Editing Descriptive statistics

{{short description|Type of statistics}}
{{Research}}

A '''descriptive statistic''' (in the [[count noun]] sense) is a [[summary statistic]] that quantitatively describes or summarizes features from a collection of [[information]],<ref>{{cite book |last=Mann |first=Prem S. |year=1995 |title=Introductory Statistics |edition=2nd |publisher=Wiley |isbn=0-471-31009-3 }}</ref> while '''descriptive statistics''' (in the [[mass noun]] sense) is the process of using and analysing those statistics. Descriptive statistics is distinguished from [[statistical inference|inferential statistics]] (or inductive statistics) by its aim to summarize a [[Sample (statistics)|sample]], rather than use the data to learn about the [[statistical population|population]] that the sample of data is thought to represent.<ref>{{Citation|author-first1=Andrew N.|author-last1=Christopher|title=Drawing Conclusions From Data: Descriptive Statistics, Inferential Statistics, and Hypothesis Testing|date=2017|url=http://dx.doi.org/10.4135/9781506304144.n6|work=Interpreting and Using Statistics in Psychological Research|pages=145–183|location=Thousand Oaks, CA|publisher=SAGE Publications, Inc|doi=10.4135/9781506304144.n6|isbn=978-1-5063-0416-8|access-date=2021-06-01}}</ref> This generally means that descriptive statistics, unlike inferential statistics, is not developed on the basis of [[probability theory]], and are frequently [[nonparametric statistics]].<ref>{{cite book |last=Dodge |first=Y. |year=2003 |title=The Oxford Dictionary of Statistical Terms |publisher=OUP |isbn=0-19-850994-4 |url-access=registration |url=https://archive.org/details/oxforddictionary0000unse }}</ref> Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented.<ref>{{Citation|author-first1=Andrew N.|author-last1=Christopher|title=Drawing Conclusions From Data: Descriptive Statistics, Inferential Statistics, and Hypothesis Testing|date=2017|url=http://dx.doi.org/10.4135/9781506304144.n6|work=Interpreting and Using Statistics in Psychological Research|pages=145–183|location=Thousand Oaks, CA|publisher=SAGE Publications, Inc|doi=10.4135/9781506304144.n6|isbn=978-1-5063-0416-8|access-date=2021-06-01}}</ref> For example, in papers reporting on human subjects, typically a table is included 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 of each sex, the proportion of subjects with related [[comorbidity|co-morbidities]], etc.

Some measures that are commonly used to describe a data set are measures of [[central tendency]] and measures of variability or [[Statistical dispersion|dispersion]]. Measures of central tendency include the [[mean]], [[median]] and [[Mode (statistics)|mode]], while measures of variability include the [[standard deviation]] (or [[variance]]), the minimum and maximum values of the variables, [[kurtosis]] and [[skewness]].<ref name=Inv>Investopedia, [http://www.investopedia.com/terms/d/descriptive_statistics.asp#axzz2DxCoTnMM Descriptive Statistics Terms]</ref>

==Use in statistical analysis==
Descriptive statistics provide simple summaries about the sample and about the observations that have been made. Such summaries may be either [[Quantitative research|quantitative]], i.e. [[summary statistics]], or visual, i.e. simple-to-understand graphs. These summaries may either form the basis of the initial description of the data as part of a more extensive statistical analysis, or they may be sufficient in and of themselves for a particular investigation.

For example, the shooting [[percentage]] in [[basketball]] is a descriptive statistic that summarizes the performance of a player or a team. This number is the number of shots made divided by the number of shots taken. For example, a player who shoots 33% is making approximately one shot in every three. The percentage summarizes or describes multiple discrete events. Consider also the [[grade point average]]. This single number describes the general performance of a student across the range of their course experiences.<ref name="trochim">{{cite web|last=Trochim|first=William M. K.|title=Descriptive statistics|url=http://www.socialresearchmethods.net/kb/statdesc.php|work=Research Methods Knowledge Base|access-date=14 March 2011|year=2006}}</ref>

The use of descriptive and summary statistics has an extensive history and, indeed, the simple tabulation of populations and of economic data was the first way the topic of [[statistics]] appeared. More recently, a collection of summarisation techniques has been formulated under the heading of [[exploratory data analysis]]: an example of such a technique is the [[box plot]].

In the business world, descriptive statistics provides a useful summary of many types of data. For example, investors and brokers may use a historical account of return behaviour by performing empirical and analytical analyses on their investments in order to make better investing decisions in the future.

===Univariate analysis===
[[Univariate analysis]] involves describing the [[Frequency distribution|distribution]] of a single variable, including its central tendency (including the [[mean]], [[median]], and [[Mode (statistics)|mode]]) and dispersion (including the [[range (statistics)|range]] and [[quartiles]] of the data-set, and measures of spread such as the [[variance]] and [[standard deviation]]). The shape of the distribution may also be described via indices such as [[skewness]] and [[kurtosis]]. Characteristics of a variable's distribution may also be depicted in graphical or tabular format, including [[histograms]] and [[stem-and-leaf display]].

===Bivariate and multivariate analysis===

When a sample consists of more than one variable, descriptive statistics may be used to describe the relationship between pairs of variables. In this case, descriptive statistics include:

* [[Contingency table|Cross-tabulations]] and [[contingency tables]]
* Graphical representation via [[scatterplot]]s
* Quantitative measures of [[Correlation and dependence|dependence]]
* Descriptions of [[conditional distribution]]s

The main reason for differentiating univariate and bivariate analysis is that bivariate analysis is not only a simple descriptive analysis, but also it describes the relationship between two different variables.<ref>{{cite book |first=Earl R. |last=Babbie |title=The Practice of Social Research |url=https://archive.org/details/isbn_9780495598428 |url-access=registration |edition=12th |publisher=Wadsworth |year=2009 |isbn=978-0-495-59841-1 |pages=[https://archive.org/details/isbn_9780495598428/page/436 436–440] }}</ref> Quantitative measures of dependence include correlation (such as [[Pearson's r]] when both variables are continuous, or [[Spearman's rho]] if one or both are not) and [[covariance]] (which reflects the scale variables are measured on). The slope, in regression analysis, also reflects the relationship between variables. The unstandardised slope indicates the unit change in the criterion variable for a one unit change in the [[prediction|predictor]]. The standardised slope indicates this change in standardised ([[z-score]]) units. Highly skewed data are often transformed by taking logarithms. The use of logarithms makes graphs more symmetrical and look more similar to the [[normal distribution]], making them easier to interpret intuitively.<ref>{{cite book |first=Todd G. |last=Nick |chapter=Descriptive Statistics |title=Topics in Biostatistics |series=[[Methods in Molecular Biology]] |volume=404 |location=New York |publisher=Springer |year=2007 |pages=33–52 |isbn=978-1-58829-531-6 |doi=10.1007/978-1-59745-530-5_3 |pmid=18450044 }}</ref>{{rp|47}}

==References==
{{Reflist}}

==External links==
* Descriptive Statistics Lecture: University of Pittsburgh Supercourse: http://www.pitt.edu/~super1/lecture/lec0421/index.htm

{{Statistics|descriptive}}
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[[Category:Descriptive statistics| ]]