Statistic: Compare

Question

If you have same information and only changes the sample size, describe the differences in σ and probability.

Answer 1

Changing the sample size has no effect on σ, assuming you are using that symbol in the conventional sense.

σ refers to the population standard deviation, not the sample standard deviation. So, σ is unaffected by the change in the sample size.

For example, if you are trying to get insight into the variability (specifically, standard deviation) of IQ in the United States, you may take a random sample of some size, say 1000. From that sample, you can estimate a mean and a standard deviation. If you try again with a larger sample size (or if you try again with the same sample size but a new sample), you will get a different estimate of standard deviation. But none of your analysis or sample sizes actually affects the true variability of IQ across the US population.

If you are asking about the effect of sample size on the sample standard deviation (usually denoted as S), one basic answer is that a higher sample size results in a sample standard deviation that is closer to the population standard deviation. In other words, the more data you have, the better an estimate you will get.

As far as the differences in probability, please be more specific.

Hope that helped :-)