The document discusses sampling in research. It defines a sample as a small representative segment of a population from which inferences can be drawn about the larger population with minimal resources. Factors that influence sample size include population characteristics, study design, and desired statistical power and significance level. Common sampling techniques include simple random sampling, systematic random sampling, stratified random sampling, and cluster random sampling. Sample size calculations depend on the type of data and study design.

1. SAMPLING IN RESEARCH
Dr. Kusum Gaur
Professor, PSM
WHO Fellow IEC

2. Selection of study population
Whole Population
Sample Population
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3. What is Sample ?
• A sample is a small representative
segment of a population
• Inferences drawn from a sample are expected
to be applicable for the source population
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4. Why do we need a sample?
To get inferences
applicable to universe
with minimum resources
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5. Sample – Qualities
Sample is a part of population but it is true
representative of whole.
Qualities
Adequate size
Appropriate sampling technique
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6. Factors on which SAMPLE SIZE depend:
• Population Factors
– Type of information available
• Type of study
– Type of Data
– Type of study design
– Type of sampling
– Type of Statistical Analysis for outcome needed
• Determined values of research by researcher
– Power
– Significance level
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7. Power: Ability to detect right answer
Alpha Error: Chance to miss right answer

8. Type of Data & level of Measurements
Qualitative – Counted Facts – Nominal Data
Measured as Numbers expressed as proportions
Quantitative- Measured Facts - Numerical Data
Measured as quantity & expressed as Mean SD
*Ordinal Data – Rank Order Data
Measured as rank & expressed as Median Percentile
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9. Sample size for Qualitative data
Z 2 PQ 4 PQ
Sample Size= ------------------- -- = ------------------
L2 L2
P= Prevalence of disease
Q = 100-P
L = allowable error
Z= 1.96 ≈ 2 for 95% CL
for descriptive/case-series type of study design
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10. Sample size for Quantitative data
Z 2 SD 2 4 SD 2
Sample Size= ------------------- -- =----------------------
L2 L2
SD= Standard Deviation
L = allowable error
Z= 1.96 ≈ 2 for 95% CL
For Descriptive Studies only
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11. Finite Correction
Sample Size – Finite Population (where the
population is less than 50,000)
SS
New SS = _________________
( 1 + ( SS – 1 ))Pop

12. How many controls?
n
k Here n0=No. of cases &
2n0 n n = expected no. of cases
• k = 13 / (2*11 – 13) = 13 / 9 = 1.44
• kn0 = 1.44*11 ≈ 16 controls (and 11 cases)
– Same precision as 13 controls and 13 cases

13. Sampling Design factors of sample size
Variance of Specified Sampling
Design Effect =
Variance of Simple Random Sampling (SRS)
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14. Sampling Technique effect on Sample Size
Sampling Technique Design Effect Size Multiplier
Simple Random Sampling 1
Systemic Random Sampling 1.2
Stratified Random Sampling 0.8
Cluster Random Sampling 2
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15. Conventionally accepted
Researcher’s Estimations
Alpha Error 0.05
Power 80%
Confidence Limit 95%
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16. Key Concepts: Sample size
• Sampling Design - larger sample for Custer
• Desired Power – more power for larger sample
• Allowable error – smaller error for larger sample
• Heterogeneity leads to have larger sample to cover
diversities
• Nature of Analysis – Complex multivariate needs
larger sample
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17. Steps -Sample Size Estimation
• Stage 1- * Base Sample Size Calculation (n)
• Stage 2 – Sample Size with Design Effect (d)
=n*d
• Stage 3- Contingency Addition (e.g. 5%)
SS Estimation for study population
=(n*d)+5%of n
*Use appropriate equation for sample size calculation
http://stat.ubc.ca/~rollin/stats/ssize/
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20. E.G. Mean 1= 5, Mean 2 = 15 & SD = 14 inputting values

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29. Sample Size Tables

34. SAMPLING
TECHNIQUES

35. SAMPLING TECHNIQUES
• PROBABILITY/RANDOM SAMPLING
• NONPROBABILITY SAMPLING
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36. Random sampling Techniques
Aim is to give equal chance to
every observation unit to be
selected for study in sample.
(Any Observation unit
should not have Zero Probability )
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37. * Random Sampling Techniques
Simple Random Technique
Systemic Random Technique
Stratified Random Technique
Multiphase Random Technique
Multistage Random Technique
Cluster Random Technique
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38. Simple Random Technique
• Lottery Method
• Random Table Method
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40. Steps –Use of Random Table
• Stage 1- Give number to each member of population
• Stage 2 – Determine total population size (N)
• Stage 3- Determine Sample size (S)
• Stage 4 – Drop one finger on Random Table with eyes closed
• Stage 5 – Drop one finger with eyes closed on direction to be
chosen – Up/Down/Rt/Lt
• Stage 6- Determine first number within 0 to N
• Stage 7- * Determine other numbers till Sample size (S)
* Once a number is chosen do not repeat it again
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41. Steps –Use of Random Table..
e.g. N=300, M=50
Random no. Selected no. (3 digits from 0-300)
49468
49699
14043 043
15013 013
12600
33122 122
94169 169
89916
74169 169
32007 007
www.evaluation
wikiog/index/how_to_use_a_random_number_Table
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42. Systemic Random Technique
The selection of sample follows a systematic
interval of selection
• Find serial interval
(K) = total population/sample size
• 1st observation through simple random sampling
among 1to K. th
• Next observation = (1st +K) Observation
• Next observation = (2 nd +K) thObservation
• -------------so on till No. of observations
= Sample Size
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43. Systemic Random Technique Population
N=100 (Given) 1 21 41 61 81
2 22 42 62 82
S=20 (Estimated) 3 23 43 63 83
K=N/S =100/20 =5 4 24 44 64 84
5 25 45 65 85
1st observation between 1 to 5 6 26 46 66 86
7 27 47 67 87
though SRS e.g. 3 8 28 48 68 88
Every 5th observation from 3rd 9 29 49 69 89
10 30 50 70 90
observation will be included in 11 31 51 71 91
sample population 12 32 52 72 92
13 33 53 73 93
So, sample population will be – 3rd 14 34 54 74 94
8th 13th 18th 23rd 28th 33rd 38th 15 35 55 75 95
16 36 56 76 96
43rd 48th 53rd 58th 63rd 68th 73rd 17 37 57 77 97
78th 83rd 88th 93rd and 98th 18 38 58 78 98
19 39 59 79 99
observation 20 40 60 80 100
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44. Stratified Random Technique
Sample selection through Simple Random/Systemic Random Technique
Sample Strata 1
Sample
Strata 2
Sample Strata 3
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45. Multiphase Random Technique
Specific test
Screening Test
S/S
Population
Probable cases Cases
Suspected cases For
study
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46. Multistage Random Technique
Each stage Simple RT is used village
district
village
village
State 1 district
Population village
Study
Of Population
Nation village
district
village
State 2
village
district
village
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47. Cluster Random Technique
The unit of random selection is a cluster rather than individual
• CI = Total population /30 (in 30 Cluster Technique)
Cluster 1 Cluster 27
Cluster 2 Cluster 28
Population Study
Of Population
Nation Cluster 3 Cluster 29
Cluster 30
Cluster 4
Through Simple RT
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48. Stratified Vs Cluster Technique
Stratified Technique Cluster Technique
• Homogenous groups are • Comparable groups of
made population are made
• Randomly select sample (usually 30)
from each group • Randomly select sample
• To make it more truly from each group
representative, take
sample population • More chances of error than
proportion to size (PPS) simple random
• Less chances of error than
simple random

49. Non Probability Sampling
• When random samples are not possible
• Rare disease
• Small population
• Special population
• Special Condition
• Difficult to reach population
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50. Non-probability Samples
Convenience
 Purposive
 Quota
 Snow ball study
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54. Snow ball sampling
Contact tracing
Initial respondent helps in recruiting
new population
Useful in network analysis approach
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55. Computer in Statistics
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56. Web sites related to Statistics
• http://stattrek.com
• http://vassarstat.net
• http://www.scribd.com
• http://www.statistixl.com
• http://statistics calculators.com
• http://stat.ubc.ca/~rollin/stats/ssize/
• ……………………………………………………………
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57. Computer Softwares in Statistics
• Microsoft Excel
• SPSS
• Epi info
• Epi tab
• Mini tab
• Graph Pad
• Primer
• Medcal
• ……………..
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58. THANKS
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