data

Sampling TechniquesB. ANISH KUMARASSISTANT DIRECTOR

Outlines Data definitionSample definitionPurpose of sampling Stages in the selection of a sampleTypes of sampling Techniques Probability sampling Techniques Non Probability sampling Techniques

a.Data is a gathered body of facts b. Data is the central thread of any activity Understanding the nature of data is most fundamental for proper and effective use of statistical skills

Sources of DataInternal Sources External SourcesPrimary DataSecondary Data

Population is defined as The Entire Group under study. Sometimes it is also called as the Universe.

i). Subpopulation It is a subset within the population that inherits the characteristics of the population also maintains some unique characteristics that is not present in other distinct subpopulations inside the population.Example All males and females are two subpopulationsDefinitions

Definitionsii)Sampling frame It is the listing of all items in the population under study.Example- telephone Directory, EnrollmentForm,Census,Patients list etc

Example we may use a telephone directory of Kerala as a sampling frame to represent the population defined as "the adult residents of Kerala". Obviously, there would be a number of elements (people) who fit our population definition, but do not figure in the telephone directory. Similarly, some who have moved out of Kerala recently would still be listed. Thus, a sampling frame is usually a practical listing of the population, or a definition of the elements or areas which can be used for the sampling exercise.

iii) Sample A finite subset of the population, selected from it with the objective of investigating its properties is called sample.

Example-When we want to study the life of electric bulbs produced by a company we select some electric bulbs anaad study their length of life.

iv) Sample Size

The number of units or subjects sampled for inclusion in the study is called sample size. It is not a formula alone that determines sample size. Sampling in practice is based on science, but is also an art

The sample size is decided based on a) use of formulae,b) experience of similar studies,c) time and budget constraints,d) output or analysis requirements,e) number of segments of the target population, f) number of centres where the study is conducted, etc.

Methods of data collection1. Census MethodUnder this method each and every item or unit constituting the universe is selected for data collection. Eg: The population Census conducted in India once in every ten years .

2. Sample Method Selection of some part of an aggregate on the basis of which a judgment or inference about the aggregate is made.

Census Vs SamplingSize of populationAmount of Funds for the studyFacilitiesTime

Stages in Sampling

Define the population Select a sampling frameSelection of the sample Collection of information about the population Making an inference about the population

Types of sampling TechniqueProbability sampling TecNon-probability sampling Tec

Probability Sampling

Every unit in the population has less or more, but valid chance of being selected as a sample. And also, this valid chance can be statistically measured.

In case the probability is equal for each unit in the population, it is called Equal Probability of Selection

Non Probability Sampling

In this method some units of the population does not have any valid chance or the chance cannot be known before, of getting selected in the sampling.

SAMPLING TECHNIQUES

Probability Sampling Tech.1. Simple Random Sampling (SRS) Sample is selected from a population in such a way that every member of the population has an equal chance of being selected and the selection of any individual does not influence the selection of any other. It can be done with or without replacement

Possibility of selecting the same item as a sampleMore convenience, more precise result

SRS with replacement (SRSWR)One unit of element is randomly selected from population is the first sampled unitThen the sampled unit is replaced in the population The second sample is drawn with equal probabilityThe procedure is repeated until the requisite sample units n are drawnThe probability of selection of an element remains unchanged after each drawThe same units could be selected more than once

Number of possible samples in SRSWR= NnExample: 2 elements from 4 (ABCD) How many ways we can draw 2 elements from a population of size 4

AA,AB,AC,ADBA, BB, BC, BD,CA, CB, CC, CD,DA, DB, DC, DD

SRSWR =16= 42

SRS without replacement (SRSWOR)once an element is selected as a sample unit, will not be replaced in the populationThe selected sample units are distinct

Number of possible samples in SRSWR= N = N! r r! (N-r)!

n ! = 1 x 2 x 3x.x n5 ! = 1 x 2 x 3 x 4 x 5 = 120

Example: 2 elements from 4 (ABCD)

How many ways we can draw 2 elements from a population of size 4 using SRSWORAA, AB, AC, AD,BA, BB, BC, BD,CA, CB, CC, CD,DA, DB, DC, DD

SRSWOR = 6 ie, = 4 2 = 4! 2! (4-2)! = 6 AB, AC, AD,BA, BC, BD,CA, CB, CD,DA, DB, DC,

Random Samples may be selected byLottery method: The name or identifying number of each item in the population is recorded on a slip of paper and placed in a box - shuffled randomly choose required sample size from the box.

random numbers table: Each item is numbered and a table of random numbers is used to select the members of the sample.

Table of random numbers Suppose your college has 500 students (population) and you need to conduct a short survey on the quality of the food served in the cafeteria. You decide that a sample of 70 students (sample) should be sufficient for your purposes.

In order to get your sample, you;

Assign a number from 001 to 500 to each students,use a table of randomly generated numbers (Random Number Tables)

Table of random numbersc. Randomly pick a starting point in the table, and look at the random number appear there.d. (In this case) The data run into three digits (500), the random number would need to contain three digits as well.e. Ignore all random numbers greater than 500 because they do not correspond to any of the students in the college.Remember !! Sample is without replacement, so if the number recurs, skip over it and use the next random number.The first 70 different numbers between 001 to 500 make up your sample.

Table of random numbers

Merits and Demerits Merits

Fair way of selecting a sampleRequire minimum knowledge about the population in advance It is an unbiased probability method

DemeritsIt requires a complete & up-to-date list of all the members of the population.Does not make use of knowledge about a population which Investigator may already have.Lots of procedure need to be done before sampling Expensive & time-consuming

2.Stratified Random SamplingA population is divided into homogenous, mutually exclusive subgroups, called strata and a sample is selected from each stratum Goal: To guarantee that all groups in the population are adequately represented.Within stratum - uniformity (homogenous), Between strata differences (heterogeneous).

For example, a group of 200 college teachers can be first divided into teachers in Arts faculty, Commerce Faculty and Science Faculty. After dividing the entire population of teachers into such classes called strata, a sample is selected from each stratum of teachers at random. These samples are put together to form a single sample. Contd

Sample size = 70Number of females =350Population size =500students Stratifying the population by gender. (Male and Female) Calculate the exact sample size from each strata; Male = (150/500)*70 = 21 male studentsFemale = (350/500)*70 = 49 female studentsGive the total sample = 21 + 49 = 70 students

ContdAllocation Proportional to Size of Strata method

Merits and Demerits Merits It represent all group in a population

Comparative analysis of data become possible Offers reliable as well as meaning full results

Demerits It require accurate information on the proportion of population in each stratum.Possibility of faulty classification

3.Systematic sampling

It is modification of simple random sampling ,it is called as quasi (it is in between probability and non-probability sampling )random sampling

Steps The procedure of quasi sampling begins with finding out the sample interval. This can be found out by the ratio of the population to the sample. Afterwards a random number is selected from the sample interval.

The market researcher might select every 5th person who enters a particular store, after selecting the first person at random.Contd.

Circular systematic sampling,In this case, the end of list is connected to the beginning of the list, making the list circular. This allows the random start r to start between 1 to N (1