Sampling distribution is such an elaborate topic that whatever information obtained from various resources can be used to understand the concept better. Textbook definition of sampling distribution is; it is a theoretical probability distribution of all possible sample values for the statistics in which we are interested. There are couple of internet sources I found which explains and illustrates the concept of sampling distribution in depth.

Below is the link to the first internet resource,

http://stattrek.com/sampling/sampling-distribution.aspx

This link provides in depth description of the all the statistical methods. It also includes a page dedicated to sampling distribution. This link has many textbook definitions and explanations. However, it also contains some more details related to the sampling distribution. It gives detailed account of sampling distribution of the proportion. There is also a section for online normal distribution calculator which makes it easy to compute cumulative probability. The sampling distribution lesson on this given link also provides 2 examples to understand the concept better. These examples also include the calculations for their solutions.

Below is the link to another internet resource which I found very interesting,

http://onlinestatbook.com/stat_sim/sampling_dist/

This is link to simulation which lets you explore various aspects of sampling distributions. It shows histogram of a normal distribution at the top and lets you adjust the sample size. It also lets you to choose a statistic like mean, standard deviation of the sample, variance and range. The best part about it is that it calculates and shows the comparison between different sample sizes of the sampling distribution. There is also an option to select number of repetitions which allows us to understand that with increasing size of the sample, the variability decreases. I found it to be a fun and interactive way of learning the sampling distribution which cannot be done with help of only textbook.

Here is the screenshot of the simulation,

In this screenshot the repetitions are 100 and we can see the comparison between sample size 10 and sample size of 20. The histogram looks more normal for sample size 20 than for sample size 10.

After reading the first internet resource and using second link for simulation of sampling distribution; do you have any more facts you liked about these two internet resources? Did they help you learn more about sampling distribution?

Ah, now we’re talking. Here’s a web-based program that takes the tedium out of doing the SPSS illustration I mentioned under Heidi’s blog. With a large number of reps, such as you’ve done here in your image, both of the distributions are normal and have means and medians almost identical to those in the population. However, the larger sample size has the smaller standard deviation, which illustrates that if you were to choose just one sample randomly from the population – which, of course, is what everyone does, you’d have a better chance to come close to the population mean than you would with the smaller sample size! I couldn’t resist pumping it up some more, so I did the ones with 5 and 25 with lots of repetitions (200,000). I encourage others to try it out!

Hi Rucha, I loved this interactive simulation! Your blog has been very helpful in understanding how a sample size affects the distribution of the sample mean.