Sample SizeFor Surveys

Dr. Muna Hassan Mustafa

Faculty of Medicine and Health SciencesInternational University of Africa

Sample Versus Census

• SAMPLE• A part of the population from which we

actually collect information which is used to draw conclusions about the whole population.

• CENSUS• when every member of the population has

data collected from them

Why take a sample ?

Sample versus census

• Efficiency in time, resources, and expense

• If conducted properly will give precise results that can be generalized to the whole population

Before starting

Set study objectives

Variables and their types

Qualitative (categorical) Quantities (numerical)

Before starting

• Study population:

– Case definition– Inclusion and exclusion criteria

Before starting

• Frame of the study population:

• A comprehensive list of the elements of the study population

Sample size (how much)

Foundations for Sample Size Determination

Cochran’s formula A/ Primary indicators (Variables) of

Measurement:• Decisions as to which indicators

(variables) will be incorporated for the estimation– Qualitative indicator (variable)– Quantitative indicator (variable)– Multi-indicator

• Calculate more than one sample

Foundations for Sample Size Determination

B/The level of precision or accuracy required by the survey:

1/ the margin of error the researcher is willing/desire to accept – how much do desire the true value to be away from your results?

the depends on what the results are intended for.

Foundations for Sample Size Determination

• For a qualitative variable, a 5% margin of error would result in the researcher being confident that the proportion of respondents who were male was within ±5% of the proportion calculated from the research sample:

• Usually taken as 5% (qualitative variables) or 3% for quantitative variables

Foundations for Sample Size Determination

2/ the alpha/Confidence level :This is how confident you feel about your error level

• The alpha/Confidence level used in

determining sample size is usually either 95% or 99% (its value in t or z distribution)

Foundations for Sample Size Determination

C/ The amount of variation present in the population for the particular aspect (variable) of interest:

(1) take the sample in two steps, and use the results of the first step.

(2) use pilot study results (3) use data from previous studies (4) estimate or guess the structure of the

population

Basic Sample Size Determination• Continuous Data: (z)2 * (s)2n= ----------------- (d)2Where: z = value for selected alpha level = 1.96s = estimate of standard deviation in the

population d = acceptable margin of error for mean

Basic Sample Size Determination• Categorical Data: (z)2 * (p)(q)n= --------------------- (d)2Where: z = value for selected alpha level = 1.96. (p)(q) = estimate of variance d = acceptable margin of error for

proportion being estimated = .05

Basic Sample Size Determination

• Design Effect• When a cluster sample is used to correct

for the difference in design, the sample size is multiplied by the design effect (D).

• The design effect is generally assumed to be 2 for nutrition surveys using cluster-sampling methodology

Basic Sample Size Determination

• Non response:• research studies often use voluntary

participation methods, the response rates are typically well below 100%

• errors of estimates are increased because the sample actually obtained is smaller than the target sample

• four methods may be used to determine the anticipated response rate:

(1) take the sample in two steps(2) use pilot study results(3) use responses rates from previous

studies (4) estimate the response rate

• After calculating the sample size you divide by (1-response rate (r))

Sampling techniques(how to select)

Types of sampling

• Probability sampling:• which every unit in the population

has a chance (greater than zero) of being selected in the sample

• and this probability can be accurately determined

• Nonprobability sampling:• where some elements of the population

have no chance of selection • where the probability of selection can't be

accurately determined.

Types of Probability sampling• simple random sample :• is the simplest of the probability sampling

techniques. • Each individual is chosen randomly and

entirely by chance, such that each individual has the same probability of being chosen at any stage during the sampling process

• It requires a complete sampling frame • suits situations where not much

information is available about the population

• Can not be used If the population is widely dispersed

• the population itself is not homogeneous

• Systematic sampling:• involve the selection of elements from an

ordered sampling frame. • The most common form of systematic sampling

is an equal-probability method, in which every kth element in the frame is selected, where k, the sampling interval (sometimes known as the 'skip'), is calculated as:

• sample size (n) = population size (N) /k

• The researcher must ensure that the chosen sampling interval does not hide a pattern

Stratified Sample

• Study population is stratified according to some specific variables

• From each stratum select sample size according to the weight of the stratum (proportional allocation)

• Use simple or systematic sampling techniques

Cluster Sample

• The study population is naturally divided into groups (clusters)

• Select a number of clusters using probability proportional to size sampling technique

• From each cluster select equal sizes of sample size

• Use simple or systematic sampling technique

non-probability sample

• Subjects in a non-probability sample are usually selected on the basis of their accessibility or by the purposive personal judgment of the researcher.

CONVENIENCE SAMPLING• is probably the most common of all

sampling techniques. • samples are selected because they are

accessible to the researcher. • Subjects are chosen because they are

easy to recruit. • is considered easiest, cheapest and least

time consuming

JUDGMENTAL SAMPLING• Is commonly known as purposive

sampling. • subjects are chosen to be part of the

sample with a specific purpose in mind. • the researcher believes that some

subjects are more fit for the research compared to other individuals.

SNOWBALL SAMPLING• is usually done when there is a very small

population size. • the researcher asks the initial subject to

identify another potential subject who also meets the criteria of the research.

• The downside of using a snowball sample is that it is hardly representative of the population.