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A Summary of the Most Notoriuos Forms of Statistical Analysis.
First, we begin with Descriptive statistics. Descriptive statistics corresponds to essentially the process of defining characteristics of a statistical measurement from a population. Descriptive statistics is based upon mechanisms and methods employed to organize and summarize raw data. In order to categorize the data from a random sample that is gathered, most statisticians use graphs, charts, tables and standard statistical measurements such as averages, percentiles, and the corresponding measures of variation.
One of the most common uses of descriptive statistics is in sports (all kind of sports). Baseball statisticians spend a lot of effort and resources observing the raw data and summarizing, categorizing to discover regularities to enlighten the audience. There are many examples that would make this obvious. Think of this, for example. In 1948 there were over 600 games played in the League. To determine 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, determine the results of each time at bat, add the total number of hits and the total number of times at bat in order to calculate with a batting average. In 1948 the American League player with the top batting average was Ted Williams. But, if your objective is to calculate who the top 25 players for the year were, the statistical calculations would be increasingly complicated.
The advent of the new generation of personal computers has created a different scenario, though. Now, statisticians have tools they never dreamed before. Software packages now bring statistical functions that make everything easier. All this have empowered the sport statisticians to a further degree and they are able to manage massive amounts of data and explore the data in a way more systematic fashion.
Inferential statistics is based upon choosing and measuring the validity of conclusions about a group based upon data obtained from a sample of the group. Political polling is an excellent example of the way inferential statistics are used. In order to be able to try to predict who the winner of a presidential election is likely to be, in most of the cases a sample of a few thousand carefully chosen sample of Americans are asked which way they will be voting. With this answers statisticians are able to predict, or infer who the general population will vote for with a reasonable confidence level. Obviously, the fundamental elements in inferential statistics are choosing the righ sample of members of the general population will be chosen and what questions will be asked. In a case such as the above, where there is a choice of two candidates, and the polled population, or sample population is asked: Will you give your vote to Candidate X in the next election? the only alternatives for the answer will be either yes, no, or undecided. From the descriptive statistics you should be able to determine that 51% of the sample group will vote for Candidate X.
Applying techniques of inferential statistics, you can {predict with a certain degree of confidence that Candidate X will win the election. However, we have to be cautious because the the sampling techniques may have created invalid inferences. Let's not forget of the classic case of the 1948 Presidential election. Based on a poll taken by the Gallup Organization, President Harry Truman believed he would get approximately 45% of the votes and would lose to Republican challenger 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 caused a change in some of the sampling techniques and the Gallup Organization has accurately predicted the Presidential election winner ever since then.
