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.