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I am Tajamul Islam Part (3)
Consistency of Data / class frequencies.
|
Theory
of Attributes |
Consistency,solved examples on consistency, |
Meaning ; It is obvious that in statistics of
attributes, when frequencies of various classes are counted no class frequency can be negative. If any
class frequency is negative, the data are said to be inconsistent. Such inconsistency may be due
to wrong counting or inaccurate additions or subtractions or may be the result
of misprints.
In order to test
whether a set of figures is consistent, various class frequencies should be
found and if no class frequency
is negative, apparently the data are consistent. The easiest way to find
out whether the data are consistent is to obtain ultimate class frequencies because if there is any
inconsistency, one or more ultimate class frequencies would be negative.. For
example, the value of (A) cannot be more than N, otherwise (α) would have a negative value. Similarly; (A)
cannot be less than 0, Otherwise (A) itself would have a negative value.
“The necessary and sufficient condition for
the consistency of a set of independent class frequencies is that no ultimate Class frequency is negative.
If
there is only one attribute then;
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Example 1. To Investigate
the consistency of the following data;
(Aβ)=414,
(αB)=260 (αβ)=238 (A)=400
Sol.
Example 2. A labour welfare officer returns the
following number of workers observed with certain classes of defects amongst a
number of factory workers. A denotes development defects and B, low nutrition.
N
= 600 (A) = 250 (αB) = 400 (Aβ) = 200
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