Parameters, Variables,

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Parameters, Variables, Evidences Identifying
Research QuestionSeeking the right variables
evidences (questions)Quality of Data
Instrument to capture information
systematicallyTechniques for Analysis
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Measurement of Perception Attitude A tendency
to evaluate a stimulus with some degree of favor
or disfavor, usually expressed in cognitive,
affective, or behavioral responses   A learned
tendency of an individual   Expressed as
opinion OR Primary Observations / Secondary
Data / Archives
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• DATA
• Primary DataSecondary Data
• SCALES (order, distance, origin)
• Nominal Scale, GenderOrdinal Scale, Grades A,
  B, C Interval Scale, Years - 2001-2007 Ratio,
  GDP

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Some Basics
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Descriptive statistics (parametric)

• Sample
• Population
• Statistics
• Parameter
• Raw data, source, authenticity

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Sampling Estimation
Sampling
  1. Simple random Sampling equal probability of
being picked 2. Systematic Sampling
selected at an uniform interval 3.
Stratified Sampling selected from homogeneous
groups / strata 4. Cluster Sampling make
clusters and choose any one of them
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Statistical inference is based on simple random
sampling
Sampling Distribution

•  Sampling distribution of the mean

A probability distribution of all the possible
means of the samples is a distribution of sample
means.

• Sampling distribution of the median
• Sampling distribution of the proportion

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Standard error
The standard deviation of the distribution of a
sample statistic is known as the standard error
of the statistics.
Example standard deviation of the distribution
of sample means is termed as standard error of
the mean.   The population
distribution   µ the mean of the
distribution
 

µ s standard deviation of this distribution
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The sample frequency distribution
x1 x2 x3
x4
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The sampling distribution of the mean
 
µ x
µx mean of the sampling distribution of the
means sx standard error of the mean
standard deviation of the sampling distribution
of mean
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Sampling from Normal Populations
           
 
Properties of the sampling distribution of the
mean when the population is normally
distributed µx µ sx s/v n
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Standard error of the mean for infinite
population
sx s/v n
Standard error of the mean for finite
populations
s (N - n) s x ---- v
---------- v n n-1
With a finite population multiplier
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Standardizing the sample mean
Standard score standard deviation from the mean
of a standard normal probability distribution
  x - µ Z ------- s x  
Sample mean, population mean, standard error of
the mean
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The Central Limit Theorem
  The mean of sampling distribution of the mean
will equal the population mean regardless of the
sampling size, even if the population is not
normal.   As the sample size increases, the
sampling distribution of the mean will approach
normality, regardless of the shape of the
population distribution.   The significance of
the central limit theorem is that it permits us
to use sample statistics to make inferences about
population parameters, without knowing anything
about the shape of the frequency distribution of
that population other than what we can get from
the sample.
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Estimation
Reason for estimates To make statistical
inferences about the population from a
sample. Types of estimate    Point Estimate It
is a single number that is used to estimate
an unknown population parameter.  
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 Limitations
Often insufficient, right or wrong Example
Total weight of students, CGPA of students in a
high school Point estimate is more
useful, if it is accompanied by an estimate of
the error that might be involved.    Interval
Estimate It is a range of values used to
estimate a population parameter.
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Criteria of a good Estimator
Unbiased
If the statistic tends to assume values that are
above the population parameter as frequently as
it assumes values that are below the population
parameter.
Efficiency It refers to the size of the standard
error of the statistic If we compare two
statistics from a sample of the same size, and
try to decide which one is the more efficient
estimator, we would pick the statistic with the
smaller standard error
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Consistency
If as the sample size increases, the statistic
becomes closer to the values of the population
parameter, then that statistic is consistent.
Sufficiency An estimator is sufficient if it
makes so much use of the information in the
sample that no other estimate could extract from
the sample, additional information about the
population parameter.
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DATAPrimary DataSecondary DataSCALES
(order, distance, origin) Nominal Scale,
GenderOrdinal Scale, Grades A, B, C
Interval Scale, Years - 2001-2007 Ratio, GDP