# Dictionary Definition

statistical adj : of or relating to statistics;
"statistical population"

# User Contributed Dictionary

## English

### Adjective

- of or pertaining to statistics

#### Translations

of or pertaining to statistics

- Finnish: tilastollinen
- French: statistique
- German: statistisch

# Extensive Definition

Statistics is a mathematical
science pertaining to the collection, analysis, interpretation
or explanation, and presentation of data. It is applicable to a wide
variety of academic
disciplines, from the natural and social sciences to the humanities, and to government
and business.

Statistical methods can be used to summarize or
describe a collection of data; this is called descriptive
statistics. In addition, patterns in the data may be modeled
in a way that accounts for randomness and uncertainty in the
observations, and then used to draw inferences about the process or
population being studied; this is called inferential
statistics. Both descriptive and inferential statistics
comprise applied statistics. There is also a discipline called
mathematical
statistics, which is concerned with the theoretical basis of
the subject.

The word statistics is also the plural of
statistic (singular),
which refers to the result of applying a statistical algorithm to a
set of data, as in economic
statistics, crime
statistics, etc.

## History

"Five men, Conring,Achenwall,
Süssmilch, Graunt and
Petty have
been honored by different writers as the founder of statistics."
claims one source (Willcox, Walter (1938) The Founder of
Statistics. Review of the International Statistical Institute
5(4):321-328.)

Some scholars pinpoint the origin of statistics
to 1662, with the publication of "Observations
on the Bills of Mortality" by John Graunt. Early applications
of statistical thinking revolved around the needs of states to base
policy on demographic and economic data. The scope of the
discipline of statistics broadened in the early 19th century
to include the collection and analysis of data in general. Today,
statistics is widely employed in government, business, and the
natural and social sciences.

Because of its empirical roots and its
applications, statistics is generally considered not to be a
subfield of pure mathematics, but rather a distinct branch of
applied mathematics. Its mathematical foundations were laid in the
17th century with the development of probability
theory by Pascal and Fermat. Probability
theory arose from the study of games of chance. The method
of least squares was first described by Carl
Friedrich Gauss around 1794. The use of modern computers has expedited
large-scale statistical computation, and has also made possible new
methods that are impractical to perform manually.

## Overview

In applying statistics to a scientific, industrial, or societal problem, one begins with a process or population to be studied. This might be a population of people in a country, of crystal grains in a rock, or of goods manufactured by a particular factory during a given period. It may instead be a process observed at various times; data collected about this kind of "population" constitute what is called a time series.For practical reasons, rather than compiling data
about an entire population, one usually studies a chosen subset of
the population, called a sample.
Data are collected about the sample in an observational or experimental setting. The
data are then subjected to statistical analysis, which serves two
related purposes: description and inference.

- Descriptive statistics can be used to summarize the data, either numerically or graphically, to describe the sample. Basic examples of numerical descriptors include the mean and standard deviation. Graphical summarizations include various kinds of charts and graphs.
- Inferential statistics is used to model patterns in the data, accounting for randomness and drawing inferences about the larger population. These inferences may take the form of answers to yes/no questions (hypothesis testing), estimates of numerical characteristics (estimation), descriptions of association (correlation), or modeling of relationships (regression). Other modeling techniques include ANOVA, time series, and data mining.

If the sample is representative of the
population, then inferences and conclusions made from the sample
can be extended to the population as a whole. A major problem lies
in determining the extent to which the chosen sample is
representative. Statistics offers methods to estimate and correct
for randomness in the sample and in the data collection procedure,
as well as methods for designing robust experiments in the first
place. (See experimental
design.)

The fundamental mathematical concept employed in
understanding such randomness is probability. Mathematical
statistics (also called statistical
theory) is the branch of applied
mathematics that uses probability theory and analysis
to examine the theoretical basis of statistics.

The use of any statistical method is valid only
when the system or population under consideration satisfies the
basic mathematical assumptions of the method. Misuse
of statistics can produce subtle but serious errors in
description and interpretation — subtle in the sense that
even experienced professionals sometimes make such errors, serious
in the sense that they may affect, for instance, social policy,
medical practice and the reliability of structures such as bridges.
Even when statistics is correctly applied, the results can be
difficult for the non-expert to interpret. For example, the
statistical significance of a trend in the data, which measures
the extent to which the trend could be caused by random variation
in the sample, may not agree with one's intuitive sense of its
significance. The set of basic statistical skills (and skepticism)
needed by people to deal with information in their everyday lives
is referred to as statistical
literacy.

## Statistical methods

### Experimental and observational studies

A common goal for a statistical research project is to investigate causality, and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on response or dependent variables. There are two major types of causal statistical studies, experimental studies and observational studies. In both types of studies, the effect of differences of an independent variable (or variables) on the behavior of the dependent variable are observed. The difference between the two types lies in how the study is actually conducted. Each can be very effective.An experimental study involves taking
measurements of the system under study, manipulating the system,
and then taking additional measurements using the same procedure to
determine if the manipulation has modified the values of the
measurements. In contrast, an observational study does not involve
experimental manipulation. Instead, data are gathered and
correlations between predictors and response are
investigated.

An example of an experimental study is the famous
Hawthorne
studies, which attempted to test the changes to the working
environment at the Hawthorne plant of the Western Electric Company.
The researchers were interested in determining whether increased
illumination would increase the productivity of the assembly
line workers. The researchers first measured the productivity
in the plant, then modified the illumination in an area of the
plant and checked if the changes in illumination affected the
productivity. It turned out that the productivity indeed improved
(under the experimental conditions). (See Hawthorne
effect.) However, the study is heavily criticized today for
errors in experimental procedures, specifically for the lack of a
control
group and blindedness.

An example of an observational study is a study
which explores the correlation between smoking and lung cancer.
This type of study typically uses a survey to collect observations
about the area of interest and then performs statistical analysis.
In this case, the researchers would collect observations of both
smokers and non-smokers, perhaps through a case-control
study, and then look for the number of cases of lung cancer in
each group.

The basic steps of an experiment are;

- Planning the research, including determining information sources, research subject selection, and ethical considerations for the proposed research and method.
- Design of experiments, concentrating on the system model and the interaction of independent and dependent variables.
- Summarizing a collection of observations to feature their commonality by suppressing details. (Descriptive statistics)
- Reaching consensus about what the observations tell about the world being observed. (Statistical inference)
- Documenting / presenting the results of the study.

### Levels of measurement

There are four types of measurements or levels of measurement or measurement scales used in statistics: nominal, ordinal, interval, and ratio. They have different degrees of usefulness in statistical research. Ratio measurements have both a zero value defined and the distances between different measurements defined; they provide the greatest flexibility in statistical methods that can be used for analyzing the data. Interval measurements have meaningful distances between measurements defined, but have no meaningful zero value defined (as in the case with IQ measurements or with temperature measurements in Fahrenheit). Ordinal measurements have imprecise differences between consecutive values, but have a meaningful order to those values. Nominal measurements have no meaningful rank order among values.Since variables conforming only to nominal or
ordinal measurements cannot be reasonably measured numerically,
sometimes they are called together as categorical variables,
whereas ratio and interval measurements are grouped together as
quantitative or continuous
variables due to their numerical nature.

### Statistical techniques

Some well known statistical tests and procedures for research observations are:## Specialized disciplines

Some fields of inquiry use applied statistics so extensively that they have specialized terminology. These disciplines include:- Actuarial science
- Applied information economics
- Biostatistics
- Bootstrap & Jackknife Resampling
- Business statistics
- Data mining (applying statistics and pattern recognition to discover knowledge from data)
- Demography
- Economic statistics (Econometrics)
- Energy statistics
- Engineering statistics
- Environmental Statistics
- Epidemiology
- Geography and Geographic Information Systems, more specifically in Spatial analysis
- Image processing
- Multivariate Analysis
- Psychological statistics
- Quality
- Social statistics
- Statistical literacy
- Statistical modeling
- Statistical surveys
- Process analysis and chemometrics (for analysis of data from analytical chemistry and chemical engineering)
- Survival analysis
- Reliability engineering

Statistics form a key basis tool in business and
manufacturing as well. It is used to understand measurement systems
variability, control processes (as in
statistical process control or SPC), for summarizing data, and
to make data-driven decisions. In these roles, it is a key tool,
and perhaps the only reliable tool.

## Statistical computing

The rapid and sustained increases in computing power starting from the second half of the 20th century have had a substantial impact on the practice of statistical science. Early statistical models were almost always from the class of linear models, but powerful computers, coupled with suitable numerical algorithms, caused an increased interest in nonlinear models (especially neural networks and decision trees) as well as the creation of new types, such as generalised linear models and multilevel models.Increased computing power has also led to the
growing popularity of computationally-intensive methods based on
resampling,
such as permutation tests and the bootstrap,
while techniques such as Gibbs
sampling have made Bayesian methods more feasible. The computer
revolution has implications for the future of statistics with new
emphasis on "experimental" and "empirical" statistics. A large
number of both general and special purpose
statistical software are now available.

## Misuse

- main Misuse of statistics

There is a general perception that statistical
knowledge is all-too-frequently intentionally misused
by finding ways to interpret only the data that are favorable to
the presenter. A famous saying attributed to Benjamin
Disraeli is, "There
are three kinds of lies: lies, damned lies, and statistics";
and Harvard President Lawrence
Lowell wrote in 1909 that statistics, "like veal pies, are good
if you know the person that made them, and are sure of the
ingredients".

If various studies appear to contradict one
another, then the public may come to distrust such studies. For
example, one study may suggest that a given diet or activity raises
blood
pressure, while another may suggest that it lowers blood
pressure. The discrepancy can arise from subtle variations in
experimental design, such as differences in the patient groups or
research protocols, that are not easily understood by the
non-expert. (Media reports sometimes omit this vital contextual
information entirely.)

By choosing (or rejecting, or modifying) a
certain sample, results can be manipulated. Such manipulations need
not be malicious or devious; they can arise from unintentional
biases of the researcher. The graphs used to summarize data can
also be misleading.

Deeper criticisms come from the fact that the
hypothesis testing approach, widely used and in many cases required
by law or regulation, forces one hypothesis (the null
hypothesis) to be "favored", and can also seem to exaggerate
the importance of minor differences in large studies. A difference
that is highly statistically significant can still be of no
practical significance. (See criticism
of hypothesis testing and controversy
over the null hypothesis.)

One response is by giving a greater emphasis on
the p-value
than simply reporting whether a hypothesis is rejected at the given
level of significance. The p-value, however, does not indicate the
size of the effect. Another increasingly common approach is to
report confidence
intervals. Although these are produced from the same
calculations as those of hypothesis tests or p-values, they
describe both the size of the effect and the uncertainty
surrounding it.

## See also

- List of basic statistics topics
- List of statistical topics
- List of academic statistical associations
- List of national and international statistical services
- List of publications in statistics
- List of statisticians
- Glossary of probability and statistics
- Notation in probability and statistics
- Forecasting
- Foundations of statistics
- Multivariate statistics
- Regression analysis
- Statistical phenomena
- Statistical consultants
- Statistician
- Structural equation modeling