Download Introduction Basic Definitions and Concepts

Introduction Basic Definitions and
Concepts
Nilesh Kulkarni
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Contents:
Defination of variables.
Types of variables.
Sampling & population & different types.
Population parameter and sample statistics.
Precision, Accuracy, bias.
Nilesh Kulkarni
• Objective: To know about the proper variables
and how to identify it properly.
• By this we will know that how to select thing
in a proper manner .
• By this study some confusions might be clear
about systematic .
Nilesh Kulkarni
• VARIABLES: A Variable is defined as anything that varies or
changes in value. Variables take on two or more value.variable
generally is anything that may assume different numerical or
categorical value.
• Variable it may be increase or decrease.
• For eg:like weight, height or income i.e family income is a
variable it can take on value from zero to billion of rupees.
• Gender is a variable it can take two value male and female.
• Marital status is a variable it can on value of never
married,single, married, divorced.
• Variables it can be in the production batch.
• ake on two or more values. Variable generally is anything that
may assume different numerical or categorical
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TYPES OF VARIABLES
1)Continuous Variables & Discrete Variables .
2)Dependent Variables &Independent Variables.
3)Moderating Variables.
4)Intervening Variables.
5)Extraneous Variables.
1) Continuous Variables & Discrete Variables:
Values of variable can be divided into fraction we
call it as a continuous variables.
• Value even in decimal point are called
continuous variables.
• Variables can take infinite number of value
• For eg:age,income, temprature.
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• Discrete Variables: It is also called as non-continuous
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variables or categorical variables or discontinuous variables.
Variables that has a limited number of distinct value & which
cannot divided into fraction is a called discontinuous variable.
Variables that are not continuous they can expressed in integral
value they are non-continuous variables.
For eg: number of children is an ex. of not –continuous.
Some variable has only 2 value i.e. Male-female,presence or
absence,employed- unemployed.such variable are refered as
dichotomous variable
Eg:same class 2 students are selected
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• 2)Dependent Variables &IndependenVariables:
• Independent variables: variable which are in the hand of
researcher .
• Dependent Variables: outcome of manipulation is
dependent
• Eg:Reduction particle size improve solubility.
• For eg:Height depend upon age. Height is dependent variable
&age is independent
• Ingredients & Tablet. Ingredients is independent ,tablet is
dependent.
• Cipla launch new medicine & market share increase. New
medicine is independent & market share is dependent.
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• 3)Moderating Variables: The presence of third variable(the
moderating variable) that modifies relationship between the
independent& the dependent variable.
• For eg:library facilities(x)& performance of the students(y)……
in this facilities is independent & performance is dependent
& interest and inclination of student is 3rd variable and i.e.
hard afford and strength of student.
• 4)Intervening Variables: It comes between the independent
&dependent variables and shows the mechanism between
them.
• Certain variable that cannot be controlled or measured
directly may have & important effect on the out come. These
modifying variables intervene between the cause and effect.
• For eg:Mobile,simcard,network. Mobile-dependent ,simcardindependent,network-mechanism
• Married people are less likely to suicide than single.
• API,Tablet,excipient.
• Coiumn,HPLC,Pressure.
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• Particle size,solubility,Temprature.
(5)Extraneous Variable: Extraneous variables are
those uncontrolled variables(i.e,Variables are not
manipulated by the experimenters) that may have a
significant influence on the result of a study. Many research
conclusion are questionable because of the influence of the
extraneous variables.
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Sample and population
• Population: A population is defined as a group of
individual which at least one common characteristic which
distinguishes that group of individuals.
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Eg.Learning disabilities
If we want to select then
Go to narrow Population in that narrow population.
Select Specific area,
After selecting specific area select specific place and from
that we
can select.
• eg.group of population suffering from diabetics
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Sample
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A sample is a small proportion of the population that is selected
for observation and analysis.
By observing the characteristics of sample one can make certain
inferences about the characterics of the population from which it was
drawn
One can also infer changes observed in the sample. changes that would
likely have occurred in the population.
Contrary to population sample are not selected haphazardly, they stare
chosen in a systematically random way. so that chance or the operation of
probability is utilized.
Where random selection is not possible other systematic methods are
used.
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Sampling Method
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Randomness.
Simple Random sample.
Random number.
Systematic sample.
Stratified random sample.
Area or cluster sample.
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• 1)Randomness:It is based on the assumption that while
individual events cannot be predicted with great accuracy
aggregate.
• Although it may not predict with great accuracy an individual
academic achievement .it will predict accurately the average
academic performance of a group.
• It has two important application:1)selection of group of
individuals for observation who are representative of the
population.
• 2)Assigning individuals by random assignment i.e each of individual
has equal chance.
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• Sampling error: A small
difference in conclusion or a
small variation in conclusion.
• 2)Simple Random Sample: Probability sampling is
also known as Random sampling or Chance sampling.
• Each has an equal & independent chance of being
selected.
• In this entire population have equal chance of being
included in the sample
• This applies to sampling without replacement i.e once an
item is selected for the sample ,it cannot appear in the
sample again.
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• 2)Simple random sample are:
• a)It gives each element in the population an equal probability of
getting into the sample & all choice are independent of one
another.
• b)It gives each possible sample combination an equal probability.
• 1) sample random sample from the finite population as a sample
which can chosen such a way that each of the N Cn Possible
sample has same probability 1/ N Cn being selected
• for more clear we take certain finite population comsisting 6
elements (say a,b,c,d,e,f) i. e N=6 & sample size n=3, then there
are 6C3 = 20
• possible distinct sample of required size element consist
abc,abd,abc,abd,abe,abf,acd,ace,acf,ade,adf,aef,bcd,bce,bcf,bde,
bdf,bef,cde,cdf,cef,def.If we chose one of the samples in such a
way that each has the probability 1/20 of being chose.
• 2)eg:on a cheat write a no & put it into one pot & see the cheat
which no as for the requirement of the sample .
Nilesh Kulkarni
• 3) Random Number: A more convenient way of
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selecting a random sample or assigning individuals to
experimental & control groups so that they are equated is by
the use of a table of random numbers.
Many such tables have been generated by computers producing
a random sequence of digitals.
This random number selected from left,right,top,bottom.
For eg: assume that sample of 30 is selected from serially
numbered population of 835, table of random no produce 30
In this 3 digit no are selected by reading from left,right,up
down.
The sample comprises 30 no members of population .the group
are divided into 2 groups 15 in one group and 15 in other group
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The Sample
503
426
197
161
590
913
449
931
337
422
530
234
408
669
333
802
381
820
457
497
092
050
242
660
273
939
982
090
897
699
161
117
074
383
234
744
407
893
In selecting this sample 8 no.were deleted number 931
,982,897,893,939,913 were deleted because they were
larger than the population of 835 no.
234 and 161 were deleted because duplicate previous
selection.
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• 4)Systematic Sample:The most practical way of
sampling is to select every or nth term from a list
sampling of this type is known as systematic sampling
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• Systematic sampling has plus point.
• For eg:Sample of 200 were to be selected from a
telephone director 20,000 listings .one would
selected the first name by random selecting page.
• Then every thousand name would selected until the
200 name & if the last page were reached before
desired no then again start from first & complete 200
• Eg: BSNL
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• 5)Stratified Random sample: Stratified random
sample is that subdivided the population into
smaller group more accurate representation.
• Eg:If an new setup of industry is done an
employ is appointed over there i.e 60 worker
then properly subdivided them category wise
like education skilled,unskilled person.
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• 6) Area or cluster sample: The total area of intrested happen to
be a big one a convenient way in which a sample can be taken is
to divided the area into a smaller area & then select is with the
ultimate sample consisting of all units in these small area or
clusters.
• For eg:for the purpose of servey researchers wanted to select a
sample from all public elementary teacher in the united states
• From 50 states a random sample of 20 could be selected
• From 20 state all countries could be listed random sample of 80
countries selected
• From 80 countries all the school districts are listed
• 30 school where selected
• Now from 30 school random selected 500 teachers,
• Successive random sampling of states,countries,school districts
,finally individuals would involve
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• For eg: best school.
Population parameter & sample
statistics
• statistics is to understand the difference between
populations and samples. Populations consist of everything
or everybody you want to measure.
• for example, “all women in the Bay Area between the ages
of 18 and 54.”
• “The light bulbs we are manufacturing in this plant.” “Every
human being on planet earth.” These are all populations.
Populations have parameters .”
• The science of statistics is based on measuring these
samples; in other words, samples have statistics. Hypothesis
testing is done by testing the sample statistics against
assumptions about the population parameters.
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Variation:
• The act ,process, or result of varying.
• Something slightly different from another of the same type.
• Variation in quality, amount or variation in temperature.
• Eg: Variation of the needle ,compass , height.
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• The mean and variance of a population are population
parameter:
• Population mean=(μ) the average value
• Sample mean =Y estimates μ
• Population median-middle value.
• Sample mean estimate population median.
• Population variance.
• Sample variance.
• Standard deviation.
• Standard error of mean.
• Coefficient of variance.
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Precision and Accuracy:
• Precision:Pression is defined as the closeness of agreement
between series of measurement obtained from multiple
sampling of the same homogeneous sample under prescribed
condition.
• Accuracy: defined as closeness of agreement between the
value which is accepted either as a conventional true value or
an accepted reference value and the found value.
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Bias:
• The different between a population mean of the
measurement of test results & accepted reference or true
value.
• Therefore bias leads to an under or overestimate of the true
value.
• Measurement bias usually does not disappear with ↑sed
sample effect as all measurement are systematically bias
away from true value.
• Eg:observed no. of species is a negatively bias estimator of
the total species richness whoes bias ↓ses with ↑sing sample
effect.
Nilesh Kulkarni
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Significant figures
Non-zero digits are always significant.
All zeros between other significant digits are significant.
The number of significant figures is determined starting with the leftmost
non-zero digit. The leftmost non-zero digit is sometimes called the most
significant digit or the most significant figure. For example, in the number
0.004205 the '4' is the most significant figure. The left-hand '0's are not
significant. The zero between the '2' and the '5' is significant.
The rightmost digit of a decimal number is the least significant digit or
least significant figure. Another way to look at the least significant figure is
to consider it to be the rightmost digit when the number is written in
scientific notation. Least significant figures are still significant! In the
number 0.004205 (which may be written as 4.205 x 10-3), the '5' is the
least significant figure. In the number 43.120 (which may be written as
4.3210 x 101), the '0' is the least significant figure.
If no decimal point is present, the rightmost non-zero digit is the least
significant figure. In the number 5800, the least significant figure is '8'.
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Conclusion
• In this we find the best way to distinguish
large population to small one in simple way.
• All work carried in properly
• No confusion occur .
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Reference
• 1)Research in Education Tenth edition. By John
W.Best,JamesV.Khan.
• 2)Research Methodology Methods and Techniques.
Second revised edition.C.R.Kothari.
• 3)Moor DS, McCabe GP & Craig BA. Introduction to the
Basic practice of Statistic. New york:W.H.Freeman & CO,
Fifth edition.
• 4)B.A .Walter Zool museum univ,of Copenhagen.
• 5) Significant Figures in Measurements and Calculations
By Anne Marie Helmensline,ph.D.
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 Jackson L. S.; Lee K. (1991-01-01). "Microencapsulation and the food industry".
Lebensmittle–WissenschaftTechnologie.
http://cat.inist.ft/?aModele=afficheN&cpsidt=5014466. Retrieved 1991-02-02.
Nilesh Kulkarni