Comparing Populations So far, our discussion of statistics has been limited to the analysis of a single population.  In many cases, we often want to compare 2 or more population sets.  In polling for example, a common problem is to compare the answers given on two or more questions asked.  In this post, we’ll discuss how to quantify the relationship between two random variables.   Continue reading “Comparing Populations”

Combinatorics Before we get too deep into statistical analysis of polling, we need to cover a basic set of probability theory known as combinatorics.  It’s been my experience that combinatorics is more of an art than a science, but we’ll cover enough of the basics to get started.

Sampling A Population So far, our discussion of statistical methods has centered on simple examples where the probability model is completely understood.  In the real world, particularly when analyzing polling data, this is often not the case.  Here we begin the discussion of analyzing a large population through data sampled from it.

Probability Distributions

While Probability Density Functions for continuous random variables are useful in describing many statistical processes in nature, they’re not much use when analyzing polling data.  In this post, we’ll introduce the discrete version of PDF’s and use it to describe some previous examples.

Playing Darts Now that we have some experience with calculating probabilities, we can start developing more sophisticated tools for describing and analyzing statistical properties.  While some of what we’ll discuss today doesn’t necessarily lend itself well to polling, we’ll cover all types of probability distributions, just to be complete.

Rolling Dice In the last post, we introduced the basic concepts of probability, as well as the events for which we calculate those probabilities.  In many statistical calculations involving polling data, we’re interested in the probabilities of combinations of multiple events.  We’ll talk about correlations and other advanced concepts soon, but today we’ll start off with some simple relationships.

Flip a Coin

This is the first in a series of posts about the fundamental rules behind probability and statistics.  If the relationship between statistics and polling isn’t completely clear yet, don’t worry, that will come soon.