Learning Objectives Understand the identifying the target
respondents Sampling and different types of sampling Understanding
sample process What are the potential errors in sampling
Determining Sampling size
Census vs. Sampling Two methods of selecting the respondents
Census Sampling Census When the number of respondents / units of
interest are limited, or When it is required to gather data from
all the individuals in the population
Census vs. Sampling Sampling When the size of the population is
too large The population is homogeneous Considerations of time and
cost play a major role in going for sampling
Sampling Process Define the population Identify the sampling
frame Specify the sampling unit Selection of sampling method
Determination of Sampling size Specify sampling plan Selection of
sample
Sampling Process The population needs to be defined in terms
of: Term Example Element Companys Product Sampling Unit Retail
outlet, super market Extent Hyderabad & Secunderabad Time April
10 May 25
Sampling Process Define the population Identify the sampling
frame Specify the sampling unit Selection of sampling method
Determination of Sampling size Specify sampling plan Selection of
sample
Sampling Process Identify the sampling frame: Need to clearly
define from which universe will the sample be picked from Ex: When
you are studying the purchase behaviour of consumers buying premium
cars, your sampling frame will be all the premium car outlets in
the city
Sampling Process Define the population Identify the sampling
frame Specify the sampling unit Selection of sampling method
Determination of Sampling size Specify sampling plan Selection of
sample
Sampling Process Specify the sampling unit We need to decide on
whom to contact in order to obtain the data required Need to be
careful while selecting the sampling unit, as we need to be sure of
whether we will get the required data from the respondent or not
Ex: When studying intention to purchase a car, the unit of sampling
would be people who are employed and having a steady income.
Whereas if we are studying the trends from a dealer perspective,
then the sampling unit will be the dealers
Sampling Process Define the population Identify the sampling
frame Specify the sampling unit Selection of sampling method
Determination of Sampling size Specify sampling plan Selection of
sample
Sampling process Need to select the kind of sampling method
used in order to identify the respondents There are two ways of
selecting the sample: Probability methods Non-probability
methods
Sampling Process Define the population Identify the sampling
frame Specify the sampling unit Selection of sampling method
Determination of Sampling size Specify sampling plan Selection of
sample
Sampling Process Need to decide how many respondents need to be
chosen from the population Generally, the sample size depends on
the type of research conducted For exploratory research the sample
size tends to be small in number, whereas for conclusive research
the sample size will be large
Sampling Process Define the population Identify the sampling
frame Specify the sampling unit Selection of sampling method
Determination of Sampling size Specify sampling plan Selection of
sample
Sampling Process A sampling plan needs to clearly specify who
is the target population Ex: when we are planning to study the
purchase pattern of groceries by households, we need to clearly
specify what household means. Is it a family who have kids, DINKS,
Empty nesters etc.
Sampling Process Define the population Identify the sampling
frame Specify the sampling unit Selection of sampling method
Determination of Sampling size Specify sampling plan Selection of
sample
Sampling Designwithin the Research Process
Step 4: Specifying the sampling method Probability Sampling
Every element in the target population or universe [sampling frame]
has equal probability of being chosen in the sample for the survey
being conducted. Scientific, operationally convenient and simple in
theory. Results may be generalized. Non-Probability Sampling Every
element in the universe [sampling frame] does not have equal
probability of being chosen in the sample. Operationally convenient
and simple in theory. Results may not be generalized.
Types of Sampling Designs Probability Nonprobability Simple
random Convenience Complex random Purposive Systematic Judgment
Cluster Quota Stratified Snowball Double
Simple Random Sampling In simple random sampling, every item of
the population has equal probability of being chosen Two methods
are used in random sampling: Lottery method Random number
table
Simple RandomAdvantages Disadvantages Easy to implement with
Requires list of random dialing population elements Time consuming
Uses larger sample sizes Produces larger errors High cost14-22
SystematicAdvantages Disadvantages Simple to design Periodicity
within Easier than simple random population may skew Easy to
determine sampling sample and results distribution of mean or
Trends in list may bias proportion results Moderate cost14-23
StratifiedAdvantages Disadvantages Control of sample size in
Increased error will result if strata subgroups are selected at
Increased statistical different rates efficiency Especially
expensive if Provides data to represent strata on population must
and analyze subgroups be created Enables use of different High cost
methods in strata14-24
ClusterAdvantages Disadvantages Provides an unbiased Often
lower statistical estimate of population efficiency due to
subgroups parameters if properly being homogeneous rather done than
heterogeneous Economically more efficient Moderate cost than simple
random Lowest cost per sample Easy to do without list14-25
Stratified and Cluster SamplingStratified Cluster Population
divided into Population divided into few subgroups many subgroups
Homogeneity within Heterogeneity within subgroups subgroups
Heterogeneity between Homogeneity between subgroups subgroups
Choice of elements Random choice of from within each subgroups
subgroup14-26
Area Sampling14-27
Double SamplingAdvantages Disadvantages May reduce costs if
first Increased costs if stage results in enough discriminately
used data to stratify or cluster the population14-28
Nonprobability Samples No need to generalize Limited
Feasibility objectives Time Cost14-29
Non-probability samples Convenience sampling Drawn at the
convenience of the researcher. Common in exploratory research. Does
not lead to any conclusion. Judgmental sampling Sampling based on
some judgment, gut-feelings or experience of the researcher. Common
in commercial marketing research projects. If inference drawing is
not necessary, these samples are quite useful. Quota sampling An
extension of judgmental sampling. It is something like a two-stage
judgmental sampling. Quite difficult to draw. Snowball sampling
Used in studies involving respondents who are rare to find. To
start with, the researcher compiles a short list of sample units
from various sources. Each of these respondents are contacted to
provide names of other probable respondents.
Quota Sampling To select a quota sample comprising 3000 persons
in country X using three control characteristics: sex, age and
level of education. Here, the three control characteristics are
considered independently of one another. In order to calculate the
desired number of sample elements possessing the various attributes
of the specified control characteristics, the distribution pattern
of the general population in country X in terms of each control
characteristics is examined. Control Characteristics Population
Distribution Sample Elements . Gender: .... Male
...................... 50.7% Male 3000 x 50.7% = 1521
................. Female .................. 49.3% Female 3000 x
49.3% = 1479 Age: .......... 20-29 years ........... 13.4% 20-29
years 3000 x 13.4% = 402 ................. 30-39 years ...........
53.3% 30-39 years 3000 x 52.3% = 1569 ................. 40 years
& over ..... 33.3% 40 years & over 3000 x 34.3% = 1029
Religion: ... Christianity............ 76.4% Christianity 3000 x
76.4% = 2292 ................. Islam ..................... 14.8%
Islam 3000 x 14.8% = 444 ................. Hinduism ...............
6.6% Hinduism 3000 x 6.6% = 198 ................. Others
................... 2.2% Others 3000 x 2.2% = 66
__________________________________________________________________________________
Types of error Non-sampling error Error associated with
collecting and analyzing the data Sampling error Error associated
with failing to interview the entire population
Non-Sampling Error Coverage error Wrong population definition
Flawed sampling frame Interviewer or management error in following
sampling frame Response error Badly worded question results in
invalid or incorrect response Interviewer bias changes response
Non-response error Respondent refuses to take survey or is away
Respondent refuses to answer certain questions Processing errors
Error in data entry or recording of responses Analysis errors
Inappropriate analytical techniques, weighting or imputation are
applied
Sampling Error Sampling error is known after the data are
collected by calculating the Margin of Error and confidence
intervals Surveys dont have a Margin of Error, questions do Power
analyses use estimates of the parameters involved in calculating
the margin of error It is common to see sample sizes of 400 and
1000 for surveys (these are associated with 5% and 3% margins of
error) In most cases the size of the population being sampled from
is irrelevant The margin of error should be calculated using the
size of the subgroups sampled
Whats Next? Computation of sample size Sampling error
Key Terms Area sampling Multiphase sampling Census
Nonprobability sampling Cluster sampling Population Convenience
sampling Population element Disproportionate Population parameters
stratified sampling Population proportion of Double sampling
incidence Judgment sampling Probability sampling14-37
Simple Random Sampling In simple random sampling, every item of
the population has equal probability of being chosen Two methods
are used in random sampling: Lottery method Random number
table
Random Number Table
Systematic Random Sampling Three steps are followed: Select the
sampling interval, K K=Total Population / Desired Sample Size
Select a unit randomly between the first unit and kth unit Add K to
the selected number to the randomly chosen number EX: If total
population = 1000, desired sample size is 50, then K = 1000/50 =
20. Randomly select a number between 1 and 20 Let us say, the
number is 17, then the sample series will be 17, 37, 57
Stratified Random Sampling Calculate the percentage of
population present in each stratum Determine the sample to be drawn
from each stratum Randomly select sample from each stratum Eg: You
need to select 40 people from an office, which has the following
staff Male, full time 90 Male, part time 18 Female, full time 9
Female, part time 63
Some Notations to rememberPopulation Parameters Symbol Sample
Notations SymbolSize N Size nMean value Mean value x-Percentage
value Percentage value(population proportion) P (sample proportion)
p Q or [1 P] q or [1 p]Standard deviation Estimated standard
deviation sVariance 2 Estimated sample s 2Standard error Estimated
standard error(population parameter) S or SP (sample statistics) Sx
or Sp Other Sampling ConceptsConfidence intervals CIx or CIp
Tolerance level of error eCritical z-value ZBConfidence levels
CLFinite correction factor (the overallsquare root of [N n/N 1]
(alsoreferred to as finite multiplier orfinite population
correction) fcf
Central Limit Theorem The theorem states that for almost all
defined target populations (virtually with disregard to the actual
shape of the original population), the sampling distribution of the
mean (x) or the percentage ( p) value derived from a simple random
sample will be approximately normally distributed, provided that
the sample size is sufficiently large (i.e., when n is greater than
or equal to 30). In turn, the sample mean value (x) of that random
sample with an estimated sampling error (Sx) fluctuates around the
true population mean value () with a standard error of /n and has
an approximately normal sampling distribution, regardless of the
shape of the probability frequency distribution curve of the
overall target population
Normal Curve
Sampling Error Sampling error is any type of bias that is
attributable to mistakes made in either the selection process of
prospective sampling units or determining the sample size
Statistical Precision Using several statistical methods, the
researcher will be able to specify the critical tolerance level of
error (i.e., allowable margin of error) prior to undertaking a
research study This critical tolerance level of error (e)
represents general precision (S) with no specific confidence level
or precise precision [(S)(ZB,CL)] when a specific level of
confidence is required
Statistical Precision General precision can be viewed as the
amount of general sampling error associated with the given sample
of raw data that was generated through some type of data collection
activity. Precise precision represents the amount of measured
sampling error associated with the raw data at a specified level of
confidence
Statistical Precision When attempting to measure the precision
of raw data, researchers must incorporate the theoretical
understanding of the concepts of sampling distributions, the
central limit theorem, and estimated standard error in order to
calculate the necessary confidence intervals.
Estimated Standard Error Estimated standard error, also
referred to as general precision, gives the researcher a
measurement of the sampling error and an indication of how far the
sample result lies from the actual target population parameter
value estimate. The formula to compute the estimated standard error
of a sample mean value (Sx) is Sx = s /n where s = Estimated
standard deviation of the sample mean n = Sample size
Confidence Interval A confidence interval represents a
statistical range of values within which the true value of the
target population parameter is expected to lie
Z-Score
Determining Sample SizeThree factors play an important role in
determining appropriate sample sizes:1. The variability of the
population characteristic under investigation ( or P). The greater
the variability of the characteristic, the larger the size of the
sample necessary.2. The level of confidence desired in the estimate
(CL). The higher the level of confidence desired, the larger the
sample size needed.3. The degree of precision desired in estimating
the population characteristic (e). The more precise the required
sample results (i.e., the smaller the e), the larger the necessary
sample size.