Real data collection with small population I performed an actual scientific experiment and I was only able to collect 2 data points. I am wondering what kind of statistical method I can use to analyze the data.
I performed a similar experiment before where I was able to collect 4 data points. I calculated the mean, the standard deviation of the population and a confidence interval for this population of N = 4. Could I also calculate the same things for a population of N = 2 ?
 A: Yes you can calculate sample means and standard deviations for samples of size 2 or 4.  But they are not going to be very accurate estimates for the population parameters.  Estimating or constructing confidence intervals for population parameters is usually the reason to compute them Suppose the population variance is 36.  So the standard devation is 6.  Say the population mean is 3.  For a sample of size two the variance of the sample mean is 36/2=18 and the standard deviation is approximately 4.24.  The width of a 95% confidence interval fro the mean would be 4 times the standard deviation. which is about 16.97.  so even if you were lucky enough to get a sample estimate very close to 3 the confidence interval would be awfully wide [-5.48, 11.48].  Increasing the sample size to 4 only halves the variance.  So the standard deviation is only reduced by a factor of square root of 2 = 1.414. The width of the interval is reduced from 17 to 12.  So even if the estimate of the mean is 3 the confidence interval would be [-3,9].  It is impossible to tell that the mean is greater than 0 when the sample size is this small!  Also it is not the population that is small it is the sample.  If you were sampling from a small finite population the story might be different.
