In the Wikipedia article about test statistic it is written
A test statistic is a statistic used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.
while the Wikipedia article about descriptive statistics states
A descriptive statistic is a summary statistic that quantitatively describes or summarizes features of a collection of information.
It seems to me that both statistics are a means to summarize the given data (e.g. a sample of a population), but, depending on the context (i.e. hypothesis testing or descriptive statistics), we use one expression rather than another. Is this correct? What are the differences between them?
Best Answer
Both descriptive statistics and test statistics are functions of the data, or in other words, numerical summaries calculated from the data. So the difference is only in your purposes, goals, and uses of them.
Descriptive statistics are used for informal summary of the data:!different statistics tells you about different aspects of the data.
When you are interested in some formal hypothesis testing, some data summary is chosen for the test, as a test statistic, from criteria such as maximizing power, good robustness, and others, which are not relevant (or meaningful) when only used as descriptives.