Introduzione alla statistica in lingua inglese

Statistics

Methodological discipline that allows the management, organization and analysis of data to study, in a quantitative way, collective phenomena.
Phase of the process:
* definition of the population
* extraction of the sample: census survey (population= sample), sample survey (population>> sample)
* observation by a source : direct source (ad hoc data collection, survey,clinical trials…), indirect source (derived from aggregated data: external accredited source/ company information system)
* processing: data analysis in a descriptive (average, frequency, graphs...it gives an overview of my sample, a picture of the situation) and inferential way (comparison test between two or more groups. It shows me the most important differences)
* interpretation of results and application to the target population 

Data types: the character

* mutable / qualitative character: express a quality (changeable disconnected-> nominal scale/ mutable ordinal -> ordinal scale)
* variable/quantitative character: express a numerical quantity: discrete (the possibilities are finite or countable -> ratio scale), continuous (the variable can assume any value in the set of real numbers-> interval scale)

Qualitative

Absolute or relative frequency:
* pie chart: highlights the contribution of each value of the variable to the total
* bar graph: either used as a pie (using relative frequencies) or to show the numerical difference (absolute frequency) between the various values. It can also be used for continuous variables and double entry tables.

Bar diagrams for continuous variables

 
In the event of a large number of different data, they can be collected in classes. 
* choose the intervals (a,b] or [a,b) 
* the set of classes will be given by a partition {Li}i=1…k with Li= (Ii,Ii+1],l1=a, lk=b
* the classes are contiguous and not overlapping, graphically separated 
* usually the limits of classes Ii are multiples of 2,5 or 10
* constant amplitudes are recommended, unless the context dictates 

Numerical rules

* k number of classes. Usually 5<k<20 and k<1/10 * N with N, number of total observations (es N=28, k = 3, rule of thumb)
* central value of each class: xi= l1+li+1/ 2 
* size of each class: w= b-a/k 

Pie chart

1%= 3.6° (because round angle= 360°=100%). For absolute frequencies: slice width= 360° * abs/N

Double entry table

 
Bar charts are also useful for representing data from double entry tables, for example to compare two or more options in the same chart (difference between males and females, treatment vs severity...)

Quantitatives

Series - * series: collection of the same data at different times (es trend of type of surgery, allergies and seasons..)
* space series: collection of the same data at the same time but in different places (es Alzheimer diffusion in Europe)

Histogram - The rectangles are contiguous and the areas are proportional to the frequency (height) and the width of the interval (base). Height of each class (if width w inhomogeneous) hi= pi/wi

Box plot (box and whisker)

This chart summarizes several indices:
* minimum and maximum (tip of the whisker)
* first (Q1), second (median) and third (Q3) quartile: values that leave respectively 25%, 50% and 75% of the sample (in ascending order) to the left (ends of the box and inner line)
* average (not always present) dot or square inside
* outliers (not always present) strange values because out of bounds, indicate possible errors in the data, evaluate whether to exclude them from the analysis