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What is parametric distribution
• When we assume that we have 2 populations
being compared
Then we, and
canwe
sayfound
thatthat they are :
they are parametrically
normally
( ordistributed
normally )
have equal
variance
distributed
have small standard of deviation
have a large sample size
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Example of a normally distributed parameters :
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Parametric tests for
significance
 T tests :
-one sample t test
-two independent sample t test
-paired t test
 The F distribution
 Chi square tests
 ANOVA
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Parametric tests for
significance
1] one sample
t test
2] two
independent
sample t test
3] Paired t
test
4] The F
distribution
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1] One sample test
 This test is applied when results from a
single group ( single set of data ) are to be
compared to a hypothetical or standard
value of the mean
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 E.g. :
Sample mean
Hypothetical or
standard mean
1. Average tablet potency
of N tablets
Label potency
2. Average dissolution of N
tablets
Quality control
specifications
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2] Two independent sample
t test
 Its also called Student's t test
This test is applied for comparison of
averages obtained from 2 independent
groups
 E.g.
group of male and group of female
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3] Paired t test
 This test is applied when independence
can not be applied
 It is applied in :
 It is applied when a single group is subjected to
2 different treatments on 2 separate occasions
 Bioequivalence studies ( bioavailability studies)
 Same material is analyzed by 2 methods one of
which is new analytical method
 Before and after control
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Advantages
over two
independent t
test
Disadvantages
• 1] Decrease variability where :
• a) In 2 independent t test : variability
arises from difference among
experiment units
• b) In paired test : variability arises
from difference within experiment
units which is for sure , less than
among experiment units
• 2] Needs less experiment materials
• 1] Treatment can not be
applied concurrently
• 2] Extended time of the
experiment
• 3] Carry over effect
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• Significance depends on the ratio
between difference of means to standard
error of the difference
• This ratio
by
SE
variability
SE
Therefore significance is more accurately
expressed
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• This design is applied in form of cross over
test design where :
Single group of experimental animals
subgroup 1
treatment 1
treatment 2
subgroup 2
treatment 1
treatment 2
Over two separate occasions
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• Paired t test is just like before and after
test
• E.g.
study speed of typing before and after
drug administration
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independent
Student t
test
paired
Paired t test
Parametric
test
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4] The F distribution
• It is used to compare two variances
• F is the ratio of the variances
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when do we use this test? :
• It is used when we are interested in the
variability between 2 sets of data and not
the means
E.g. :
• When an active ingredient is mixed in a powder to
be capsulated , this powdered mixture is analyzed
for homogenous mixing
• When two batches are compared we are
interested in the variation among batches not in
the means of the assays because the means are
indicative for the homogeneity of mixing
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