Title: Some basics of sampling inference
Course: UGQuants (SSPS) > Section: Probability

Some basics of sampling inference

There are two things to take note of before we move on.

1 | The ‘confidence interval’ is what we call the range of values that we think our population parameter lies within: we call it this because our calculation of the probability that it lies within this interval can be interpreted as how 'confident' we are about it.
2 | As the number of cases in our sample increases, so the confidence interval gets smaller.

We can make much safer estimates of the population characteristic with 1000 tosses than with 100, or 10. However the increase in accuracy depends on an exponential increase in sample size. This is because the size of our confidence interval will vary with the square root of the size of the sample. Thus in order to reduce a confidence interval obtained with a sample of 100 by half we would need to increase the sample size fourfold to 400. To make it ten times smaller we would need to increase the sample size one hundred times: to 10,000. Thus, as a trade off between cost and confidence survey companies generally favour a sample of around one thousand cases. However, since we are often interested in sub groups within a population, we may well take a bigger sample, so that we can compare within it (men compared to women, young to old, urban to rural, and so on).

A further, and rather surprising, aspect of the logic of sampling and probability is that the likelihood of securing an accurate estimate has nothing to do with the size of the population (unless it is very small indeed). It only depends upon the size of our sample.

Using the properties of the normal curve, we can calculate the confidence interval for our statistic, so that we can state how probable it is that the population parameter lies within a certain distance of our sample statistic. We will now look at how we calculate these probabilities and confidence intervals.