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Introduction of Statistics

Statistics is the study of the analysis, collection, organization, interpretation and presentation of data. It deals with all aspects of this which involves the planning of data collection in terms of the design of surveys and experiments.

A statistician is someone who is principally well versed in the ways of thinking essentially for the successful application of statistical analysis. These people have regularly gained this experience through working in any of a broad number of fields. There is one more discipline known as mathematical statistics which studies statistics mathematically.

The term statistics whenever referring to the scientific discipline is specifically as in "Statistics is an art". This must not be confused with the word statistic, that is referring to a quantity (such as mean or median) computed from a set of data. Whose plural is statistics ("this statistic appears wrong" or "these statistics are ambiguous").

Key terms used in statistics:

Null hypothesis:

Interpretation of the statistical information can frequently include the development of a null hypothesis in that the postulation is that whatever is proposed as a cause has no effect on the variable being measured.

The best illustration for a novice is the predicament encountered by a jury trial. The null hypothesis that is represented by H0, asserts that the defendant is innocent, whereas the alternative hypothesis H1, asserts that the defendant is responsible. The indictment comes due to suspicion of the guilt. The H0 positions in opposition to H1 and is maintained unless H1 is supported by proof "beyond a reasonable doubt". Although, "the failure to reject H0" in this situation does not imply innocence, but only that the proof was insufficient to convict. Therefore the jury does not accept essentially H0 but fails to reject H0. While one cannot confirm a null hypothesis HO one can test how close it is to being true with a power test, which is the tests for type II of errors.

Error:

Working from a null hypothesis, the two primary forms of error is recognized:

Type I: errors where the null hypothesis is incorrectly rejected giving a "false positive".

Type II: the errors where null hypothesis fails to be rejected and a real difference between populations is missed giving a "false negative".

The error also refers to the extent to which separate observations in a sample vary from a central value, such as the population mean or sample. Most of the statistical methods seek to minimize the mean-squared error, and these are known as "methods of least squares."

The measurement processes, which generate statistical data, are also subject to error. Most of these errors can be categorized as random (noise) or systematic (bias), but other significant kinds of errors (example, blunder, like when an analyst reports wrong units) can also be significant.

Symbols used in statistics

Relational Symbols

  =  

equals
is the same as

  ≠  

is not equal to
is different from

  >  

is greater than
is more than
exceeds
is above

  ≥
or >=  

is greater than or equal to
is at least
is not less than

  <  

is less than
is fewer than
is below

  ≤
or <=  

is less than or equal to
is at most
does not exceed
is not greater than
is no more than

A < x < B

x is between A and B, exclusive

A ≤ x ≤ B

x is between A and B, inclusive

A ≅ B

A is approximately equal to B

Here are symbols for various sample statistics and the corresponding population parameters. They are not repeated in the list below.

sample
statistic

population
parameter

description

x¯ "x-bar"

μ "mu"
or μx

mean

M 
(TIs say Med)

(none)

median

s 
(TIs say Sx)

σ "sigma" 
or σx

Standard deviation
For variance, apply a squared symbol (s² or σ²).

r

ρ "rho"

coefficient of linear correlation

p^ "p-hat"

p

proportion

zo   to   χ²o

(n/a)

calculated test statistic

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