Populations and Sampling

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Lecture 2

• Populations and Sampling
• Types of variables and scales of measurement

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Populations and Sampling a. Reasons for using
samples

• There are many good reasons for studying a sample
  instead of an entire population
• Samples can be studied more quickly than
  populations. Speed can be important if a
  physician needs to determine something quickly,
  such as a vaccine or treatment for a new disease.
• A study of a sample is less expensive than a
  study of an entire population because a smaller
  number of items or subjects are examined. This
  consideration is especially important in the
  design of large studies that require a long
  follow-up.
• A study of the entire populations is impossible
  in most situations.
• Sample results are often more accurate than
  results based on a population.
• If samples are properly selected, probability
  methods can be used to estimate the error in the
  resulting statistics.

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Types of Sampling Methods
Samples
Probability Samples
Non-Probability Samples
Simple Random
Stratified
Consecutive
Judgemental
Cluster
Systematic
Convenience
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Sampling Methods Non-probability samples

• Depends on experts opinion,
• Probabilities of selection not considered.
• Advantages include convenience, speed, and lower
  cost.
• Disadvantages
• Lack of accuracy,
• lack of results generalizability.

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Sampling Methods Non-probability samples (cont)

• Consecutive sampling
• It involves taking every patient who meets the
  selection criteria over a specified time interval
  or number of patients.
• It is the best of the nonprobability techniques
  and one that is very often practical.
• Judgmental sampling
• It involves hand-picking from the accessible
  population those individuals judged most
  appropriate for the study.
• Convenience sampling
• It is the process of taking those members of the
  accessible population who are easily available.
• It is widely used in clinical research because of
  its obvious advantages in cost and logistics.

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Probability Samples
Subjects of the sample are chosen based on known
probabilities. Guarantees that every element in
the population of interest has the same
probability of being chosen for the sample as all
other elements in the population random
selection.
Probability Samples
Simple Random
Systematic
Stratified
Cluster
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Advantages of Probability sampling methods

• The population of interest is clear (because it
  must be identified before sampling from it.)
• Possible sources of bias are removed, such as
  self-selection and interviewer selection effects.
• The general size of the sampling error can be
  estimated.

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Simple Random Sampling

• Every individual or item from the target
  population has an equal chance of being selected.
• One may use table of random numbers or computers
  programs for obtaining samples.

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How to select a simple random sample

• Define the population
• Determine the desired sample size
• List all members of the population or the
  potential subjects
• For example
• 4th grade boys who have demonstrated problem
  behaviors
• Lets select 10

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Potential Subject Pool
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So our selected subjects are numbers 10, 22, 24,
15, 6, 1, 25, 11, 13, 16.
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Systematic Sampling

• Decide on sample size n
• Divide population of N individuals into groups
  of
• k individuals k N/n
• Randomly select one individual from the 1st
  group.
• Select every k-th individual thereafter.

N 64 n 8 k 8
First Group
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Systematic Sampling (cont)

• Advantage The sample usually will be easier to
  identify than it would be if simple random
  sampling were used.
• Example Selecting every 100th listing in a
  telephone book after the first randomly selected
  listing.

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Stratified Random Sampling

• The population is first divided into groups of
  elements called strata.
• Each element in the population belongs to one
  and only one stratum.
• Best results are obtained when the elements
  within each stratum are as much alike as possible
  (i.e. homogeneous group).
• A simple random sample is taken from each
  stratum.
• Formulas are available for combining the stratum
  sample results into one population parameter
  estimate.

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Stratified Random Sampling (cont)

• Advantage If strata are homogeneous, this
  method is as precise as simple random sampling
  but with a smaller total sample size.
• Example The basis for forming the strata might
  be sex, occupation, location, age, industry type,
  etc.

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Cluster Sampling

• The population is first divided into separate
  groups of elements called clusters.
• Ideally, each cluster is a representative
  small-scale version of the population (i.e.
  heterogeneous group).
• A simple random sample of the clusters is then
  taken.
• All elements within each sampled (chosen)
  cluster form the sample.

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Cluster Sampling (cont)

• Advantage The close proximity of elements can
  be cost effective (I.e. many sample observations
  can be obtained in a short time).
• Disadvantage This method generally requires a
  larger total sample size than simple or
  stratified random sampling.
• Example A primary application is area
  sampling, where clusters are city blocks or other
  well-defined areas.

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Random . . .

• Random Selection vs. Random Assignment
• Random Selection every member of the population
  has an equal chance of being selected for the
  sample.
• Random Assignment every member of the sample
  (however chosen) has an equal chance of being
  placed in the experimental group or the control
  group.
• Random assignment allows for individual
  differences among test participants to be
  averaged out.

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Subject Selection (Random Selection)
Choosing which potential subjects will actually
participate in the study
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Subject Assignment (Random Assignment)
Deciding which group or condition each subject
will be part of
Group B
Group A
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Population 200 8th Graders
40 High IQ students
120 Avg. IQ students
40 Low IQ students
Random Selection
30 students
30 students
30 students
Random Assignment
15 students
15 students
15 students
15 students
15 students
15 students
Group A
Group B
Group A
Group B
Group A
Group B
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Randomization (Random assignment to two
treatments)

• Randomization tends to produce study groups
  comparable with respect to known and unknown risk
  factors,
• removes investigator bias in the allocation of
  participants
• and guarantees that statistical tests will have
  valid significance levels
• Trialists most powerful weapon against bias

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Randomization (Cont)

• Simple randomizationToss a Coin
• AAABBAAAAABABABBAAAABAA
• Random permuted blocks (Block Randomization)
• AABB-ABBA-BBAA-BAAB-ABAB-AABB-

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Block Randomization

• Each block contains all conditions of the
  experiment in a randomized order.

E, C, C, E
C, E, C, E
E, E, C, C
Control Group N 6
Experimental Group N 6
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Several ways to classify the variables

• They may be defined as
• quantitative variables
• qualitative (categorical) variables

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Quantitative variables

• Measured in the usual sense
• heights of adult males,
• weights,
• age of patients seen in a clinic.
• Measurements made on quantitative variables
  convey information regarding amount

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• Quantitative variables are either
• Discrete
• only take values from some discrete set of
  possible values (whole integer)
• number of patients admitted to the hospital
• Continuous
• Values from a continuous range of possible
  values, although the recorded measurements are
  rounded
• weight,
• height,
• hemoglobin levels, etc..

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Qualitative (categorical) variables

• Some characteristics are not capable of being
  measured in the sense that height, weight, and
  age are measured.
• These characteristics are categorized only
• an ill person is given a medical diagnosis
  (hepatitis, cancer, etc..)
• a person is designated as belonging to an ethnic
  group,
• black,
• white,
• Hispanic, etc.

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Scales of measurement

• Another way to classify the variables is to
  assign number to the objects or events according
  to a set of rules.
• These rules are the scales of measurement
• They are commonly broken down into four types
• Nominal
• Ordinal
• Interval (numerical)
• Ratio (numerical)

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Nominal scale

• Simplest level of measurement
• Data values fit into categories.
• No ordering,
• it makes no sense to state that M gt F
• Arbitrary labels,
• m/f, 0/1, etc
• Many classifications in medical research are
  evaluated on a nominal scale
• Outcomes of a medical treatment occurring or not
  occurring
• Surgical procedure types of procedures
• Presence of possible risk or exposure factors.

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Nominal scale (cont)

• Dichotomous variables
• take on only one of two values
• presence of pain (yes/no),
• sex (male/female)
• Data that can take on more than two values, as
  anemia, for example, may be classified as
• microcytic anemia, including iron deficiency
• macrocytic or megaloblastic anemia, including
  vitamin B12 deficiency
• normocytic anemia, often associated with chronic
  disease.
• A study examining the prognosis for patients with
  lung cancer might sort the type of cancer into
  several categories, such as
• small cell,
• large cell,
• squamous cell.

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Nominal scale (cont)

• The easiest way to determine whether observations
  are measured on a nominal scale is to ask whether
  the observations are classified or placed into
  categories.
• Data evaluated on a nominal scale are also called
  qualitative observations, because the values fit
  into categories.
• Nominal or qualitative data are generally
  described in terms of percentages or proportions.

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Ordinal scale

• There is an inherent order among the categories
• Tumors, for example, are staged according to
  their degree of development.
• The international classification for staging of
  carcinoma of the cervix is an ordinal scale from
  0 to IV
• 0 Carcinoma in situ (localized)
• I Cancer is confined to the cervix
• II Cancer extends to the upper third of the
  vagina, or the tissue around the uterus, but not
  the pelvic wall
• III The lower third of the vagina and/or the
  pelvic sidewall and possibly the kidneys are
  diseased
• IV Cancer has spread beyond the reproductive
  tract involving the bladder or rectum, and has
  invaded distant organs (most often the lungs or
  liver), the bones, or other systems in the body

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Ordinal scale (cont)

• Stage IV is worse than stage 0 with respect to
  prognosis
• This is an inherent order
• An important characteristic of ordinal scales is
  that although order exists among categories, the
  difference between two adjacent categories is not
  the same throughout the scale.
• To illustrate, consider Apgar scores, which
  describe the maturity of newborn infants on a
  scale of 0 to 10,
• lower scores indicating depression of
  cardiorespiratory and neurologic functioning
• higher scores indicating good cardiorespiratory
  and neurologic functioning
• difference between a score of 8 and a score of 10
  is probably not of the same magnitude,
• as the difference between a score of 0 and a
  score of 2.
• As with nominal scales, percentages and
  proportions are often used with ordinal scales.

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Numerical scale

• Observations in which the difference between
  numbers has meaning on a numerical scale
• Also called quantitative observations, because
  they measure the quantity of something.
• There are two types of numerical scales
• A continuous scale has values on a continuum
• age
• a discrete has values equal to integers
• number of fractures, number of admissions

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Numerical scale (cont)

• If only a certain level of precision is required,
  continuous data may be reported to the closest
  integer. The important point, however, is that
  more precise measurement is possible, at least
  theoretically.
• For example, the age of a group of patients can
  be any value between zero and the age of the
  oldest patient, i.e. age can be specified as
  precisely as necessary.
• In studies of adults, age to the nearest year
  will generally suffice.
• For younger children, age to the nearest month is
  better.
• In infants, age to the nearest hour or even
  minute may be appropriate, depending on the
  purpose of the study.
• Other examples of continuous data include height,
  weight, and length of time of survival, range of
  joint motion and many laboratory values, such as
  serum glucose, sodium, potassium or uric acid.

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Numerical scale (cont)

• Characteristics measured on numerical scale are
• displayed in tables and graphs
• summarize as means and standard deviations