# Descriptive statistics: Wikis

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# Encyclopedia

Descriptive statistics are used to describe the main features of a collection of data in quantitative terms. Descriptive statistics are distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aim to quantitatively summarize a data set, rather than being used to support inferential statements about the population that the data are thought to represent. Even when a data analysis draws its main conclusions using inductive statistical analysis, descriptive statistics are generally presented along with more formal analyses. For example in a paper reporting on a study involving human subjects, there typically appears a table giving the overall sample size, sample sizes in important subgroups (e.g. for each treatment or exposure group), and demographic or clinical characteristics such as the average age, the proportion of subjects with each gender, and the proportion of subjects with related comorbidities.

In research involving comparisons between groups, a major emphasis is often placed on the significance level for the hypothesis that the groups being compared differ to a greater degree than would be expected by chance. This significance level is often represented as a p-value, or sometimes as the standard score of a test statistic. In contrast, an effect size is a descriptive statistic that conveys the estimated magnitude and direction of the difference between groups, without regard to whether the difference is statistically significant. Reporting significance levels without effect sizes is often criticized, since for large sample sizes even small effects of little practical importance can be highly statistically significant.

## Examples of descriptive statistics

Most statistics can be used either as a descriptive statistic, or in an inductive analysis. For example, we can report the average reading test score for the students in each classroom in a school, to give a descriptive sense of the typical scores and their variation. If we perform a formal hypothesis test on the scores, we are doing inductive rather than descriptive analysis.

Some statistical summaries are especially common in descriptive analyses. Some examples follow.

# Study guide

Up to date as of January 14, 2010

# Simple English

Descriptive statistics is a branch of statistics. Its aim is to summarize a set of statistical data. The data are usually taken by sampling a population. This means that the different items of data will be grouped and the groups will be described, in some way. That way, a set of measurements can be described by giving a probability distribution, the "center" of the values, and the "spread". Another way might be to give a histogram. A histogram shows how often certain values occur.