Editing Biostatistics (section)

=== Descriptive tools ===
{{Main| Descriptive statistics}}

Data can be represented through [[Table (information)|tables]] or [[chart|graphical]] representation, such as line charts, bar charts, histograms, scatter plot. Also, [[Central tendency|measures of central]] tendency and [[Statistical dispersion|variability]] can be very useful to describe an overview of the data. Follow some examples:

==== Frequency tables ====

One type of table is the [[frequency]] table, which consists of data arranged in rows and columns, where the frequency is the number of occurrences or repetitions of data. Frequency can be:<ref>{{Cite web|url=https://www.sangakoo.com/en/unit/absolute-relative-cumulative-frequency-and-statistical-tables|title=Absolute, relative, cumulative frequency and statistical tables – Probability and Statistics|last=Maths|first=Sangaku|website=www.sangakoo.com|language=en|access-date=2018-04-10}}</ref>

'''Absolute''': represents the number of times that a determined value appear;

<math display="block">N = f_1 + f_2 + f_3 + ... + f_n</math>

'''Relative''': obtained by the division of the absolute frequency by the total number;

<math display="block">n_i = \frac{f_i}{N}</math>

In the next example, we have the number of genes in ten [[operon]]s of the same organism.

: {{math|1=Genes = {{mset|2,3,3,4,5,3,3,3,3,4}}}}
{| class="wikitable"
|+
!Genes number
!Absolute frequency
!Relative frequency
|-
|1
|0
|0
|-
|2
|1
|0.1
|-
|3
|6
|0.6
|-
|4
|2
|0.2
|-
|5
|1
|0.1
|}

==== Line graph ====

[[File:Examples of descriptive tools.png|thumb| Figure A: '''Line graph example'''. The birth rate in Brazil (2010–2016);<ref name=":1">{{Cite web|url=http://tabnet.datasus.gov.br/cgi/deftohtm.exe?sinasc/cnv/nvuf.def|title=DATASUS: TabNet Win32 3.0: Nascidos vivos – Brasil|website=DATASUS: Tecnologia da Informação a Serviço do SUS}}</ref> Figure B: '''Bar chart example.''' The birth rate in [[Brazil]] for the December months from 2010 to 2016; Figure C: '''Example of Box Plot''': number of glycines in the proteome of eight different organisms (A-H); Figure D: '''Example of a scatter plot.''']]

[[Line graph]]s represent the variation of a value over another metric, such as time. In general, values are represented in the vertical axis, while the time variation is represented in the horizontal axis.<ref name=":0">{{Cite book|title=Introduction to Biostatistics. A Guide to Design, Analysis, and Discovery|last1=Forthofer|first1=Ronald N.|last2=Lee|first2=Eun Sul|publisher=Academic Press|year=1995|isbn=978-0-12-262270-0}}</ref>

==== Bar chart ====

A [[bar chart]] is a graph that shows categorical data as bars presenting heights (vertical bar) or widths (horizontal bar) proportional to represent values. Bar charts provide an image that could also be represented in a tabular format.<ref name=":0" />

In the bar chart example, we have the birth rate in Brazil for the December months from 2010 to 2016.<ref name=":1" /> The sharp fall in December 2016 reflects the outbreak of [[Zika virus]] in the birth rate in Brazil.

==== Histograms ====

[[File:Example histogram.png|thumb|'''Example of a histogram.'''|350x350px]]The [[histogram]] (or frequency distribution) is a graphical representation of a dataset tabulated and divided into uniform or non-uniform classes. It was first introduced by [[Karl Pearson]].<ref>{{Cite journal|last=Pearson|first=Karl|date=1895-01-01|title=X. Contributions to the mathematical theory of evolution.—II. Skew variation in homogeneous material|journal=Phil. Trans. R. Soc. Lond. A|language=en|volume=186|pages=343–414|doi=10.1098/rsta.1895.0010|issn=0264-3820|bibcode=1895RSPTA.186..343P|doi-access=free}}</ref>

==== Scatter plot ====

A [[scatter plot]] is a mathematical diagram that uses Cartesian coordinates to display values of a dataset. A scatter plot shows the data as a set of points, each one presenting the value of one variable determining the position on the horizontal axis and another variable on the vertical axis.<ref>{{Cite book|title=Seeing through statistics|last=Utts|first=Jessica M.|date=2005|publisher=Thomson, Brooks/Cole|isbn=978-0534394028|edition= 3rd|location=Belmont, CA|oclc=56568530}}</ref> They are also called '''scatter graph''', '''scatter chart''', '''scattergram''', or '''scatter diagram'''.<ref>{{Cite book|title=Basic statistics|last=Jarrell|first=Stephen B.|date=1994|publisher=Wm. C. Brown Pub|isbn=978-0697215956|location=Dubuque, Iowa|oclc=30301196}}</ref>

==== Mean ====
{{Main| Mean}}

The [[arithmetic mean]] is the sum of a collection of values (<math>{x_1+x_2+x_3+\cdots +x_n}</math>) divided by the number of items of this collection (<math>{n}</math>).

: <math>\bar{x} = \frac{1}{n}\left (\sum_{i=1}^n{x_i}\right ) = \frac{x_1+x_2+\cdots +x_n}{n}</math>

==== Median ====
{{Main| Median}}

The [[median]] is the value in the middle of a dataset.

==== Mode ====
{{Main| Mode (statistics)}}

The [[mode (statistics)|mode]] is the value of a set of data that appears most often.<ref>{{Cite book|title=Econometrics|last=Gujarati|first=Damodar N.|publisher=McGraw-Hill Irwin|year=2006}}</ref>
{| class="wikitable" 
|+  |Comparison among mean, median and mode<br />
Values = { 2,3,3,3,3,3,4,4,11 }
!Type
!Example
!Result
|-
| align="center"  |[[Arithmetic mean|Mean]]
| align="center" | ( 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 11 ) / 9
| align="center" |'''4'''
|-
| align="center" |[[Median]]
| align="center" |2, 3, 3, 3, '''3''', 3, 4, 4, 11
| align="center" |'''3'''
|-
| align="center" |Mode
| align="center" |2, '''3, 3, 3, 3, 3''', 4, 4, 11
| align="center" |'''3'''
|}

==== Box plot ====

[[Box plot]] is a method for graphically depicting groups of numerical data. The maximum and minimum values are represented by the lines, and the interquartile range (IQR) represent 25–75% of the data. [[Outlier]]s may be plotted as circles.

==== Correlation coefficients ====

Although correlations between two different kinds of data could be inferred by graphs, such as scatter plot, it is necessary validate this though numerical information. For this reason, [[correlation coefficient]]s are required. They provide a numerical value that reflects the strength of an association.<ref name=":0" />

==== Pearson correlation coefficient ====

[[File:Correlation coefficient.png|right|thumb|Scatter diagram that demonstrates the Pearson correlation for different values of ''ρ.'']] [[Pearson correlation coefficient]] is a measure of association between two variables, X and Y. This coefficient, usually represented by ''ρ'' (rho) for the population and ''r'' for the sample, assumes values between −1 and 1, where ''ρ''  = 1 represents a perfect positive correlation, ''ρ'' = −1 represents a perfect negative correlation, and ''ρ'' = 0 is no linear correlation.<ref name=":0" />