The analysis of statistical data or using statistical tests on data is commonly described as statistical inference. These statistical methods are used to extract meaning from the available data.
Descriptive statistics is the process of gathering data and summarizing it. Data is gathered by taking observations or making measurements. An example of this data gathering are the exit polls during an election. By gauging the voters opinion right after casting their ballots, a statistician can predict an election's outcome with only a small margin of error. A set of observations, which are taken from a larger population or from measurements taken from a process, are called a sample. Design of experiments uses a disciplined methodology to deliver samples that are purer, that is with fewer errors.
Using the samples gathered, various statistical methods or statistical tests can be used to draw conclusions about the population. The normal distribution is used often because of its frequent occurrence in natural phenomenon. The sign test is another method used when normality can not be established. The t-test can be used when only small sample sizes are available. Control charts are used extensively in monitoring industrial processes. Some of these methods and tests, as well as explanatory topics are linked to below:
Central Limit Theorem - A fundamental premise of statistics.
Control Charts - A method of statistically monitoring process to ensure that they have not fundamentally changed.
Normally Distributed - Over 90% of all natural populations have a normal distribution.
Standard Normal Distribution - A probability distribution that is normally distributed with a mean of 0 and a standard deviation of 1.
Sampling Distribution - The distribution of a given statistic of the equally sized samples from the same population.
Sign Test - The non-parametric test that can be used when your data is not normally distributed.
Significance Test - A test used to accept or reject claims or hypotheses about a population.
Design Of Experiment - Controlled experiments in experimental research resulting in purer data samples.
Binomial Distribution - Alternatively called the Bernoulli distribution, it is a discrete probability distribution where a single observation can have have only two outcomes.
t-Distribution - The t statistic estimates a population mean from small sample sizes, where the population standard deviation is not known.
The analysis of statistical data is important for permitting conclusions to be made about a process or a population. Although the nature of statistics do not permit one to make absolute statements from the samples taken, high probabilities can lead to solid conclusions.