4.sampling design

Sampling Design

D.A. Asir John Samuel, BSc (Psy), MPT (Neuro Paed), MAc, DYScEd,

C/BLS, FAGE

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

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

Steps in sampling design

Target population

Study population

Sample

Study participation Dr. Asir John Samuel (PT), Lecturer, ACP 4

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

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


Types of sample design

Sample design

Random sampling

Simple Stratified Systematic Cluster Multistage

Non-random sampling

convenience Quota Judgment


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

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

SRS - Merits

• No personal bias

• Easy to assess the accuracy


SRS - Demerits

• Need a complete catalogue of universe

• Large size sample

• Widely dispersed


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


SRs - Merits

• More representative

• Greater accuracy

• Can acquire information about whole

population and individual strata


SRs - Demerits

• Careful stratification

• Random selection in each stratum

• Time consuming


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


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


SS - Merits

• Simple and convenient

• Less time and work


SS - Demerits

• Need complete list of units

• Periodicity

• Less representation


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


Cluster Sampling

• It is always assumed that the individual items

within each cluster are representation of

population

• E.g. District, wards, schools, industries


CS - Merits

• Saving of travelling time and consequent

reduction in cost

• Cuts down on the cost of preparing the

sampling frame


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


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

Multistage Sampling

• Continue until the final sampling units are

selected

• E.g. Few states – District – Taulk


MS - Merits

• Cut down the cost of preparing the sampling

frame


MS - Demerits

• Sampling error is increased compared to

simple random sampling


Quota Sampling

• Interviewers are requested to find cases with

particular types of people to interview


Judgment (Purposive Sampling)

• Researcher attempts to obtain sample that

appear to be representative of the population

selected by the researcher subjectively


Convenience Sampling

• Sampling comprises subject who are simply

avail in a convenient way to the researcher

• No randomness and likelihood of bias is high


Snowball Sampling

• Investigators start with a few subjects and

then recruit more via word of mouth from the

original participants


Merits

• Easy

• Low cost

• Limited time

• Total list population


Demerits

• Selection bias

• Sample is not representation of population

• doesn’t allow generalization


Sample Size

Determination

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


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”


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


Type I & II errors

Possible states of Null Hypothesis

Possible actions on

Null Hypothesis

True False

Accept Correct Action

Type II error

Reject Type I error

Correct Action

Prob (Type I error) – α (LoS) Prob (Type II error) – β 1-β – power of test


Z values

Z 0.05 – 1.96 – 95%

Z 0.10 – 1.282 – 90%

Z 0.20 – 0.84 – 80%


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


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.


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


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


Estimating mean

n = (Zα σ / d)²

σ – anticipated SD of population

d – acceptable margin of error in estimating true population mean


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


Comparison of 2 proportions

n = (Zα √2PQ + Zβ√P1Q1+P2Q2)²/(P1-P2)²

P = P1+P2/2 Q = 1-P


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)


Technology

4.sampling design