Statistical Analysis: a Brief Summary of the Most Relevant Types

We have two different areas of statistics which are related to but still different from each other. Primarily, we have descriptive statistics and then is inferential statistics.

First, we begin with Descriptive statistics. Descriptive statistics is simply the process of defining characteristics of a statistical measurement. Roughly speaking, descriptive statistics involves a observational study of a population, which is achieved by summarizing and organizing data obtained from a random sample. There are several ways statisticians acomplish this. Charts and graphs play an important role, plus some standard measurements such as averages, percentiles, and measures of variation, such as the standard deviaton.

One of the most common uses of descriptive statistics is in sports (all kind of sports). In fact, baseball statisticians spend a lot of effort and resources looking at the raw data and summarizing, categorizing to come up with statements of fact regarding the season. Think of this, for example. In 1948 more than 600 games were played in the American League. Determining who had the best batting average in that year, you would need to take the official score sheets for each of the games, make a list each batter, compute the results of each time the player is at bat, add the total number of hits and the total number of times the player is at bat in order to come up with a batting average. The statistics showed that the winner in 1948 was Ted Williams. But, if your objective is to calculate who the top 25 players for the current or past years were, the statistical computations would be increasingly complicated.

The wonders of the new generation of personal computers has changed everything, though. Now, statisticians possess tools they never conceived before. Applications now bring statistical functions that make this calculations a breeze. All this have given more power and flexibility to the sport statisticians to a further degree and they are able to handle massive amounts of data and explore the data in a way more systematic way.

Inferential statistics consists of choosing and measuring the trustworthiness of conclusions about a population parameter based on information from a reduced portion of that population, which is a random sample. Among the many possible uses of inferential statistics, political predictions ar one good example. In order to be able to attempt to predict who the winner of a presidential election is likely to be, typically a sample of a few thousand carefully chosen sample of Americans are asked which way they will be voting. From the answers given to this question, statisticians are able to predict, or infer who the general population will vote for with a surprinsingly high level of confidence. Obviously, the two keys to inferential statistics are choosing which members of the general population will be polled and which questions will be asked. Imagine a situation where there is a choice of two candidates, and the polled population, or sample population is asked: Are you planning to vote for X in the upcoming election? the only alternatives for the answer will be either yes, no, or undecided. Based on the results you should be able to determine that 51% of the sample group (for instance) will Give their vote to Candidate X.

Applying techniques of inferential statistics, we can {predict with a certain degree of confidence that Candidate X will win the election. However, in some instances, the sampling techniques may have given rise to incorrect inferences. Let’s recall the classic case of the 1948 Presidential election. The preliminary results posted by Gallup made the wrong prediction and President Harry Truman believed he would get approximately 45% of the votes which would imply losing to Thomas Dewey. As a matter of fact, as history proves, Truman won more than 49% of the votes and of course, won the election. This incident changed the way samples were collected, and much more rigorous methods were created to assure that more accurate predictions are cast.