The document outlines the principles and methodologies of sampling design, discussing the definitions of key terms like population and sample, as well as the importance and benefits of sampling in research. It details various sampling techniques including random, stratified, systematic, cluster, and non-probability methods, along with their merits, demerits, and steps involved. Additionally, it addresses sample size determination, hypothesis testing, and considerations for statistical analysis in research studies.

1. Sampling
Design
D.A. Asir John Samuel, BSc (Psy),
MPT (Neuro Paed), MAc, DYScEd,
C/BLS, FAGE

2. Basic definitions
• Population
- Collection of all the units that are of interest
to the investigator
• Sample
- Representative part of population
• Sampling
- Technique of selecting a representative group
from a population
Dr. Asir John Samuel (PT), Lecturer, ACP 2

3. Why ?
• Only feasible method for collecting information
• Reduces demands on resources (time, finance,.)
• Results obtained more quickly
• Better accuracy of collected data
• Ethically acceptable
Dr. Asir John Samuel (PT), Lecturer, ACP 3

4. Steps in sampling design
Target
population
Study
population
Sample
Study
participation
Dr. Asir John Samuel (PT), Lecturer, ACP 4

5. Characteristic of good sample design
• True representation of population
• May result in small sampling error
• Each member in population should get an
opportunity of being selected
• Systematic bias can be controlled in a better way
• Results should be capable of being extrapolated
Dr. Asir John Samuel (PT), Lecturer, ACP 5

6. Types of sample design
• Probability/Random sampling
- Selection of subjects are according to any
predicted chance of probability
• Non-probability/non-random sampling
- Does not depend on any chance of predecided
probability
Dr. Asir John Samuel (PT), Lecturer, ACP 6

7. Types of sample design
Sample
design
Random Non-random
sampling sampling
Simple Stratified Systematic Cluster Multistage convenience Quota Judgment
Dr. Asir John Samuel (PT), Lecturer, ACP 7

8. Simple random sampling
• Equal and independent chance or probability
of drawing each unit
• Take sampling population
• Need listing of all sampling units (sampling
frame)
• Number all units
• Randomly draw units
Dr. Asir John Samuel (PT), Lecturer, ACP 8

9. How to ensure randomness?
• Lottery method
• Table of random numbers
- e.g. Tippett’s series
- Fisher and Yates series
- Kendall and Smith series
- Rand corporation series
Dr. Asir John Samuel (PT), Lecturer, ACP 9

10. SRS - Merits
• No personal bias
• Easy to assess the accuracy
Dr. Asir John Samuel (PT), Lecturer, ACP 10

11. SRS - Demerits
• Need a complete catalogue of universe
• Large size sample
• Widely dispersed
Dr. Asir John Samuel (PT), Lecturer, ACP 11

12. Stratified Random Sampling
• Used for heterogeneous population
• Population is divided into homogeneous
groups (strata), according to a characteristic of
interest (e.g. sex, religion, location)
• Then a simple random sample is selected from
each stratum
Dr. Asir John Samuel (PT), Lecturer, ACP 12

13. SRs - Merits
• More representative
• Greater accuracy
• Can acquire information about whole
population and individual strata
Dr. Asir John Samuel (PT), Lecturer, ACP 13

14. SRs - Demerits
• Careful stratification
• Random selection in each stratum
• Time consuming
Dr. Asir John Samuel (PT), Lecturer, ACP 14

15. Systematic Sampling
• Sampling units are selected in a systematic
way, that is, every Kth unit in the population is
selected
• First divide the population size by the,
required sample size (sampling fraction). Let
the sampling fraction be K
Dr. Asir John Samuel (PT), Lecturer, ACP 15

16. Systematic Sampling
• Select a unit at random from the first K units
and thereafter every Kth unit is selected
• If, N=1200
• And n=60
• Then, SF=20
Dr. Asir John Samuel (PT), Lecturer, ACP 16

17. SS - Merits
• Simple and convenient
• Less time and work
Dr. Asir John Samuel (PT), Lecturer, ACP 17

18. SS - Demerits
• Need complete list of units
• Periodicity
• Less representation
Dr. Asir John Samuel (PT), Lecturer, ACP 18

19. Cluster Sampling
• The sampling units are groups or clusters
• The population is divided into clusters, and a
sample of clusters are selected randomly
• All the units in the selected clusters are then
examined or studied
Dr. Asir John Samuel (PT), Lecturer, ACP 19

20. Cluster Sampling
• It is always assumed that the individual items
within each cluster are representation of
population
• E.g. District, wards, schools, industries
Dr. Asir John Samuel (PT), Lecturer, ACP 20

21. CS - Merits
• Saving of travelling time and consequent
reduction in cost
• Cuts down on the cost of preparing the
sampling frame
Dr. Asir John Samuel (PT), Lecturer, ACP 21

22. CS - Demerits
• Units close to each other may be very similar
and so, less likely to represent the whole
population
• Larger sampling error than simple random
sampling
Dr. Asir John Samuel (PT), Lecturer, ACP 22

23. Multistage Sampling
• Selection is done in stages until final sampling
units are arrived
• At first stage, Random sampling of large sized
sampling units are selected, from the selected
1st stage sampling units another sampling
units of smaller sampling units are selected,
randomly Dr. Asir John Samuel (PT), Lecturer, ACP 23

24. Multistage Sampling
• Continue until the final sampling units are
selected
• E.g. Few states – District – Taulk
Dr. Asir John Samuel (PT), Lecturer, ACP 24

25. MS - Merits
• Cut down the cost of preparing the sampling
frame
Dr. Asir John Samuel (PT), Lecturer, ACP 25

26. MS - Demerits
• Sampling error is increased compared to
simple random sampling
Dr. Asir John Samuel (PT), Lecturer, ACP 26

27. Quota Sampling
• Interviewers are requested to find cases with
particular types of people to interview
Dr. Asir John Samuel (PT), Lecturer, ACP 27

28. Judgment (Purposive Sampling)
• Researcher attempts to obtain sample that
appear to be representative of the population
selected by the researcher subjectively
Dr. Asir John Samuel (PT), Lecturer, ACP 28

29. Convenience Sampling
• Sampling comprises subject who are simply
avail in a convenient way to the researcher
• No randomness and likelihood of bias is high
Dr. Asir John Samuel (PT), Lecturer, ACP 29

30. Snowball Sampling
• Investigators start with a few subjects and
then recruit more via word of mouth from the
original participants
Dr. Asir John Samuel (PT), Lecturer, ACP 30

31. Merits
• Easy
• Low cost
• Limited time
• Total list population
Dr. Asir John Samuel (PT), Lecturer, ACP 31

32. Demerits
• Selection bias
• Sample is not representation of population
• doesn’t allow generalization
Dr. Asir John Samuel (PT), Lecturer, ACP 32

33. Sample Size
Determination

34. p-value
• Probability of getting a minimal difference of
what has observed is due to chance
• Probability that the difference of at least as
large as those found in the data would have
occurred by chance
Dr. Asir John Samuel (PT), Lecturer, ACP 34

35. Hypothesis
• Alternate hypothesis (HA)
- Statement predict that a difference or
relationship b/w groups will be demonstrated
• Null hypothesis (H0)
- Researcher anticipate “no difference” or “no
relationship”
Dr. Asir John Samuel (PT), Lecturer, ACP 35

36. Decision for 5% LOS
• If p-value <0.05, then data is against null
hypothesis
• If p-value ≥0.05, then data favours null
hypothesis
Dr. Asir John Samuel (PT), Lecturer, ACP 36

37. Type I & II errors
Possible states of Null Hypothesis
Possible True False
actions on Accept Correct Type II
Null Action error
Hypothesis Reject Type I Correct
error Action
Prob (Type I error) – α (LoS)
Prob (Type II error) – β
1-β – power of test
Dr. Asir John Samuel (PT), Lecturer, ACP 37

38. Z values
Z 0.05 – 1.96 – 95%
Z 0.10 – 1.282 – 90%
Z 0.20 – 0.84 – 80%
Dr. Asir John Samuel (PT), Lecturer, ACP 38

39. Comparison of 2 means
n= 2 [(Zα+Zβ)s/d]²
Zα – LoS
Zβ – power of study
s – pooled SD of the two sample
d – clinically significant difference
Dr. Asir John Samuel (PT), Lecturer, ACP 39

40. Eg. for Comparison of 2 means
• A RCT to study the effect of BP reduction. One
group received a control diet and other-test
diet. What would be the sample size in order
to provide the study with power of 90% to
detect a difference in sys. BP of 2 mm Hg b/w
two groups at 5% LoS? The SD of sys. BP is
observed to be 6 mmHg.
Dr. Asir John Samuel (PT), Lecturer, ACP 40

41. Estimating proportion
n = Z α² P (1-P) / d²
P – proportion of event in population
d – acceptable margin of error in estimating the
true population proportion
Dr. Asir John Samuel (PT), Lecturer, ACP 41

42. Eg. Estimating proportion
• To determine the prevalence of navicular drop
in ACL injured population by anticipating of
15% with acceptable margin of error is 3%
= (1.96)²(0.15)(0.85) / (0.03)²
= 544.2
Dr. Asir John Samuel (PT), Lecturer, ACP 42

43. Estimating mean
n = (Zα σ / d)²
σ – anticipated SD of population
d – acceptable margin of error in estimating true
population mean
Dr. Asir John Samuel (PT), Lecturer, ACP 43

44. Eg. Estimating mean
• To determine the mean no. of days to
ambulate pt undergoing stroke rehabilation
among stroke pts. Where anticipated SD of
days are 60 and acceptable margin of error is
20 days
n = (1.96 x 60/20)²
n = (5.88)² = 34.6
Dr. Asir John Samuel (PT), Lecturer, ACP 44

45. Comparison of 2 proportions
n = (Zα √2PQ + Zβ√P1Q1+P2Q2)²/(P1-P2)²
P = P1+P2/2 Q = 1-P
Dr. Asir John Samuel (PT), Lecturer, ACP 45

46. Eg. Comparison of 2 proportions
• To see whether there is any sig. difference in
percentage of strength increase after 4 wks of
intervention b/w a new technique and
standard one
• Standard one – 70% (P1)
• New technique – 75% (P2)
Dr. Asir John Samuel (PT), Lecturer, ACP 46