This post follows up on a question from a user, who saw small diferences in the Expostats results when entering the data in a different order : inputing the same data in the same order will lead to the exact same results in Expostats, but the same data in different order will lead to minute variations, albeit negligible in terms of decision making. This phenomenon is called Monte Carlo variability and at the creation of Expostats we used a little trick to camouflage it :
Bayesian analysis is based on simulations using random numbers. Because of this, the results can change slightly each time you run a calculation. However, this small variation is normal and much smaller than the uncertainty that comes from having only a few samples ( for example, just 6 data points to estimate a distribution).
To avoid confusion (when users saw their results change a little bit each time they entered the same data), we added a small trick. When someone enters data, we use that data to create a seed — a number that controls the random number generation. If the seed is the same, the random numbers are the same, and the results are the same.
This means: if you enter the same dataset in the same order, the results will not change. But if you change the order of the data, the seed changes, so the random numbers change slightly — and then the results can also change a little. You can see this with the default data in the expostats tools: just move one value to a different position, and you will see the results shift slightly. This effect is usually only visible in very uncertain results, like the confidence interval limits.
We might or might not keep this trick in the next Expostats update (people are better used to Bayesian analysis nowdays), but I wanted to make it transparent.