Statistics is the science of learning about the world around us.

# Project Scarlet: To Practice Statisical Calculations

Learning takes practice. This is as true in basketball as it is in statistics. Practice is difficult, however, for both the teacher and the student. It takes repeated effort by the student to obtain the skills to the point that contemplation is no longer done about the calculations. For the teacher, it is difficult to create a large number of practice problems for the student.

This website seeks to solve both problems by providing a seemingly infinite number of problems upon which you can practice. That these problems are randomly generated by a computer program should also emphasize that these calculations are mechanical in nature.

And so, please enter the site. Find the statistical calculations you would like to practice. Then, practice until the mechanics are second-nature to you.

## Sample Statistics

At its very simplest, a sample statistic is just a value that attempts to describe one aspect of the variable. From a mathematical standpoint, a sample statistic is any function of the data.

Sometimes, the function is useful in summarizing that aspect of the data. If one desires to find a typical value for the variable, one would use an average of some type. The type of average selected depends on the variable, itself.

## Distributions and Probabilities

While the world is random, we are frequently able to describe that randomness. We may not know the outcome of flipping a fair coin, but we know everything else about the next flip. There is a 50% chance (the probability is 0.50) that the coin will come up heads. If we flip the coin 100 times, the expected number of heads is 50. There is a 95% probability that there will be between 40 and 60 heads.

Probability distributions are named when scientists experience them frequently in their studies. Beyond the Binomial distribution described above, Project Scarlet provides practice to you with several other distributions. Among these are the Categorical, the Poisson, the Hypergeometric, and the Normal distribution.

## Statistical Inference

Probability is the second leg of the statistics stool. The first leg is the mathematics of the sample statistics. This second leg allows us to calculate probabilities of observing specific outcomes. Putting these together allow us to draw conclusions about the population (data-generating process) from a simple sample from that population.

This is the goal of statistics. Statistical inference is, most likely, the reason you are taking a statistics course at the college level. In this part of Project Scarlet, you are able to examine many tests and calculate critical values, test statistics, p-values, and confidence intervals: the foundation of statistical inference.

In addition to the practice provided here at Project Scarlet, there is a lot of help available on the Internet. The following are links to some of those sources.

Make good use of the videos. Some will be helpful to you. Others will not. There is no guarantee on the Internet except that the video was helpful to someone at sometime.

# Statistical Programs

While being able to calculate statistics by hand is a nice skill to have, once you start using statistics as a scientist, you will quickly discover that it takes too much time and that there is too much of a chance for a simple error to be made. Real scientists use statistical programs to perform those calculations. Note that while the computer can perform the calculations, it is up to you to interpret the results.

As a practitioner, I have my preference in terms of statistical program. However, as a consultant, it is important to be fluent in several of the more-popular programs. Here is a non-exhaustive list of some of the more-popular statistical programs.

# Denouement

As time passes, more areas will be open, allowing you to practice more statistics skills. Check back often. The globe shows the locations of all of the visitors to this webpage since its inception on January 9, 2016. This does not count those who have bypassed this page.