9. Selecting a sample

KNOWLEDGE FOR THE BENEFIT OF HUMANITYKNOWLEDGE FOR THE BENEFIT OF HUMANITY
RESEARCH METHODOLOGY (HFS4343)
SELECTING A SAMPLE
Dr.Dr. MohdMohd RazifRazif ShahrilShahril
School of Nutrition & DieteticsSchool of Nutrition & Dietetics
Faculty of Health SciencesFaculty of Health Sciences
UniversitiUniversiti SultanSultan ZainalZainal AbidinAbidin
1

S C H O O L O F N U T R I T I O N A N D D I E T E T I C S • U N I V E R S I T I S U L T A N Z A I N A L A B I D I N
Topic Learning Outcomes
At the end of this lecture, students should be able to;
• define sampling terminology
• differentiate types of sampling in quantitative and
qualitative research
• calculate sample size
2

Sample
The concept of sampling
3
Study population:
sampling units
Select a few sampling
units from the study
population
Collect information from
these people to find
answers to your research
questions

The concept of sampling
• Sampling is the process of selecting a few (a sample)
from a bigger group (the sampling population)
– to become the basis for estimating or predicting the prevalence
of an unknown piece of information, situation or outcome
regarding the bigger group.
• A sample is a subgroup of the population you are
interested in
• Advantages of selection sample
– Saves time as well as financial and human resource
• Disadvantages of selecting sample
– Possibility of error in estimation exists
4

Sampling terminology
• Study population
• Sample
• Sample size (n)
• Sampling design/ strategy
• Sampling unit/ element
• Sampling frame
• Sample statistics
• Population mean
5
Briefly explain these
terminologies in e-Kelip Forum

Principles of sampling
6
11
• In a majority of cases of sampling there will be a difference
between the sample statistics and the true population mean,
which is attributable to the selection of the units in the sample
22
• The greater the sample size, the more accurate the estimate of
the true population mean
3
• The greater the difference in the variable under study in a
population for a given sample size, the greater the difference
between the sample statistics and the true population mean

Factors affecting the inferences drawn
from a sample
• The size of the sample
– Findings based upon larger samples have more certainty than
those based on smaller ones.
– The larger the sample size, the more accurate the findings
• The extent of variation in the sampling unit
– The greater the standard deviation, the higher the standard error
for a given sample size in your estimates.
– The higher the variation with respect to the characteristics under
study in the study population, the greater the uncertainty for a
given sample.
7

Aims in selecting a sample
• Maximum precision in estimates within the given sample
size
• Avoid bias in the selection of your sample. Bias in
selection of sample can occur if;
– Sampling is done by a non-random method
– The sampling frame does not cover the sampling population
accurately and completely
– A section of a sampling population is imposible to find or refuses
to co-operate
8

Types of sampling
Random/
probability
sampling design
Non-random/
non-probability
sampling design
Systematic
sampling: mixed
design
9

Random/ probability sampling design
• Simple random sampling
• Stratified random sampling
– Proportionate stratified sampling
– Disproportionate stratified sampling
• Cluster sampling
10
Activity: Find videos or animations related to
sampling design and share in Blendspace. Briefly
present to class member

Non-random/ non-probability sampling
design
• Quota sampling
• Accidental sampling
• Judgemental/ purposive sampling
• Expert sampling
• Snowball sampling
11
Systematic sampling: mixed design
Activity: Find videos or animations related to
sampling design and share in Blendspace. Briefly
present to class member

CALCULATION OF SAMPLE SIZECALCULATION OF SAMPLE SIZE
12
The following slides till the end was prepared by Prof Dr Lua Pei Lin, UniSZA

WHY SAMPLE SIZE CALCULATION?WHY SAMPLE SIZE CALCULATION?
• Common Q: How many subjects needed to obtain a significant result?
• If sample size (n) is too small:
 Waste of time
 No conclusive results
 Clinically significant differences may not be ‘statistically significant’
• If sample size (n) is too large:
 Extra subjects given therapy which may not be efficacous
 Waste of resources (unnecessary exposure)
Kamarul Imran Musa (2012). Sample Size Estimation. In Research Methodology in Health Sciences. KKMED Publications, Universiti Sains Malaysia,
Kota Bharu.

IF NOT CALCULATED?IF NOT CALCULATED?
• Is the study ethical?
• Would the study waste resources?
• Should the study still be conducted?
• Could it be a study limitation?
• Statistically insignificant results may be generated i.e. no real difference OR
lack of power?
• How does it affect the budget?
• Problems on sampling method?
• Study outcomes cannot be compared/generalised?
Kota Bharu.

STUDY AIMS vs. SAMPLE SIZESTUDY AIMS vs. SAMPLE SIZE
• Study aims/objectives are almost always:
• To estimate prevalence or proportion of a disease, condition etc.
• To compare prevalence or proportion of a disease, condition etc.
• For categorical variables – point prevalence/proportion and 95% confidence
interval (CI).
• For numerical variables - exact mean and and 95% confidence interval (CI).
• Each aim/objective should have its own sample size.
• Choose the biggest sample size.
Kota Bharu.

RECALL!RECALL! TYPES OF ERRORTYPES OF ERROR
• Type I error; Alpha:
• Reject Ho when it is true.
• No difference in reality, but the p value is < 0.05.
• Type II error; Beta:
• Ho not rejected when it is false.
• Difference exists in reality, but the p value is > 0.05.
• Power of study = 1 – Type II error (or 1 – Beta)
• Higher power, bigger sample size needed.
• Typically, power set at 80%.
Kota Bharu.

RECALL!RECALL! ONEONE-- VS. TWOVS. TWO--TAILEDTAILED
• Also one-sided or two-sided test.
• One-tailed test:
• Only ONE assumption/direction – negative OR positive.
• Researcher is very confident of outcome.
• Unusual in health or medical study.
• E.g.: Does treatment A enhance patient satisfaction?
• Two-tailed test:
• BOTH negative OR positive assumption/direction allowed.
• Outcome can be either good or bad.
• More conservative (‘safe’).
• Requires bigger sample size.
• E.g.: Does treatment A alter patient satisfaction?
Kota Bharu.

TYPES OF CALCULATIONTYPES OF CALCULATION
• Sample size for ESTIMATION.
• Sample size for HYPOTHESIS TESTING.
• For estimation:
– To produce estimation with acceptable CI.
– Too large – very narrow CI (over-precise).
– Too small – very wide CI (imprecise).
• For hypothesis testing:
– To enable study to have acceptable power to detect significant
differences between two groups.
– Too large – statistically significant differences although clinical
difference is very small (not practically important).
– Too small – no statistically significant difference although clinical
difference is large (cannot show difference although important).
Kota Bharu.

1) n FOR ESTIMATION1) n FOR ESTIMATION
• Applies to studies which plan to estimate:
a) Means of variables
• Example of study aim = To estimate the MEAN stress
score among patients in Hospital ABC.
b) Proportions of variables
• Example of study aim = To estimate the PROPORTION of
obesity among sumo wrestlers.
Kota Bharu.

1a) ESTIMATION OF MEANS1a) ESTIMATION OF MEANS
• Use the SINGLE MEAN FORMULA:
n = Z 1-α/2 * σ
--------------------
Δ
n = sample size required
Z 1-α/2 = desired confidence level (if 95% CI, z = 1.96)
σ = standard deviation (from previous/pilot study)
Δ = precision (researcher decide)
Kota Bharu.

1a) EXAMPLE:1a) EXAMPLE: Mean EstimateMean Estimate
• To estimate the mean exercise duration for UniSZA
athletes in a week, how many samples are needed?
1. At 95% CI, Z = 1.96
2. Standard deviation, σ from previous study = 43 mins
3. Precision, Δ decided at = 10
4. Calculate:
n = 1.96 * 43
10
= 71 athletes
Kota Bharu.

1b) ESTIMATION OF1b) ESTIMATION OF
PROPORTIONSPROPORTIONS
• Use the SINGLE PROPORTION FORMULA:
n = Z 1-α/2
-------------- * P (1-P)
Δ
n = sample size required
Z 1-α/2 = desired confidence level (if 95% CI, z = 1.96)
P = proportion with the disease (from previous/pilot study)
Δ = precision (researcher decide)
Kota Bharu.

1b) EXAMPLE:1b) EXAMPLE:
Proportion EstimateProportion Estimate
• To estimate the proportion of adults with metabolic
syndrome, how many samples are needed?
1. At 95% CI, Z = 1.96
2. Proportion, P from previous study = 40%
3. Precision, Δ decided at = 2.5%
4. Calculate:
n = 1.96 2 * 0.4 (1-0.4)
0.025
= 1,476 adults.
Kota Bharu.

ISSUES IN ESTIMATIONSISSUES IN ESTIMATIONS
• If proportion, report as ‘Prevalence’.
Interpretation:
• Prevalence of obesity = 37% (95% CI: 27%, 47%)
• The proportion of obese individuals in our study group is 37% and we are
95% confident that the proportion of obese individuals in the population
ranges between 27% to 47%.
• Deciding the precision, Δ is hardest.
• If past research did indicate 95% CI somewhere in their results for the same
variable studied, then the precision is HALF of the 95% CI WIDTH.
Kota Bharu.

2) n FOR HYPOTHESIS TESTING2) n FOR HYPOTHESIS TESTING
Applies to studies which plan to compare:
a) Means between two groups
Example of study aim = To compare mean systolic BP between patients with and
without stroke.
b) Proportions between two groups
Example of study aim = To compare the prevalence (proportion) of obese male
and female athletes.
Kota Bharu.

2a) COMPARING MEANS2a) COMPARING MEANS
n = 2 (SD2)
--------------- x (Z 1-α/2 + Z 1-β)2
Δ
n = sample size required per group
SD or σ = standard deviation (from previous/pilot study)
Z 1-α/2 = 1.96 if Type I error (alpha) at 5% (2-sided)
Z 1-β = 0.84 if Type II error (beta) at 20% (power=80%)
Δ = detectable difference (researcher decide)
Kota Bharu.

22a) EXAMPLE:a) EXAMPLE:
Compare MeansCompare Means
• To compare means systolic BP between patients with
stroke (A) vs. patients without stroke (B):
1. SD (from previous study) = 10mmHg
2. Detectable Difference, Δ decided at = 5mmHg
3. Type I error at 5%; Z 1-α/2 = 1.96
4. Type II error at 20%; Power = 80%; Z 1-β = 0.84
5. Calculate:
n = 2 (102) x (1.96 + 0.84)2
5
• = 314 per group
Kota Bharu.

2a) COMPARING PROPORTIONS2a) COMPARING PROPORTIONS
Kota Bharu.
n = p1 (1 - p1) + p0 (1 - p0)
--------------------------------- * [ (Z 1-α/2 + Z 1-β)2 ]
(p1 – p0) 2
n = sample size required per group
p1= proportion in Group 1 (from previous/pilot study)
p0 = proportion in Group 2 (from previous/pilot study/decide)
Z 1-α/2 = 1.96 if Type I error (alpha) at 5% (2-sided)
Z 1-β = 0.84 if Type II error (beta) at 20% (power=80%)
Δ = detectable difference (researcher decide)

Compare Proportion (Compare Proportion (ii))
• To compare the prevalence of obesity between male and
female athletes:
1. p1= 27% (from previous/pilot study)
2. p0 = 37% (expected 10% more than p1)
3. Z 1-α/2 = 1.96 for Type I error at 5% (2-sided)
4. Z 1-β = 0.84 for Type II error at 20% (power=80%)
5. Δ = 10% (detectable difference, clinically important)
Kota Bharu.

Compare Proportion (ii)Compare Proportion (ii)
• n = p1 (1 - p1) + p0 (1 - p0)
--------------------------------- * [ (Z 1-α/2 + Z 1-β)2 ]
(p1 – p0) 2
= 0.37 (1-0.37) + 0.27 (1-0.27) * [(1.96 + 0.84)2]
(0.37-0.27)2
= 337 athletes per group i.e. 337 males & 337 females
Kota Bharu.

REMEMBER!REMEMBER!
Kota Bharu.
• Type I error (alpha) – False Positive
• Type II error (beta) – False Negative
• Power of Study (1-beta) = True Positive
• Detectable Difference (DD) =
Detectable Alternative

INFLUENTIAL FACTORSINFLUENTIAL FACTORS
http://stattrek.com/sample-size/simple-random-sample.aspx
• Cost considerations (e.g., maximum budget,
desire to minimize cost).
• Administrative concerns (e.g., complexity of the
design, research deadlines).
• Minimum acceptable level of precision.
• Confidence level.
• Variability within the population or subpopulation
(e.g., stratum, cluster) of interest.
• Sampling method.

9. Selecting a sample

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