstrating. It is a pedagogical tool used to show where confidence intervals come from and why we use the language we do in inferential statistics.

1. First the app generates a big population of, say, 1000, with a specified normal distribution. It then checks the actual population mean and population standard deviation and plots the histogram.

2. It allows setting a sample size and takes many (on the order of 100) samples of this size and calculates the standard deviations of the sample means and the standard deviation of the sample standard deviations.

3. If desired, it can then plot a histogram of these and tell us what the standard deviation of all the sample means and standard deviation of all the sample standard deviations are. Several checks with different sample sizes show these histograms get narrower and taller as sample sizes get larger and larger, and the histograms have normal distributions.

3. It also allows incrementing the sample size by a specified amount and repeating this all the way from a small sample size up to some specified large sample size.

4. The sample sizes, the standard deviations of the sample means, and the standard deviations of the sample standard deviations are stored in lists.

5. It then plots the standard deviations of sample means versus sample size, and also the standard deviations of sample standard deviations versus sample size.

6. These plots fit very nicely sigma/sqrt(N) for the sample means, and sigma/sqrt(2N) for the sample standard deviations as expected.

The nice thing about the HP Prime is that it is so fast that it takes very little time to generate all these data and make these plots.