Monday, November 28, 2011

Concept of Sampling

Concept of Sampling
Introduction
Statistical analysis – Data Analyzing
Collection of Data
Census Method
Sample Method
Universe or population
Sample
Average and variance of sample = Sample statistic
Such values of population is parameters (µ , б)

Census Method
Information collected from each and every unit of population
Also called as Complete Enumeration Method
Merits
Reliable and accurate data
Extensive Information
Suitability
Demerits
More expensive
More time consuming
More labor required
Not suitable for Specific Problem

Sampling Method
Data is collected from the sample of items selected from population
Merits
Saving time and money
Intensive study
Organizational Convenience
More reliable results
More scientific
Demerits
Less accurate
Wrong conclusion
Less reliable
Not suitable
Difference between Census and Sampling
Census
All Items
Expensive time ,money and labor
Investigation with limited field
Heterogeneous
Each and every unit

Sampling
Few items
Economical
Investigation with large field
Homogenous
Few unit

Sampling Method
Probability Sampling Method
Simple random sampling
Lottery method
Tables of random numbers
Merits
Free from personal bias
Equal chance of being selected
Save time , labor and money
Demerits
Sample size is small , then sample is not adequately
Universe small , not suitable
Stratified Random sampling
Heterogeneous
Different strata acc to characteristics
Merits
More likelihood of representation of unit
Comparative study
More accuracy
Demerits
Limited scope
Possibility of prejudice


Systematic random sampling
Systematically arranged and numbered
Sample unit , equal interval
Merits
Simple method
Little time
Demerits
Each unit doesn’t stand equal chance

Multistage Random sampling
Many stages
Merits
Regional basis
Decision on the basis of sample alone
Demerits
Lot of time and labor
Cluster Sampling
Applied in pharmaceutical industry

Non - Probability Sampling Method
Judgment sampling
Merits
Less expensive
Simple and easy
Demerits
Greater chance of prejudice
Not very accurate and reliable
Quota Sampling
Merits
Greater chance important unit being included
Inquiry is more organized
Convenience Sampling
Extensive sampling
Merits of Sampling
Less time
Less cost
More reliable
Mors detailed information
Demerits
Inaccurate and misleading
Absence of qualified staff
Sampling and Non Sampling Errors
Error = Difference between Sample static and Population parameter
Sampling errors = error arising due to drawing interferences about the population on the basis of few observation
Two types of error
Sampling error
Non sampling error
Errors may be occur in the collection , processing and analyzing of data
Sampling Errors
Biased errors
Unbiased errors
Faulty selection of the sampling method
Faulty demarcation(Boundaries) of sampling unit
Variability of the population which has different characteristic
Bias in analysis

Method of reducing Sampling errors
Sample size – larger – less error

Non Sampling Errors
Faulty planning
Faulty selection of the sample unit
Lack of trained and experienced staff
Errors in compilation
Errors due to wrong statistical measures
Framing of a wrong questionnaire
Incomplete investigation of the sample survey

Principle of Sampling
Principle of Statistical Regularity
According to king this law states that a moderately large number of items chosen at random from a large group are almost sure on the average possess the characteristic of large group
Principle of Inertia of Large number
Corollary of the principle of Statistical regularity
Larger the size of the sample , more accurate result likely to be.
Estimation of parameters
Statistical inference is the estimation of population parameters from the corresponding sample static
Statistical estimation
It is the procedure of using a sample statistic to estimate a population parameter.
Statistic used to estimate a parameter is called estimator
Value taken by the estimator is called an estimate
SE can be divided in two
Point estimation and interval estimation
Estimation of parameters
Properties of good estimator
Unbiasedness
Average of the sample values = population parameter
Estimator is unbiased = expected value of estimator = population
Consistency
Sample size increases and decrease in error
Efficiency
Variance of estimator is small , the distribution of estimator will be better in that its value is closer to Parameter value

Sufficiency
Sir R.A. Fisher
A sufficient estimator is one that uses all information about the population parameter contained in the sample
Test of Hypothesis
It is an assumption about the population parameter to be tested based on sample information
Hypothesis testing for making decision
In attempting to reach decision , it is useful to make assumptions or guesses about the populations involved. Such assumption , which mat or may not be true are called statistical hypothesis
Test of Hypothesis
Procedure of hypothesis testing
Set up the hypothesis
Null hypothesis denoted by H0
Alternate hypothesis by H1
Set up the suitable significance level
Determination of a suitable test statistic
Test statistic = sample statistic – hypothesized PP
Standard error of SS
Determine the critical region
Doing computation
Making decision

Type 1 and type 11 errors
The hypothesis is true but our test rejects it
The hypothesis is false but our test Accepts it
The hypothesis is true but our test accepts it
The hypothesis is false but our test rejects it

One tailed and two-tailed test
One tailed and two-tailed test
Central limit theorem
It is widely used in the field of estimation and inference. This states that if we select random sample of large size n from any population with mean and SD and compute the mean of each sample , then sampling distribution of mean approaches normal distribution with mean and SD б/√n. This is true even if population itself is not normal.