Population & sample lecture 04

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Populations & SAMPLING

By Dr Zahid Khan

King Faisal University, KSA

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Objectives

Define and identify the different levels of measurement and variables

Define, appraise, use and interpret the different tools used for data analysis

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POPULATION The entire aggregation of items from

which samples can be drawn is known as a population.

In sampling, the population may refer to the units, from which the sample is drawn.

A population of interest may be the universe of nations or cities.

This is one of the first things the analyst needs to define properly while conducting a business research.

“N” represents the size of the population.

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Definitions Population Parameters. Statistics such as averages and standard

deviations, median, mode etc are population parameters.

Bias.

Bias is a term which refers to how far the average statistic lies from the parameter it is estimating, that is, the error which arises when estimating a quantity. OR

A statistic is biased if it is calculated in such a way that is systematically different from the population parameter of interest Unbiasedness. This means that the average of

large set of unbiased measurements will be close to the true value.

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Definitions Precision.

This means that repeated measurements would be close to one another but not necessarily to true value. Randomization.

The allocation of patients to both treatment and control groups in a random manner. This enables the minimization of selection bias. Blocked Randomization.

When participants are allocated to two groups as blocks of 2, 4, 6 or 8 and so on and both groups contain equal number of blocks at each time interval.

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What is sampling ?

In simple words, sampling consists of obtaining information from a portion of a larger group or an universe. Elements are selected in a manner that they yield almost all information about the whole universe, if and when selected according to some scientific principles and procedures.

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CENSUS

A complete study of all the elements present in the population is known as a census. The national population census is an example of census survey

SAMPLE A Sample is a selection of units from the entire

group called the population or universe of interest. It is Subset of a larger population

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SAMPLE DESIGN

NON-PROBABILITY SAMPLES PROBABILITY SAMPLES

.CONVENIENCE ● SIMPLE RANDOM

.JUDGMENTAL ● STRATIFIED

.QUOTA ● CLUSTER

.SNOWBALL ● SYSTEMATIC

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NON-PROBABILITY SAMPLING

The probability of any particular member being chosen for the sample is unknown.

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CONVENIENCE SAMPLING The sampling procedure of obtaining

the people or units that are most conveniently available

Accidental sampling is a type of non-probability sampling which involves the sample being drawn from that part of the population which is close to hand

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QUOTA SAMPLING in quota sampling, the population is

first segmented into mutually exclusive In quota sampling the selection of the sample is non-random sub-groups

In the quota sampling the interviewers are instructed to interview a specified no of persons from each category. In studying peoples status, living conditions, preference, opinions, attitudes, etc

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JUDGEMENT SAMPLING Samples in which the selection criteria are

based on personal judgment that the element is representative of the population under study.

Example:--In test marketing, a judgement is made as to which cities would constitute the best ones for testing the marketability of a new product.

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SNOWBALL SAMPLING

samples in which selection of additional respondents is based on referrals from the initial respondents

Initial respondents are selected by probability methods

Additional respondents are obtained from information provided by the initial respondents

PROBABILITY SAMPLING

Every member of the population has a known, non-zero probability of being selected

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Simple random sampling

Random sampling mean, the arrangement of conditions in such a manner that every item of the whole universe from which we are to select the sample shall have the same chance of being selected as any other item.

Among all the probability sampling procedures random sampling is the most basic and least complicated.

Systematic sampling

1. Prepare a list of all the elements in the universe and number them. This list can be according to alphabetical order, as in records etc.

2. Then from the list, every third/every 8th / or any other number in the like manner can be selected.

For this method, population needs to be homogeneous. This method is frequently used, because it is simple, direct and inexpensive. Also known as patterned, serial or chain sampling.

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Stratified sampling

When the population is divided into different stratas or groups and then samples are selected from each stratum by simple random sampling procedure, we call it as stratified random sampling

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Cluster Sampling

The whole population is divided in small clusters it may be according to location. Then clusters are selected in sample

The purpose of cluster sampling is to sample economically while retaining the characteristics of a probability sample.

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SAMPLING PROCESS

Defining the target population.

Specifying the sampling frame.

Specifying the sampling unit.

Selection of the sampling method.

Determination of sample size.

Specifying the sampling plan.

Selecting the sample.

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Advantages of sampling

Helps to collect vital information more quickly and it helps to make estimates of the characteristics of the total population in a shorter time

Sampling cuts costs. Much of time and money is saved at each stage of research

Sampling techniques often increases the accuracy of the data. With small samples it become easier to check the accuracy of the data.

From the administrative point of view also sampling become easier – problem of hiring the staff, task of training and supervising will become easier

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Disadvantages of sampling Sampling is not flexible in a situation where

knowledge about each unit is needed. E.g. estimation of national income for the current year.

Reliability of information depends upon the representativeness of the sample of the total population

Most of the sampling techniques require the service of a sampling experts or statisticians.

Hospital patients may be different than those in the community

Volunteers are not typical of non-volunteers.

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Standard Error of Mean

SEM = SD√n. Printers SEM = 4.5 √72 = 0.53mmHg Farmers SEM = 4.2 √ 48 = 0.61 mmHg

Number Mean DBP SD ( mmHg)

Printers 72 88 4.5

Farmers 48 79 4.2

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Standard Error of a proportion or Percentage

Total No. of patients diagnosed with Appendicitis = 120

No. of Males = 73 ( 60.8%) No. of Females = 47 ( 39.2%) If P represents one percentage then 100 – P is

percentage for the other so SE Percentage = P(100-P) n

SE Percentage = 60.8 * 39.2/120 = 4.46

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Difference between Standard Deviation & Standard Error SD is a sample estimate of the population parameters. In other words it is the estimate of variability of observations. Each population has a unique SD and as the population size enlarges, the more precise estimate of population SD is provided by it.

SE is on the other hand is a measure of precision of an estimate of a population parameter.SE is always attached to a parameter and it can be calculated for any parameter like Mean, Median, Fifth centile and even for SD itself.

As sample size increases, the SE of the estimate will decrease as the precision of the estimate will increase with increasing sample size.

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When to use SD & SE!!!!

If the purpose of the data is to describe the data and it is normally distributed, then use Standard Deviation denoted by SD.

If the purpose is to describe the outcome of a study, e.g to estimate the prevalence of a disease or the difference between two treatment groups, then one should use standard error denoted by SE.

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