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Distributions Commonly Used in Statistics
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Several types of probability distributions are
used in process of making statistical inferences
about a population on the basis of a sample.
The knowledge in this commonly used distributions
and their properties is needed to use and
interpret statistical methods correctly.

• We can differ between two groups of the most
  often used distributions
• Distributions used for populations
• Distributions used for samples

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Distibutions most often used in statistics
(Summary)

1. For PopulationsGaussian normal
   distributionStandard normal disributionNonnormal
   distribution
2. For Samplest-distribution (Students)
   Chi-square distribution (Pearsons)F-
   distribution (Fisher-Snedecors)

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A) Gaussian Normal Distribution
Commonly, most of biological data follow Gaussian
Normal Distribution bell-shaped curve - the
majority of values is located around the mean
(centre of symmetry) with progressively less
observations toward the extremes.
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A) Gaussian Normal Distribution
The shape of the curve is determined by 2
parameters? - defines the centre of symmetry
of the curve (middle of the population),
indicates location of the curve on the numerical
axis of studied variable? - defines the spread
of the curve in the inflexion point (variability
of the population)
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A) Gaussian Normal Distribution
Within the range of ? ? 1? - 68.3 of all
values in the population ? ? 2? - 95.5 ?
? 3? - 99.7
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A) Standard Normal Distribution
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A) Non-normal Distribution (Irregular, Unknown)
We can define the median only (as a centre). The
spread of the curve is not possible to assess.
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B) Sample Distributions
t Distribution (Student) is defined for a
theoretical variable t - is calculated from the
mean and SD in a sample. (was
published in 1908 by William Gosset under the
pseudonym Student) is used for samples selected
from the population with Gaussian Normal
Distribution ? there are several (many) curves
for samples differing in number of items (n).
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B) t - Distribution (Student)
Normal
Height and spread of the curve - according to the
sample size - the smaller is the sample size the
broader and lower is the curve - the bigger is
the sample size the narrower and higher is the
curve (in the extreme n? the curve joins the
normal distribution)
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B) t - Distribution (Student)
Normal
Spread of the curve is defined by ?/?-2 when
n? ? spread 1 (normal) when n6 ?
spread 5/3
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• t-distribution - Use
• Statistical tables of t-distribution
• critical values in testing for difference between
  two means (Student t-test)
• coefficients used in calculations

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B) Chi-square (? 2- Distribution (Pearson)

• Asymmetrical curve different shapes for
  different sample sizes (?n-1 determines the
  shape)
• the smaller is the sample size the higher and
  more asymmetrical is the curve shape
• the bigger is the sample size the lower and more
  symmetrical is the curve shape

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• Chi-square distribution - Use
• Statistical tables of ? 2- distribution
• critical values in testing for difference
  between frequencies
• coefficients used in calculations

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B) F - Distribution (Fisher Snedecor)

• Asymmetrical curve different shapes for
  different sample sizes (?1,?2 determine the
  shape)
• the smaller is the sample size the lower and more
  asymmetrical is the curve shape
• the bigger is the sample size the higher and more
  symmetrical is the curve shape

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• F-distribution - Use
• Statistical tables of F- distribution
• critical values in testing for difference
  between 2 variances (F-test)