What use is all this stuff about variability? Sampling – the big idea Sampling In Practice Sampling – the big idea Need For Sampling Disadvantages Of Sampling Types Of Sampling Factors Affecting Sample Size Sampling Distribution Calculating A Confidence Interval Using Software

1. Sampling Variability And The
Precision Of A Sample Estimate
Dr. Sindhu Almas
PhD (Scholar)
Department Of Public Administration
University Of Sindh Jamshoro

2. What use is all this stuff about variability?

3. Variability measures how well an individual score
(or group of scores) represents the entire
distribution. This aspect of variability is very
important for inferential statistics where relatively
small samples are used to answer questions about
populations.

4. Sampling Variability
Sampling variability refers to the different values which a
given function of the data takes when it is computed for two
or more samples drawn from the same population.
Factors affecting sampling variability:
1.Inherent variation in the population
2. Sample size
3.Sampling distribution of the mean
4.Sampling error and bias. Sampling variability

5. Irrespective of sample size , the sample means are expected to
fluctuate evenly about the true population mean.
The variation in sample means exhibited in the table is an
example of sampling variation due to chance.
If we take 50 observations ,mean is 3.46 kg. sampling error 3.46-
3.36= 0.10
The means vary less(by chance) if the sample size is large; that is
sampling error is smaller, the larger is the sample.

6. The distribution more closely clustered around a middle
value as the sample size increases.
The mean do not systematically increase or decrease with
increasing sampling and have more variability(larger SD)
when the sample size is small.
The standard deviation of the means steadily decrease as
sample size increases, more quickly when the sample size
is small.

9. Sampling – the big idea

10. Definitions
Population: The target group to which the findings (of a
study) would ultimately apply is called population1 Or
Population is the term statisticians use to describe a large
set or collection of items that have something in common.
Sample: is that part of the target population which is
actually enquired upon or investigated. Or
Sample is a subset of population, selected in such a way that
it is representative of the larger population.
1. Indrayan A., Satyanarayana L., Medical Biostatistics, third edition, 2009
2. Last JM. Dictionary of Epidemiology, 3rd edition, 2000.

11. Definitions (Cont.)
Sampling: is the process of selecting a small
number of elements from a larger defined target
group of elements such that the information
gathered from the small group will allow
judgments to be made about the larger groups.
conclusions based on the sample results may be
attributed only to the population sampled
Dawson B., Trapp RG, Basic and Clinical Biostatistics, second edition, 1994

12. Sampling In Practice

13. Definitions Cont..
 Sampling unit: is the unit of selection
 Unit of study or element: is the subject on which information is
obtained.
 Sampling frame: list of all sampling units in the target population is
called a sampling frame.
 Sample size: the number of units or subjects sampled for inclusion in
the study is called sample size.
 Sampling technique: Method of selecting sampling units from sampling
frame

16. Need For Sampling
 1. Complete enumeration may not be possible.
 2. Resources: Lower cost, Lesser demand on personnel.
 3. Speed: Faster results due to lesser coverage.
 4. Reliable information: Due to small size - better trained personnel, more
accurate methods, better supervision.
 To draw conclusions about population from sample, there are two major
requirements for a sample.
 Firstly, the sample size should be large.
 Secondly, the sample has to be selected appropriately so that it is
representative of the population. Sample should have all the characteristics
of the population.

17. Disadvantages Of Sampling
1. Sampling entails an argument from the fraction to the
whole. Validity depends on representativeness of the sample.
2. Fails to provide precise information in case of small
segments containing few individuals.
3. Not necessary in studies where complete enumeration is
needed.
4. May cause a feeling of discrimination among the subjects
who are not included in the study.

18. Types Of Sampling
 Probability Sampling
 Probability of selection of each
individual is known and pre
determined
 Simple random sampling
 Systematic random sampling
 Stratified random sampling
 Cluster random sampling
 Multistage random sampling
 Non Probability Sampling
 Probability of selection of each
individual is not known
 Quota sampling
 Purposive/ Judgmental sampling
 Snowball/ Network sampling
 Convenience/ Grab sampling (man
in the street)

19. Factors Affecting Sample Size
 1. Study design: descriptive or
comparison study
 2. Sampling design: smaller if stratified,
larger if cluster
 3. Type and number of variables being
studied.
 4. Maximum tolerable probability of type
I error.
 5. Required power for a specified
clinically important difference.
 6. Specification of the magnitude of
difference that would be considered
significant.
 7. The extent of variability among
measurements( S.D.)
 8. Whether underlying distribution is
normal or skewed
 9. Heterogeneity of population: need
larger sample to study more diverse
population
 10. Desired precision: need larger sample
to get smaller error
 11. Nature of analysis: complex
multivariate statistics need larger
samples
 12. Resources and time at hand

28. Sampling Distribution

29. A sampling distribution is a probability
distribution of a statistic obtained from a larger
number of samples drawn from a specific
population. The sampling distribution of a given
population is the distribution of frequencies of a
range of different outcomes that could possibly
occur for a statistic of a population.

30. The Normal Distribution And Confidence Intervals

31. A normal distribution is the proper term for a
probability bell curve. In a normal distribution the mean
is zero and the standard deviation is 0.
A confidence interval displays the probability that a
parameter will fall between a pair of values around
mean. Confidence intervals measure the degree of
uncertainty or certainty in a sampling method. They are
most often constructed using confidence levels of 95% or
99%.

32. Calculating A Confidence Interval Using Software

33. Spread sheets/ excel
SPSS
EPI Info
Formula
 CI = confidence interval
 bar{x} = sample mean
 z = confidence level value
 {s} = sample standard deviation
 {n} = sample size