Page 1 of 156
Sample Size & Sampling methods BY Abdel-Hady El-Gilany Prof. of Public Health
[email protected] Prof. El-Gilany
01060714481
Studying whole population:
Page 2 of 156
(Carried out in censuses)
-Time consuming. -High costs -Higher error chances: many persons, equipment & wide geographic area covered. -May destroy the objects Prof. El-Gilany
Sample Size (SS) *Basic definitions *Advantages & disadvantages *When not to calculate SS? *Hypothesis *Requirements for SSC *SSC using formula (manual) : -descriptive studies -comparative studies (paired & unpaired) -correlation - screening - survival analysis
*SSC *SSC *SSC *SSC Prof. El-Gilany
from tables from nomograms software programs online
Page 3 of 156
Page 4 of 156
Basic definitions
Prof. El-Gilany
Page 5 of 156
Prof. El-Gilany
Page 6 of 156
Prof. El-Gilany
Page 7 of 156
Advantages & disadvantages
Prof. El-Gilany
Why do we calculate SS?
Page 8 of 156
*Used to estimate population parameters *Ethical considerations: Small or large SS is unethical *Ensure study power & validity of results (EBM) *Funding agencies require SSC to justify & estimate budget *International journals needs SSC & sampling methods *Decrease time, resources & risks Prof. El-Gilany
Page 9 of 156
Prof. El-Gilany
Page 10 of 156
Representative
unbiased
Characters of good sample
Adequate Prof. El-Gilany
Accessible
Page 11 of 156
When not to calculate SS?
Prof. El-Gilany
Page 12 of 156
(1)Limited resources: human, funds, technology, time. (2)Ethical considerations
(3)Fixed number of subjects available to researchers (4)Novelty of study: unknown population variability (5)Qualitative research Prof. El-Gilany
Page 13 of 156
(6)Pilot (feasibility) studies (7)Case report/case series (8) ???Ecological studies (9)Similar studies being underway !!!Argument: several small studies pooled together in MA are more generalized than one big study Prof. El-Gilany
Page 14 of 156
Sample size in pilot study
Prof. El-Gilany
Page 15 of 156
No SS justification is needed. No prior data Pilot study not for SSC: 10-20% of SS for full-scale study is reasonable. Qualitative research: few number, even single participant. Quantitative studies: 10-30 (per group) participants. Prof. El-Gilany
Page 16 of 156
Hypothesis
Prof. El-Gilany
True state
Decision
Guilty
Innocent
Guilty
Innocent
Correct decision (1- )
Type I error
Type II error
Correct decision (1- )
( ) Prof. El-Gilany
Page 17 of 156
( )
True state
Decision
Reject H0
Accept HO
HA
H0
Correct decision (1- ) {Study power}
Type I error
Type II error
Correct decision (1- ) {Confidence level}
( ) FN Prof. El-Gilany
Page 18 of 156
( ) FP {Sign. level (P)}
Page 19 of 156
Requirements for SSC
Prof. El-Gilany
9 factors must be known/estimated for SSC: *2 fixed *2 unique to study *5 Conditional
Page 20 of 156
1. Significance level (Alpha) 2. Study power (1-B)
Prof. El-Gilany
Fixed by convention
Page 21 of 156
3. Magnitude & variability of outcome (expected effect=EE) 4. ES (difference between groups) =MID (Minimum important difference) =MRE (margin of random error)
Prof. El-Gilany
Unique to study
Page 22 of 156
5. Attrition 6. Design effect 7. Group ratio
(non-SRS)
(comparative studies)
8. Study hypothesis (sidedness of stat. test)
9. Finite population correction(FPC)
Prof. El-Gilany
Conditional
Page 23 of 156
Prof. El-Gilany
1. Significance level (Alpha error = Type I error)
Page 24 of 156
• Probability of finding significance where there is none • False positive • Probability of Type I error • Usually set to 0.05
Prof. El-Gilany
Page 25 of 156
Normal deviates for Type I error (Alpha)
Prof. El-Gilany
2. Study power (1-B) (Complementary of B)
Page 26 of 156
Where B: • Probability of not finding significance when it is there • False negative • Probability of Type II error • Usually set to 0.20
Prof. El-Gilany
2. Study power (1-B) (Complementary of B)
Page 27 of 156
Study power: probability of finding significant difference that actually exist. Probability of detecting true effect of specified size. Probability of rejecting false nullhypothesis Usually set to 0.80 Prof. El-Gilany
Normal deviates for statistical power
Page 28 of 156
Prof. El-Gilany
3. Magnitude & variability of outcome (Expected effect) Page 29 of 156
*Used to calculate ES *Low variability (stable parameter): small SS (e.g. temp. of healthy subject, CBC) *Large variability: large SS (e.g. cholesterol in healthy subjects) Prof. El-Gilany
3 possible categories of outcome: *2 alternatives exist (Yes/no, death/alive) *Multiple, mutually exclusive alternatives (blood groups).
Page 30 of 156
These 2 categories are expressed as percentages or rates *Continuous response variables (Wt, Ht, BP, VAS score) are summarized as means & SD. Prof. El-Gilany
Page 31 of 156
‘Expected effect’ is ascertained from:
• Published findings from similar study • Pilot study results • May need to be calculated from results if not reported (internal pilot) • Educated guess (based on informal observations & expertise) P of 50% is conservative estimate Prof. El-Gilany
Page 32 of 156
Prof. El-Gilany
Page 33 of 156
Outcome
Magnitude
Variability
Qualitative
% or rate
Standard error of proportion (SEp)= P(1-P) SD
Quantitative
Mean
BP (continuous variable) is better than HTN (nominal variable). Exact measurement reduce sample size by decreasing SD. Prof. El-Gilany
Page 34 of 156
SSC for multiple outcomes:
• Calculate SS for one primary outcome of interest. OR • Calculate separate SS for each outcome & choose the largest SS. Prof. El-Gilany
4. ES a.k.a: -Effect strength -Anticipated difference -Anticipated response -Anticipated benefit -Size of expected effect -Minimum important difference (MID) -Minimum detectable difference -Minimal clinically relevant difference (MCRD) -Margin of random error (MRE) -Clinical meaningful difference -Precision (degree of precision) -Allowable margin of error (d=) Prof. El-Gilany -Error (E)
Page 35 of 156
Page 36 of 156
ES refers to magnitude of effect under alternative hypothesis. The smallest difference that would be of clinical or biological significance. A measure of magnitude of difference between two groups. Varies from study to study. Prof. El-Gilany
ES Unstandardized
Standardized (Commonly used)
Outcome (effect)
Formula
Simple (absolute)
Qualitative
│P1-P0│
Quantitative
│M1-M0│
Relative
Qualitative
│P1-P0│ P0
Quantitative
│M1-M0│ M0
Qualitative
│P1-P0│ √P1(1-P1)
Quantitative
│M1-M0│ SD1
Qualitative
│P1-P0│ √P(1-P)
Quantitative
│M1-M0│ SDpooled
Single group
2 groups
N.B.
Page 37 of 156
Original unit Not used currently
No units
*P1, M1=expected proportion or mean (single group) or cases or exposed group (2 groups). *P0, M0=acceptable proportion or mean (single group) or control or nonProf. El-Gilany exposed group (2 groups).
Interpretation of ES (Cohen)
Not recommended • < 0.1 = trivial effect • 0.1 - 0.3 = small effect • 0.3 - 0.5 = moderate effect • > 0.5 = large difference effect Prof. El-Gilany
Page 38 of 156
Cohen’s ES benchmarks
Page 39 of 156
Not recommended ES
Statistics
Small
Medium
Large
Association, Chi-square
0.1
0.3
0.5
Association, OR (2X2 table)
1.5
3.5
9
Means (Cohen’s d)
0.2
0.5
0.8
ANOVA (F)
0.1
0.25
0.4
0.02
0.15
0.35
0.1
0.3
0.5
0.01
0.06
0.14
Logistic regression Correlation (r)
Linear regression (R2) Prof. El-Gilany
5. Attrition
Page 40 of 156
Includes: Non-responders Withdrawals Loss to follow-up Death (lab. animals) Final sample size should be adjusted for expected attrition. Prof. El-Gilany
Should not exceed 10-20% of SSC
6. Design effect (DE)
Page 41 of 156
DE for different sample methods To compensate for deviation from SRS
Sampling method DE SRS 1 Cluster, systematic, 1.5 - 2 stratified Non-probability samples 10 or more Prof. El-Gilany
7. Group ratio
Page 42 of 156
(comparative studies)
In comparative studies SS is calculated per group Groups must be equal: unequal groups reduces statistical power
In case-control: best case-control ratio 1:4 Prof. El-Gilany
8. Study hypothesis
Page 43 of 156
(Sidedness of stat. test)
Test may be one-tailed or two-tailed, depending on type HA. Two-tailed tests require larger SS Two tailed tests are usually used, unless there is a good reason for onetailed
If one-tailed is used: specify its direction in advance Never use one-tailed to make NS difference significant Prof. El-Gilany
9. Finite Population correction (FPC)
Page 44 of 156
n=
n0 N n0+N-1
Where: n=sample for finite population n0 SS for infinite populations for both population mean & proportion N=total population Prof. El-Gilany
Example: N=1000 n0=400
n=
400X1000 = 400000 = 286 400+1000-1 1399
Prof. El-Gilany
Page 45 of 156
Page 46 of 156
4 types of power analysis
*A priori: Compute N, given alpha, power & ES *Post-hoc: compute power, given alpha, N & ES *Criterion: compute alpha, given power, ES & N *Sensitivity: computes ES, given alpha, power & N Prof. El-Gilany
Steps of SSC in estimation & hypothesis testing
Page 47 of 156
Hypothesis testing (≥2 groups)
Estimation (one group) 1-Define variable of primary interest
2-Defin parameter of interest: mean, proportion, OR, r,…….etc. 3-Define variability between subjects 4-Define minimum precision: absolute (e.g. 2%) or relative (e.g.10% of expected outcome)
4A-Minimal difference of medical importance 4B-Study power (1-B)
5-Define least confidence level
5A-Define least significance level 5B-One-tail or two-tails test
6-Consider subgroup analysis 7-Cosider expected attrition 8-Consider deign effect: e.g. non-SRS 9-Distribution of outcome: ND is the best 10-Number of co-variables considered simultaneously: more covariables, increase SS Prof. El-Gilany
11-Study design: matching & repeated measures require small SS
5 approaches for SSC
Page 48 of 156
*Manual: use of formulae (equation) *Readymade tables *Nomograms *Computer software
*Online programs Prof. El-Gilany
Page 49 of 156
Manual SSC {Use of formulae (equation)}
Prof. El-Gilany
Universal formula for single & 2 groups both qualitative & quantitative outcome
Page 50 of 156
Prof. El-Gilany
Page 51 of 156
SS in descriptive studies {Single group}
Prof. El-Gilany
Page 52 of 156
Prof. El-Gilany
Page 53 of 156
SSC in Comparative studies (Unpaired & paired) SS calculation is per group
Prof. El-Gilany
Page 54 of 156
Prof. El-Gilany
Page 55 of 156
SSC in correlation
Prof. El-Gilany
Page 56 of 156
Prof. El-Gilany
Page 57 of 156
SSC in screening
Prof. El-Gilany
Page 58 of 156
SS formula for estimating Sn, Sp & AUROC curve
Estimate Formula (for
=0.05) (d=precision)
Sn
[(1.96)2X anticipated Sn(1anticipated Sn) X anticipated prevalence]/d2
Sp
[(1.96)2X anticipated Sp(1anticipated Sp)X (1-anticipated prevalence)]/d2
AUC
Sample size = [(1.96)2X (1-k) X anticipated variance of AUC]/d2 k= ratio of prevalence of nondiseased to diseased subjects
Prof. El-Gilany
Page 59 of 156
SS in survival analysis
Prof. El-Gilany
Page 60 of 156
• Event is qualitative
• Event is continuous variable:
Prof. El-Gilany
Page 61 of 156
SSC in lab. animal studies
Prof. El-Gilany
Explain how you determined number of groups & group sizes. Following statements are NOT sufficient: *We will use 5 animals per group & 3 groups, thus need 15 animals. *Experience tells us that we need 10 animals per group. We will need 10 animals per group in order to achieve statistical signif." *(reference) used 10 animals per group & found significance so we will also use 10 animals per group Page 62 of 156
Prof. El-Gilany
4 methods for SSC:
Page 63 of 156
*Testing hypothesis (power analysis) method: (best, preferred) (reject or accept H0) *Resource equation method: (crude) *Mead's resource equation: (crude)
*Sequential sampling (not preferred) Prof. El-Gilany
*Resource equation method: E=N–T *Mead's resource equation: E = (N-1) – (B-1) – (T-1)
Page 64 of 156
E (=DF) lies within 10 - 20 for optimum SS. N =Total number of individuals/units in study B =Blocking component (stratification) T =Number of groups (including control group)
Prof. El-Gilany
Example: E = N – T • Animal study: 4 groups of animal having 8 animals each for different interventions then total 32 (4 × 8). E = 32 – 4 = 28 • More than 20, animals should be decreased in each group. So, 5 rats in each group then E will be E = 20 – 4 = 16 • E is 16 which lies within 10-20 hence 5 rats per group for 4 groups can be considered as appropriate sample size. Page 65 of 156
Prof. El-Gilany
Example: E = (N-1) – (B-1) – (T-1) A study using lab. animals with four treatment groups (T=4), with eight animals per group, making 32 animals total (N=32), without any further stratification (B=0), E would equal 28, which is above cutoff of 20, indicating that SS is large, & six animals per group might be more appropriate.
Page 66 of 156
Prof. El-Gilany
*Sequential sampling: -Unethical -Number is undecided & is determined only by sample observations as they are completed -Test one animal, look at data, decide, test another animal, look at data, decide, & so on. 3 possible decisions: reject H0, accept H0, either keep or stop sampling & conclude that decision cannot be made. Page 67 of 156
Prof. El-Gilany
Page 68 of 156
SSC from readymade tables
Prof. El-Gilany
SSC using estimation with precision Valid but not commonly used in health research Used in political, social & educational research Page 69 of 156
Requirements: *Total population *Estimated outcome *Margin of error (level of precision – CL): error accepted by researcher *Alpha error Prof. El-Gilany
Page 70 of 156
Prof. El-Gilany
Page 71 of 156
Prof. El-Gilany
Page 72 of 156
Prof. El-Gilany
Page 73 of 156
Prof. El-Gilany
Page 74 of 156
SSC from nomograms
Prof. El-Gilany
Page 75 of 156
Prof. El-Gilany
Page 76 of 156
Prof. El-Gilany
Nomogram for SSC in screening: This nomogram uses varying absolute precision, known prevalence of disease, & 95% confidence level. It is applicable only when both diagnostic test & gold standard results have dichotomous category. Nomogram instantly provides required number of subjects by just moving ruler & can be repeatedly used without redoing calculations. Page 77 of 156
Prof. El-Gilany
Page 78 of 156
Prof. El-Gilany
Page 79 of 156
Prof. El-Gilany
Page 80 of 156
SSC using computer software
Prof. El-Gilany
EpiInfo (statcalc) (free from CDC) G*Power (http://www.gpower.hhu.de/) powerandsamplesize.com Free Medcalc program PSPowerUp: excel-based PowerUpR i R package Statistical packages such as SPSS, MINITAB & SAS
Page 81 of 156
Prof. El-Gilany
Page 82 of 156
Prof. El-Gilany
Page 83 of 156
Prof. El-Gilany
Page 84 of 156
SSC using online programs
Prof. El-Gilany
• http://www.stat.ubc.ca/~rollin/stats/ssize/ • http://www.raosoft.com/samplesize.html • http://www.dssresearch.com/KnowledgeCenter/t oolkitcalculators/samplesizecalculators.aspx • http://vassarstats.net/ • https://www.surveysystem.com/sscalc.htm) • http://www.macorr.com/sample-sizecalculator.htm • http://www.nss.gov.au/nss/home.nsf/pages/Sam ple+size+calculator • http://www.gifted.uconn.edu/siegle/research/sa mples/samplecalculator.htm Page 85 of 156
Prof. El-Gilany
Page 86 of 156
Weighting samples
Prof. El-Gilany
Reasons for weighting: -Non-response -Post-stratification adjustment -Account for probability of selection
Page 87 of 156
Advantages of weighting: -Compensate for imbalances between proportions of targeted participants among subgroups in population & proportions in those subgroups who choose to respond. Weighting provides more accurate population estimates. .
Prof. El-Gilany
Page 88 of 156
• A sample of 384 was calculated to estimate prevalence of specific disease in region with 3 localities (North, Middle, South) {50% estimated proportion, 5% precision & 5% CL)
Prof. El-Gilany
Locality
Population
Number
% (A)
Sample Number selected diseased
Unweighted proportion
Page 89 of 156 Weighted proportion
(B)
(C)
(C/B)
(C/B)*A
North
50.000
13
128
21
16%
2%
Middle
250.000
67
153
98
64%
43%
South
75,000
20
103
21
22%
4%
Total
345,000
100
384
142
37%
49%
*Unweighted prevalence=37% *Weighted prevalence=49% (assumed 50%) Prof. El-Gilany
Sampling methods *Probability (random=formal) samples
Page 90 of 156
-Simple random sample (SRS) -Systematic random sample (Syst RS) -Cluster sample -Stratified random sample (Strat RS) -Multistage random sample (MSRS) -Other random samples
*Non-probability (nonrandom=informal) samples -Convenience -Quota -Delphi method
-Purposive -Snowball -Heterogeneity sampling
*Errors & bias in sampling Prof. El-Gilany
Random sample
Non-random sample Page 91 of 156
Likelihood of sampling unit being selected
Known (non-zero probability)
Unknown
SS
Determined by sampling theory
Matter of convenience
Sampling error
Can be calculated
Can not be calculated
Selection bias
No or low
Yes
Generalization of results
Yes (representative)
No (illustrative)
Estimate study precision
Yes
No
Require sample frame
Yes/No
No
Fixed procedure that is costly & unfeasible
Yes
No
Replicable (for measuring trends)
Yes
No
Use of statistics & Hypothesis testing
Yes
No (exploratory, generate hypothesis)
Estimation of population parameter
Yes
Not of interest
Sample adequacy
Yes
No
Others
Random selection of units
Cheaper, easier & quick
Prof. El-Gilany
Page 92 of 156
Probability (random) samples 1-Simple random sample (SRS) 2-Systematic random sample (Syst RS) 3-Cluster sample 4-Stratified random sample (Strat RS) 5-Multistage random sample (MSRS) 6-Other random samples
Prof. El-Gilany
Page 93 of 156
1-Simple random (unrestricted) sample (SRS) ()عينة عشوائية بسيطة
Prof. El-Gilany
• Objective: Select n units out of N such that each unit has equal chance of being selected.
Page 94 of 156
• Procedure: – Preparing sampling frame (homogenous population). – Deciding SS to be chosen. – Select required number of units at random. Prof. El-Gilany
• Random samples can be drawn by: – Lottery method – Random number tables – Computer random number generator – Online programs
Page 95 of 156
Prof. El-Gilany
Lottery
How to use random number table
Page 96 of 156
• Assign equal number of digits to each units of population. • Start at any place & may go on in any direction such as column wise or rowwise in random number table. But consecutive numbers are to be used. • Based on size of population proceed according to convenience. • Exclude any random number greater than population size N. Prof. 96El-Gilany
Page 97 of 156 Example 1: In area there are 500 families. Select sample of 15 families to find out standard of living of those families.
4652 3819 8431 2150 2352 2472 0043 3488 9031 7617 1220 4129 7148 1943 4890 1749 2030 2327 7353 6007 9410 9179 2722 8445 0641 1489 0828 0385 8488 0422 7209 4950
203 023 277 353 600 794 109 179 272 284 450 641 148 908 280
Prof. El-Gilany
N=500 n=15
203 023 277 353 100 294 109 179 272 284 450 141 148 408 280
Page 98 of 156
Prof. El-Gilany
Advantages
Disadvantages
Page 99 of 156
-Representative to homogenous population
-Require sampling frame (tedious to prepare for large population)
-Estimates are easy to calculate
-Impractical with large sampling frame
-Simple to conduct & to generalize -No personal bias
-Small number from minority groups (Unsuitable for heterogeneous population)
-Can be used in other methods of sampling
-More cost & money if dispersed geographically
Prof. El-Gilany
Page 100 of 156
2-Systematic random sample (Syst RS) ()عينة عشوائية منتظمة
Prof. El-Gilany
A sampling method which determine randomly where to start selecting in sample frame then follow a rule to select every kth element in sampling frame list (ordering of the list is assumed to be random).
Page 101 of 156
Prof. El-Gilany
Steps to follow : • Number units in population from 1 to N randomly • Decide on n (sample size) • Define interval size k = N/n • Randomly select integer between 1 to k • then take every kth unit
Page 102 of 156
Prof. El-Gilany
Page 103 of 156
Prof. El-Gilany
Advantages -Easy to select
-Evenly spread over entire population -Sampling error easily measured
Page 104 of 156
Disadvantages
-Biased if there hidden periodicity of population -Difficult to assess precision of estimate from one study -Requires sampling frame
-Requires less time & effort
-Only 1st subject is selected randomly
-Relatively small SS -Chance of researcher -Accurate results if large personal bias homogenous population El-Gilany &Prof.each unit is numbered
Page 105 of 156
3-Cluster sample ()عينة عنقو ية
Prof. El-Gilany
Sampling by dividing population into groups (clusters), randomly selecting clusters & sampling each element in selected clusters.
Page 106 of 156
Uses: -Sampling population across wide geographic area. -Heterogeneous population -No sampling frame at individual level Prof. El-Gilany
Steps: • Divide population into homogenous clusters (e.g. geographic boundaries) • Select a number of clusters from population by SRS • Include all units within sampled clusters Sample units identified in group “cluster” not independently Page 107 of 156
• Typical example: “30 clusters, each of 7 children” for vaccination coverage Prof. El-Gilany
Page 108 of 156
Prof. El-Gilany
Page 109 of 156
Advantages Disadvantages -No need for sampling -Cluster members are more frame (only list of likely to be alike than clusters) those in another cluster -Less cost & effort (cost-effective)
-More error (less precise) than SRS of same SS
-Can combine SRS, Syst S, stratification & cluster sampling
-Larger SS (design effect) -Not intended for calculation of estimates from individual clusters
Large number of small clusters is better than small number of large clusters
Prof. El-Gilany
Page 110 of 156
4-Stratified random (known quota) sample (Strat RS) ()عينة عشوائية ط قية
Prof. El-Gilany
• Preferred with heterogeneous population (differ systemically) in characteristic under study • Principle: – Divide sampling frame into nonoverlapping homogeneous subgroups (strata) e.g. age-group, sex, occupation – Respect proportional allocation – Draw random sample in each strata – Gives equal chance to units in each stratum to be selected. – Total sample is sum of samples of Page 111 of 156
Prof. El-Gilany
Sample Allocation
Page 112 of 156
*Equal Allocation: commonly used, not preferred *Proportionate Allocation (probability proportional to size=PPS) *Quasi-Proportionate Allocation with Minimum Size Constraint (more weight to minorities) If study aims at providing reliable estimates at level of whole population & at level of each stratum Prof. El-Gilany
Page 113 of 156
1 2
3
4
1
5
2
6
3
7
8
4
9
5
10
6
11
12
7
8
13
14
9
10
15
16
11
17
18
12
Non-Proportional Equalstratified allocation sampling 1
10 Prof. El-Gilany
2
3
2
4
8
5
4
6
1
6
12
8
4
2
1
6
Page 114 of 156
1
2
3
1
4
2
5
3
6
7
4
8
5
9
10
6
11
7
12
13
8
9
14
15
16
10
17
11
18
12
Proportional Proportionate stratified sampling
allocation 1
2
3
10
2
8
Prof. El-Gilany
4
5
4
6
1
6
12
8
4
2
1
6
Advantages
Disadvantages
-More representative. -Give information about whole population & each stratum -Greater accuracy (precision) than SRS if strata are nonhomogenous -Easy to administer (universe is sub –divided). -Represent key subgroups (small minorities) by stratification & varying sampling fraction between strata -Use different frame for different strata -Every unit in stratum has same chance of being selected
-More money, time & statistical experience. -Bias due to improper stratification (strata overlap, non-representative) -Difficult to identify strata -Loss precision if small numbers in individual strata -Prepare sampling frame for each stratum -Giving more weight to minority subgroups, affect proportion allocation
Prof. El-Gilany
Page 115 of 156
Page 116 of 156
5-Multi-(multiple) stage random sample (MSRS) ((عينة عشوائية متعد المراحل
Prof. El-Gilany
Combine several sampling techniques to create more efficient sample than use of any one sampling type can achieve on its own. Page 117 of 156
Principle: Consecutive sampling: 2 or more stages
-Prepare list of large-sized sampling units -Select random sample proportionate to size -For each 1st stage units: prepare list of smaller sampling units -Select random sample from 2ry units (study units) Prof. El-Gilany
Page 118 of 156
Advantages -Concentrate resources -No need for sampling frame for whole population(only list of 1st stage units, frame for selected last-stage units)
Prof. El-Gilany
Disadvantages -More sampling error compared to SRS
Multistage sampling Egypt Regions Governorates Districts Urban/rural Households
Prof. El-Gilany
Persons
Page 119 of 156
Page 120 of 156
6-Other random samples
Prof. El-Gilany
Page 121 of 156
6.1.Multiphase sample 6.2.Consecutive subjects 6.3.Inverse sampling 6.4.Area sampling 6.5.Sequential sampling
Prof. El-Gilany
Page 122 of 156
6.1.Multiphase sample ()متعد األطوار
Prof. El-Gilany
Page 123 of 156
• Part of information is collected from whole sample & part from subsample. • Number sub-samples in 2nd & 3rd phases will become successively smaller & smaller. • Survey by such methods will be less costly, less laborious & more purposeful.
Prof. El-Gilany
Page 124 of 156
In tuberculosis survey First phase: physical examination or tuberculin test done in all cases of sample
Second phase: chest x-ray done in tuberculin positive cases & in those with clinical symptoms
Third phase: sputum may be examined in X-ray positive cases Prof. El-Gilany
Page 125 of 156
6.2.Consecutive sample ()عينة متتالية
Prof. El-Gilany
Clinical study can be carried out in consecutive eligible cases attending particular clinic at any time. Good as SRS if there is no bias. Sequence of arrival of cases is random & represent cross section of target population Page 126 of 156
2 sources of bias: *Clustering effect may affect random selection (e.g. cases are neighbors/relatives with similar socioeconomic & health status) *Selecting cases attending at specific days may be related to availability of particular doctor. Prof. El-Gilany
Page 127 of 156
6.3.Inverse sampling ()عينة عكسية
Prof. El-Gilany
• No available sampling frame, continue sampling until SS is achieved • E.g.: in ODP all kinds of patients come randomly. SS=35 cases of DM, filter patients & select the first 35 cases meeting legibility criteria
Page 128 of 156
Prof. El-Gilany
Page 129 of 156
6.4.Area (spatial) sampling ()عينة المناطق
Prof. El-Gilany
• Used in multi-stage sampling of household studies with no sampling frame. -Select area with help of map. -Divide locality into appropriate areas & select randomly, then select a predefined number of houses randomly.
Page 130 of 156
• Advantage: work is restricted to selected areas • Disadvantages: unbalanced sample (areas are of different sizes) Prof. El-Gilany
Page 131 of 156
6.5.Sequential sampling ()عينة متتابعة
Prof. El-Gilany
Eligible subjects from target population are selected randomly one by one. Stop sampling if reliable results were obtained. Not popular in medicine
Page 132 of 156
Prof. El-Gilany
Page 133 of 156
Non-probability samples
Prof. El-Gilany
Non-probability (non-random) samples Page 134 of 156
*Focus on volunteers, easily available units, or those that just happen to be present when research is done. *Useful for quick & cheap studies e.g. case studies, qualitative research, pilot studies & developing hypotheses for future research. *Only method that is practical for comparative historical research Prof. El-Gilany
Page 135 of 156
1-Convenience 2-Purposive 3-Quota 4-Snowball 5-Delphi method 6-Heterogeneity sampling
Prof. El-Gilany
Page 136 of 156
1-Convenience (accidental=man-in-thestreet) sample ()عينة متاحة =عرضية
Prof. El-Gilany
Types:
Page 137 of 156
-Volunteers -Captive population (medical students for pulmonary functions) -Referred cases: complicated case, not representative -Telephone sampling: 4 limitations (many household have >1 telephones, some households without telephones, telephone number may not be listed, high attrition rate) -Phase I clinical trial
-1st 10 patients in clinic Prof. El-Gilany
Page 138 of 156
2-Purposive (judgmental) sample ()عينة غرضية = حكمية
Prof. El-Gilany
• Selected by researcher subjectively (choice).
Page 139 of 156
• Researcher attempts to obtain sample that appears to him to be representative of population. • Based on intent • E.g.:
-Students who live in campus -Experts in specific field Prof. El-Gilany
Page 140 of 156
3-Quota sample ()عينة الحصص
Prof. El-Gilany
• Divide population into subgroups • Select purpose units from each subgroup based on specific number or proportion • Constructs quotas for different types of units. • E.g.: interview fixed number of students at library, half of whom are male & half of whom are female Page 141 of 156
Prof. El-Gilany
2 types of Quota Sampling:
Page 142 of 156
1-Proportional: Represent characteristics of population by sampling proportional amount of each. 2-Non-Proportional: Continue select until achieve specific number of sampled units for each subgroup of population (unequal proportions in each group) Prof. El-Gilany
Page 143 of 156
4-Snowball (chain =network) sample ()عينة كر الثلج =السلسلة=الش كة
Prof. El-Gilany
Page 144 of 156 • Identify small group or subject (meet specific criteria)
• Each subject refers another subject to sample • Hard-to-reach, or equivalently hidden populations. – – – –
Population is small relative to general population Geographically dispersed When population membership involves stigma Group has networks that are difficult for outsiders to penetrate
• E.g.: People exposed to sex workers Those injecting drugs in context of HIV Homeless people
Prof. El-Gilany
Page 145 of 156
5-Delphi (sample) method (Expert sample) ()عينة لفى = مجموعة من ال راء
Prof. El-Gilany
• Sample of people with known or demonstrable experience & expertise in some area. • Used for 2 reasons: -The best way to elicit views of persons who have specific expertise. -Provide evidence for validity of another sampling approach that was chosen.
Page 146 of 156
Prof. El-Gilany
Page 147 of 156
6-Heterogeneity sampling ()عينة غير متجانسة
Prof. El-Gilany
Page 148 of 156
• Include all opinions or views irrespective of representing these views proportionately. • Used in many brainstorming or nominal group processes (including concept mapping) because primary interest is in getting broad spectrum of ideas, not identifying "average" or "modal instance" ones. • What we would like to be sampling is not people, but ideas. Prof. El-Gilany
Page 149 of 156
Prof. El-Gilany
Page 150 of 156
Errors & bias in sampling
Prof. El-Gilany
Page 151 of 156
Prof. El-Gilany
Sampling errors theory
Page 152 of 156
I-When performing statistical test: correct decision when: 1- Reject false H0 2- Accept true H0 II-Researcher can make two errors 1- Reject true HA type I error (alpha error) at 0.05 used sample size 2- Accept false HA type II error (beta error) accepted to be 20 used in study power (1-type II error) Prof. El-Gilany
Page 153 of 156
*Sampling errors (difference between estimate & true population parameter) Due to: -Sampling Design (scheme, method) -Sampling Fraction *Non-sampling error: associated with collecting & analyzing data
Prof. El-Gilany
Page 154 of 156
Prof. El-Gilany
Page 155 of 156
Prof. El-Gilany
Page 156 of 156
Prof. El-Gilany
