## 4.3 The difference between HDI and confidence intervals

The confidence interval is computed directly from the sample data and theoretically offers no direct evidence regarding the mean difference in the population.
95% is a value associated with the long run instead of a particular process.
In our Markov chain Monte Carlo technique, HDI is gradually constructed from more than 100,000 steps, where each step represents a potential combination of the population parameters.
The BEST HDI explicitly models **the relevant population parameters and displays probability distributions for those parameters**,
whereas the confidence interval uses **sample data to determine one and only one example** of an upper and lower bound for the population mean.
The confidence interval assumes that t distributions are symmetric similar to the normal distribution but the tails are thicker representing a larger uncertainty.
T distribution perform well as a model of population mean difference when the two samples with good-sized and normal-looking and equal variance, while badly when the samples are skew with unequal variance or outliers.
No such assumptions are required for the MCMC process. The anomalies in the sample results in wider HDI and raise the tails appropriately to signal the greater uncertainty in those samples.