It describes about sample and sample size determination.

1. SAMPLE AND SAMPLE SIZE
Prepared by
Manoj Xavier
Research Scholar
Reg.No. 69/2016
M.G. University
Kottayam

2. SAMPLE
Sample is a subset of the
population.
Population refers to an entire group
or elements with common
characteristics.

4. Population Sample
Measurable characteristics of
a population is called
parameters
Measurable characteristic of
a sample is called statistics
Population mean is denoted
the symbol “u”
Sample mean is denoted the
symbol “x”
Each and every unit of the
group
Only a handful of units of
population
Identifying the characteristics Making inference about the
population
Complete enumeration or
census
Sample survey
POPULATION V/S SAMPLE

6. TYPES OF SAMPLE
Homogeneous sample: As similar as possible so
as to control for extraneous variables. All the items
in the samples have similar or identical traits.
Heterogeneous sample: Represents a broad
range of values. In heterogeneous sample, every
member has a different value or characteristics.

8.  Representative
 Adequate size of the sample
 Free from bias & prejudice
 Conformity to subject matter
 Based on past practical experience
 Focus on objectives
 Flexibility
 Method of sampling
 Small sampling error
 Economically viable

9. SAMPLE SIZE
The number of sampling units selected
from the population called sample size.
Sample size is generally represented
by the variable ‘n’

10. In census, the sample size is equal to the
population size.
However, in research, because of time constraint
& budget ,a representative sample are used
normally.
The larger the sample size the more accurate the
findings from a study. Optimum sample size is an
essential components of any research.

11. Determination of Sample
Size

12. THE MOST PERVASIVE MYTHS
a. A sample must be large or it is not representative.
b. A sample should bear some proportional relationship to
the size of the population from which it is drawn.

13. PRINCIPLES INFLUENCING SAMPLE SIZE
1. The greater the dispersion or variance within the
population, the larger the sample must be to provide
estimation precision.
2. The greater the desired precision of the estimate, the
larger the sample size must be.
3. The narrower the interval range, the larger the sample
must be.
4. The higher the confidence level in the estimate, the
larger the sample must be.
5. The greater the number of subgroups of interest within
a sample, the larger the sample size must be, as each
subgroup must meet minimum sample size

14. FACTORS IN DETERMINING SAMPLE SIZE
FOR QUESTIONS INVOLVING MEANS
 VARIANCE (STANDARD
DEVIATION - how
homogeneous is the
population)
 Based on a pilot study
or as a rule of thumb it
is expected to be one-
sixth of the range.
 MAGNITUDE OF ERROR
(or the confidence interval,
indicates how precise the
estimate must be. Usually
based on the importance of
the decision to be made)
• CONFIDENCE LEVEL
(sets the probability of
the true population
parameter being
incorrectly estimated)

15. SAMPLE SIZE FORMULA
2






E
zs
n
Z = standardized value corresponding to a
confidence level
S = sample standard deviation or estimate
E = acceptable magnitude of error,
+ or - an error factor

16. SAMPLE SIZE FORMULA - EXAMPLE
Suppose a survey researcher, studying expenditures on lipstick, wishes to
have a 95 percent confident level (Z) and a range of error (E) of less than
Rs. 2.00. The estimate of the standard deviation is Rs.29.00.

17. SAMPLE SIZE FORMULA - EXAMPLE
2
E
zs
n 






   2
00.2
00.2996.1







2
00.2
84.56






  2
42.28 808

18. SAMPLE SIZE FORMULA - EXAMPLE
Suppose, in the same example as the one before, the range of error (E) is
acceptable at Rs. 4.00, sample size is reduced.

19. SAMPLE SIZE FORMULA - EXAMPLE
2
E
zs
n 






   2
00.4
00.2996.1







2
00.4
84.56






  2
21.14 202
What sample size would you need at a 99% confidence level.

20. [ ]
1389
265.37
2

2
53.74
2




2
)29)(57.2(
n
2





]
347
[ 6325.18
2

4
53.74
2







4
)29)(57.2(
n
2







99% Confidence
Calculating Sample Size

21. CHRACTERSTICS OF GOOD SAMPLE SIZE
 Low sampling error
 High confidence level
 Degree of variability

22. OPTIMUM SAMPLE SIZE DETERMINATION IS
REQUIRED FOR THE FOLLOWING REASON
 To allow for appropriate analysis
 To provide the desired level of accuracy
 To allow the validity of significance level

23. FACTORS AFFECTING THE SAMPLE SIZE
 Nature of the study
 Nature of the universe
 Number of classes
 Desired precision
 Size of the population
 Cost of selection
 Research objectives
 Sampling error
 Purpose of the study
 Degree of variability
 Confidence level
 Nature of the analysis

24. Sampling is a process of choosing a
representative portion of the entire
population. It is an integral part of
research methodology.

25. THANK YOU