Populations
Definition - a complete set of elements (persons or objects) that possess
some common characteristic defined by the sampling criteria established
by the researcher
Composed of two groups - target population & accessible population
Target population (universe)
The entire group of people or objects to which the
researcher wishes to generalize the study findings
Meet set of criteria of interest to researcher
Examples
All institutionalized elderly with Alzheimer's
All people with AIDS
All low birth weight infants
All school-age children with asthma
All pregnant teens
Accessible population
the portion of the population to which the researcher has
reasonable access; may be a subset of the target
population
May be limited to region, state, city, county, or institution
Examples
All institutionalized elderly with Alzheimer's in St.
Louis county nursing homes
All people with AIDS in the metropolitan St. Louis
area
All low birth weight infants admitted to the
neonatal ICUs in St. Louis city & county
All school-age children with asthma treated in
pediatric asthma clinics in university-affiliated
medical centers in the Midwest
All pregnant teens in the state of Missouri
Samples
Terminology used to describe samples and sampling methods
Sample = the selected elements (people or objects) chosen for
participation in a study; people are referred to as subjects or
participants
Sampling = the process of selecting a group of people, events,
behaviors, or other elements with which to conduct a study
Sampling frame = a list of all the elements in the population from
which the sample is drawn
Could be extremely large if population is national or
international in nature
Frame is needed so that everyone in the population is
identified so they will have an equal opportunity for
selection as a subject (element)
Examples
A list of all institutionalized elderly with
Alzheimer's in St. Louis county nursing homes
affiliated with BJC
A list of all people with AIDS in the metropolitan St.
Louis area who are members of the St. Louis Effort
for AIDS
A list of all low birth weight infants admitted to the
neonatal ICUs in St. Louis city & county in 1998
A list of all school-age children with asthma treated
in pediatric asthma clinics in university-affiliated
medical centers in the Midwest
A list of all pregnant teens in the Henderson school
district
Randomization = each individual in the population has an equal
opportunity to be selected for the sample
Representativeness = sample must be as much like the
population in as many ways as possible
Sample reflects the characteristics of the population, so
those sample findings can be generalized to the
population
Most effective way to achieve representativeness is
through randomization; random selection or random
assignment
Parameter = a numerical value or measure of a characteristic of
the population; remember P for parameter & population
Statistic = numerical value or measure of a characteristic of the
sample; remember S for sample & statistic
Precision = the accuracy with which the population parameters
have been estimated; remember that population parameters often
are based on the sample statistics
Types of Sampling Methods - probability & nonprobability
Probability Sampling Methods
Also called random sampling

Every element (member) of the population has a
probability greater than) of being selected for the sample

Everyone in the population has equal opportunity for
selection as a subject

Increases sample's representativeness of the population

Decreases sampling error and sampling bias
Types of probability sampling - see table in course materials for details
Simple random

Elements selected at random

Assign each element a number

Select elements for study by:
1. Using a table of random numbers in book
A table displaying hundreds of digits from 0
to 9 set up in such a way that each number is
equally likely to follow any other
See text for random sampling details & table
of random numbers
 Computer generated random numbers table
 Draw numbers for box (hat)
 Bingo #=s
Stratified random
Population is divided into subgroups, called strata,
according to some variable or variables in importance
to the study
Variables often used include: age, gender, ethnic origin,
SES, diagnosis, geographic region, institution, or type of
care
Two approaches to stratification - proportional &
disproportional
Proportional
Subgroup sample sizes equal the proportions
of the subgroup in the population
Example: A high school population has
15% seniors
25% juniors
25% sophomores
35% freshmen
With proportional sample the sample
has the same proportions as the
population
Disproportional
Subgroup sample sizes are not equal to the
proportion of the subgroup in the population
Example
Class
Population
Sample
Seniors
15%
25%
Juniors
25%
25%
Sophomores
25%
25%
Freshmen
35%
25%
With disproportional sample the
sample does not have the same
proportions as the population
Cluster random sampling
A random sampling process that involves stages of
sampling
The population is first listed by clusters or categories
Procedure
Randomly select 1 or more clusters and take all of
their elements (single stage cluster sampling); e.g.
Midwest region of the US
Or, in a second stage randomly select clusters from
the first stage of clusters; eg 3 states within the
Midwest region
In a third stage, randomly select elements from the
second stage of clusters; e.g. 30 county health dept.
nursing administrators from each state
Systematic
A random sampling process in which every kth (e.g.
every 5th element) or member of the population is
selected for the sample after a random start is
determined
Example
Population (N) = 2000, sample size (n) = 50, k=N/n,
so k = 2000 ) 50 = 40
Use a table of random numbers to determine the
starting point for selecting every 40th subject
With list of the 2000 subjects in the sampling
frame, go to the starting point, and select every
40th name on the list until the sample size is
reached. Probably will have to return to the
beginning of the list to complete the selection of the
sample.
Non-probability sampling methods
Characteristics
Not every element of the population has the opportunity for
selection in the sample
No sampling frame
Population parameters may be unknown
Non-random selection
More likely to produce a biased sample
Restricts generalization
Historically, used in most nursing studies
Types of non-probability sampling methods
Convenience - aka chunk, accidental & incidental sampling
Selection of the most readily available people or objects
for a study
No way to determine representativeness
Saves time and money
Quota
Selection of sample to reflect certain characteristics of the
population
Similar to stratified but does not involve random
selection
Quotas for subgroups (proportions) are established
E.g. 50 males & 50 females; recruit the first 50 men and
first 50 women that meet inclusion criteria
Purposive - aka judgmental or expert's choice sampling
Researcher uses personal judgement to select subjects
that are considered to be representative of the
population
Handpicked subjects
Typical subjects experiencing problem being studied
Snowball
Also known as network sampling
Subjects refer the researcher to others who might be
recruited as subjects
Time Frame for Studying the Sample
See design notes on longitudinal & cross-sectional studies
Longitudinal
Cross-sectional
Sample Size
General rule - as large as possible to increase the representativeness of
the sample
Increased size decreases sampling error
Relatively small samples in qualitative, exploratory, case studies,
experimental and quasi-experimental studies
Descriptive studies need large samples; e.g. 10 subjects for each item on
the questionnaire or interview guide
As the number of variables studied increases, the sample size also needs
to increase in order to detect significant relationships or differences
A minimum of 30 subjects is needed for use of the central limit theorem
(statistics based on the mean)
Large samples are needed if:
There are many uncontrolled variables
Small differences are expected in the sample/population on
variables of interest
The sample is divided into subgroups
Dropout rate (mortality) is expected to be high
Statistical tests used require minimum sample or subgroup size
Power Analysis
Power analysis = a procedure for estimating either the likelihood of committing a
Type II error or a procedure for estimating sample size requirements
Background Information for Understanding Power Analysis:
Type I and Type II errors
Type I error
Based on the statistical analysis of data, the researcher wrongly
rejects a true null hypothesis; and therefore, accepts a false
alternative hypothesis
Probability of committing a type I error is controlled by the
researcher with the level of significance, alpha.
Alpha  is the probability that a Type I error will occur
Alpha  is established by researcher; usually  = .05 or .01
lpha = .05 means there is a 5% chance of rejecting a
true null hypothesis; OR out of 100 samples, a true null
hypothesis would be rejected 5 times out of 100 and
accepted 95 times out of 100.
Alpha  = .01 means there is a 1% chance of rejecting a true
null hypothesis; OR out of 100 samples, a true null
hypothesis would be rejected 1 time out of 100 and
accepted 99 times out of 100
Type II error
Based on the statistical analysis of data, the researcher wrongly
accepts a false null hypothesis; and therefore, rejects a true
alternate hypothesis
Probability of committing a Type II error is reduced by a power
analysis
Probability of a Type II error is called beta 
Power, or 1-  is the probability of rejecting the null
hypothesis and obtaining a statistically significant result

Type I & Type II Errors
In the real world,
the actual
situations is that
In the real world,
the actual
situations is that
Based on statistical
analysis, the researcher
concludes that:
Null true: Null hypothesis is
accepted
Based on statistical
analysis, the researcher
concludes that:
Null false: Null hypothesis is
rejected & alternate is
accepted
the null hypothesis
is :
the null hypothesis
is :
True
False
Correct decision:
the actual true null
is accepted
Type II error: the
actual false null is
accepted
Type I error: the
actual true null
hypothesis is
rejected
Correct decision:
the actual false null
is rejected &
alternate is
accepted
Background Information for Understanding Power Analysis:
Population Effect Size - Gamma 
Gamma  measures how wrong the null hypothesis is; it measures how
strong the effect of the IV is on the DV; and it is used in performing a
power analysis
Gamma  is calculated based on population data from prior research
studies, or determined several different ways depending on the nature of
the data and the statistical tests to be performed
The textbook discusses 4 ways to estimate gamma (population effect size)
based upon:
Testing the difference between 2 means (t-test)
Testing the difference between 3> means (ANOVA)
Testing bivariate correlation (relationship) between 2 variables
(Pearson's r)
Testing the difference in proportions between 2 groups (chisquare)
If there is no relevant research on topic to estimate the population effect
size (gamma), then use guidelines for gamma  or its equivalent
Testing the difference between 2 means (t-test) - gamma  for
small effects  = .20; medium effects  = .50; large effects  = .80
Testing the difference between 3> means (ANOVA) - eta
squared 2for small effects 2 = .01; medium effects 2 = .06;
large effects 2 = .14
Testing bivariate correlation (relationship) between 2 variables
(Pearson's r) gamma  for small effects  = .10; medium effects  =
.30; large effects  = .50
Testing the difference in proportions between 2 groups (chisquare - no conventions for unknown populations
Determining Sample Size through Power Analysis
Need to have the following data:
Level of significance criterion = alpha , use .05 for most nursing studies
and your calculations
Power = 1 -  (beta); if beta is not known standard power is .80, so use this
when you are determining sample size
Population size effect = gamma  or its equivalent, e.g. eta squared 2; use
recommended values for small, medium, or large effect for the statistical
test you plan to use to answer research questions or test hypothesis
Use tables on pages 455-459 of Polit & Hungler or other reference
Mathematical formulas and computer programs can also be used for calculation of
sample size
Sampling Error and Sampling Bias
Sampling error = The difference between the sample statistic (e.g. sample
mean) and the population parameter (e.g. population mean) that is due to
the random fluctuations in data that occur when the sample is selected
Sampling bias
Also called systematic bias or systematic variance
The difference between sample data and population data that
can be attributed to faulty sampling of the population
Consequence of selecting subjects whose characteristics (scores)
are different in some way from the population they are suppose
to represent
This usually occurs when randomization is not used
Randomization Procedures in Research
Randomization = each individual in the population has an equal
opportunity to be selected for the sample
Random selection = from all people who meet the inclusion criteria, a
sample is randomly chosen
Random assignment
The assignment of subjects to treatment conditions in a random
manner.
It has no bearing on how the subjects participating in an
experiment are initially selected.
See Polit & Hungler, pg. 160-162 for random assignment to
groups and group random assignment to tx. using a random
numbers table