Basic Statistics in Python — Probability

Basic Statistics in Python — Probability

What is probability?

At the most basic level, probability seeks to answer the question, “What is the chance of an event happening?” An event is some outcome of interest. To calculate the chance of an event happening, we also need to consider all the other events that can occur. The quintessential representation of probability is the humble coin toss. In a coin toss the only events that can happen are:

  • Flipping a heads
  • Flipping a tails

These two events form the sample space, the set of all possible events that can happen. To calculate the probability of an event occurring, we count how many times are event of interest can occur (say flipping heads) and dividing it by the sample space. Thus, probability will tell us that an ideal coin will have a 1-in-2 chance of being heads or tails. By looking at the events that can occur, probability gives us a framework for making predictions about how often events will happen. However, even though it seems obvious, if we actually try to toss some coins, we’re likely to get an abnormally high or low counts of heads every once in a while. If we don’t want to make the assumption that the coin is fair, what can we do? We can gather data! We can use statistics to calculate probabilities based on observations from the real world and check how it compares to the ideal.

From statistics to probability

Our data will be generated by flipping a coin 10 times and counting how many times we get heads. We will call a set of 10 coin tosses a trial. Our data point will be the number of heads we observe. We may not get the “ideal” 5 heads, but we won’t worry too much since one trial is only one data point. If we perform many, many trials, we expect the average number of heads over all of our trials to approach the 50%. The code below simulates 10, 100, 1000, and 1000000 trials, and then calculates the average proportion of heads observed. Our process is summarized in the image below as well.

The data and the distribution

Before we can tackle the question of “which wine is better than average,” we have to mind the nature of our data. Intuitively, we’d like to use the scores of the wines to compare groups, but there comes a problem: the scores usually fall in a range. How do we compare groups of scores between types of wines and know with some degree of certainty that one is better than the other? Enter the normal distribution. The normal distribution refers to a particularly important phenomenon in the realm of probability and statistics.

Conclusion

We started with descriptive statistics and then connected them to probability. From probability, we developed a way to quantatively show if two groups come from the same distribution. In this case, we compared two wine recommendations and found that they most likely do not come from the same score distribution. In other words, one wine type is most likely better than the other one. Statistics doesn’t have to be a field relegated to just statisticians. As a data scientist, having an intuitive understanding on common statistical measures represent will give you an edge on developing your own theories and the ability to subsequently test these theories. We barely scratched the surface of inferential statistics here, but the same general ideas here will help guide your intuition in your statistical journey. Our article discussed the advantages of the normal distribution, but statisticians have also developed techniques to adjust for distributions that aren’t normal.