Statistics

Statistics is the application of mathematics to the understanding of data. It involves all stages of data collection and processing from the initial collection, to the analysis and ultimately to the conclusions and interpretations of the data. It is used in all research oriented disciplines from physics, chemistry and biology to economics, anthropology and psychology as well as many thousands of other fields. It is also used in businesses and governments.

Statistics analyzes data in two primary ways, the first is called descriptive statistics which describes and summarizes the data. Often this will include things like: the mean, standard error, or standard deviation. Also statistics can attempt to infer relationships between the data collected and various hypothesis or populations, this is called inferential statistics. Both descriptive and inferential statistics comprise applied statistics. There is also a discipline called mathematical statistics, which is concerned with the theoretical basis of the subject.

Statistics takes its name from the fact that it was traditionally taught to monarchs to enable them to manage affairs of state.

Frequentist Approaches

Frequentist approaches are often referred to as classical approaches because it is the oldest and most used method of statistical analysis. The heart of this approach is to try and understand data as a relative frequency or ratio of a particular occurrence out of a total possible number of occurrences. For example, a frequentist would describe the number of times a coin turns up heads as a ratio of total number of heads out of total number of flips.

Descriptive statistics

Frequentist approahces to descriptive statistics mostly involve averaging. For example, the mean of a sample is calculated as the total value of all observations divided by total number of trials, and the standard error is calculated by taking the total error size for all samples and dividing by total number of trials.

These methods stem from the view of data as ratios probabilities.

Inferential statistics

Frequentist approaches to inferential statistics primarily involve trying to compare descriptive statistics of two data sets to determine if they are significantly different. One of the most common approaches is to test a given data set against a null hypothesis or the data set that would be created if the values were the result of random chance alone. For example, if a given head came up 9 times as heads and 1 time as tails you would compare the number of heads, 9, to the number of heads that would be expected if chance alone was operating, or 5.

Testing against the null hypothesis is sometimes referred to as an omnibus test since it is testing the idea that a given data set is the result of anything other than chance. Often it is much more desirable to test specific data sets against each other.