DATA
The Nature of Data and Variation
Although natural phenomena in the real life are unpredictable, the designs of experiments are bounded to generate data that varies because of intrinsic (internal to the system) or extrinsic (due to the ambient environment) effects. How many natural processes or phenomena in the real life that have an exact mathematical closed-form description and are completely deterministic can we describe? How do we model the rest of the processes that are unpredictable and have random characteristics?
Uses and Abuses of Statistics
Statistics is the science of variation, randomness and chance. As such, statistics is different from other sciences, where the processes being studied obey exact deterministic mathematical laws. Statistics provides quantitative inference represented as long-time probability values, confidence or prediction intervals, odds, chances, etc., which may ultimately be subjected to varyious interpretations. The phrase Uses and Abuses of Statistics refers to the notion that in some cases statistical results may be used as evidence to seemingly opposite theses. However, most of the time, common principles of logic allow us to disambiguate the obtained statistical inference.
Design of Experiments
Design of experiments is the blueprint for planning a study or experiment, performing the data collection protocol and controlling the study parameters for accuracy and consistency. Data, or information, is typically collected in regard to a specific process or phenomenon being studied to investigate the effects of some controlled variables (independent variables or predictors) on other observed measurements (responses or dependent variables). Both types of variables are associated with specific observational units (living beings, components, objects, materials, etc.)
Statistics with Tools (Calculators and Computers)
All methods for data analysis, understanding or visualizing are based on models that often have compact analytical representations (e.g., formulas, symbolic equations, etc.) Models are used to study processes theoretically. Empirical validations of the utility of models are achieved by inputting data and executing tests of the models. This validation step may be done manually, by computing the model prediction or model inference from recorded measurements. This process may be possibly done by hand, but only for small numbers of observations (<10). In practice, we write (or use existent) algorithms and computer programs that automate these calculations for greater efficiency, accuracy and consistency in applying models to larger datasets.
Read More
Add your Comment
0
comments
INTRODUCTION TO DESCRIPTIVE STATISTICS
Descriptive
statistics
is the
discipline of quantitatively describing the main features of a collection ofdata, or the
quantitative description itself. Descriptive statistics are distinguished
from inferential
statistics (or inductive
statistics), in that descriptive statistics aim to summarize
a sample, rather than
use the data to learn about the population that the
sample of data is thought to represent. This generally means that descriptive
statistics, unlike inferential statistics, are not developed on the basis
of probability
theory. Even
when a data analysis draws its main conclusions using inferential statistics,
descriptive statistics are generally also presented. 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 of
each sex, and the proportion of subjects with relatedcomorbidities.
Some measures
that are commonly used to describe a data set are measures of central tendency and
measures of variability or dispersion. Measures of
central tendency include the mean, median and mode, while
measures of variability include the standard
deviation (or variance), the minimum
and maximum values of the variables, kurtosis and skewness.
Use in statistical analysis
Descriptive
statistics provides simple summaries about the sample and about the
observations that have been made. Such summaries may be either 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.
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 provide a useful summary of security
returns when researchers perform empirical and analytical analysis, as they
give a historical account of return behavior.
Univariate analysis
Univariate
analysis involves describing the distribution of a
single variable, including its central tendency (including the mean, median, and mode) and
dispersion (including the range and quantiles 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 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:
·
Cross-tabulations
and contingency tables
·
Graphical
representation via scatterplots
·
Quantitative
measures of dependence
·
Descriptions
of conditional
distributions
The main
reason for differentiating univariate and bivariate analysis is that bivariate
analysis is not only simple descriptive analysis, but also it describes the
relationship between two different variables.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 predictor. The standardised slope indicates this change in standardised
(z-score) units. Highly skewed data are often transformed by taking logarithms.
Use of logarithms makes graphs more symmetrical and look more similar to
the normal
distribution, making them easier to interpret intuitively
Read More
Add your Comment
0
comments
