# 11 Populations and Samples.

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11 Populations and Samples

Learning Objectives Define Population And Sample
Distinguish Between Target And Accessible Population Discuss Probability And Nonprobability Sampling Procedures Compare Four Methods Of Probability Sampling

Learning Objectives Compare Three Methods Of Nonprobability Sampling
Determine Which Sampling Technique To Use In Various Types Of Research Studies Compare Longitudinal And Cross-Sectional Studies Enumerate Factors To Be Considered In Deciding The Size Of The Sample 3

Learning Objectives Discuss Sampling Error And Sampling Bias
Critique The Sampling Procedure Described In Research Reports And Articles 4

Learning Objective One Define Population And Sample

Population Complete set of persons or objects Common characteristic
Of interest to the researcher

Sample Subset of a population Sample represents the population.

Sample Selection Representation of the population
Method for getting the sample Sample size for the study

Sample Terms Element Sampling frame Single member of a population
Listing of all elements Study sample, if from this frame

Learning Objective Two Distinguish Between Target And Accessible Population
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Population Terms Target population Accessible population

Target Population Definition Entire group of people or objects
People or objects meet designated set of criteria. Generalization of the findings

Accessible Population

Population Importance
Conclusions based on data Data from accessible population Decisions made from study results

Learning Objective Three Discuss Probability And Nonprobability Sampling Procedures
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Types of Sampling Methods
Probability Nonprobability

Probability Sampling Uses random sampling procedures
Selects sample from elements or members of population Types Simple Stratified Cluster Systematic

Nonprobability Sampling
Uses nonrandom sampling procedures Selects sample from elements or members of population Types Convenience Quota Purposive

Learning Objective Four Compare Four Methods Of Probability Sampling
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Probability Sampling Simple random Stratified Cluster Systematic

Random Selection Key word in sample selection
Every subject has an equal chance.

Probability Sampling Allows researcher to estimate the chance
Helps with inferential statistics with greater confidence Gives the ability to generalize the findings

Simple Random Sampling
Type of probability sampling Importance of this sampling Equal chance of selection Independent chance of selection

Little knowledge of population is needed. Most unbiased of probability method Easy to analyze data and compute errors

Complete listing of population is necessary. It is time consuming to use.

Steps for Simple Random Sampling
Identify the accessible population or list of elements Choose the method for getting the sample Note how easy it is through this example Names of elements on slips of paper Papers are placed into a hat. Individual draws a slip of paper. Individual continues until sample number is met.

Stratified Random Sampling
Type of probability sampling Population is divided into subgroups or strata. Simple random sample taken from each strata

Approaches for Stratified Random Sampling
Proportional stratified sampling Determine sampling fraction for each stratum Ensure that this stratum is equal Proportion in total population Disproportional stratified sampling Determine stratum is represented Used when strata are very unequal Note the key word disproportional

Advantages of Stratified Random Sampling (cont’d)
Increases probability of being representative Ensures adequate number of cases for strata

Requires accurate knowledge of population May be costly to prepare stratified lists Statistics are more complicated.

Cluster Random Stratified Sampling
Large groups or clusters, not people, are selected from population. Simple, stratified or systematic random sampling may be used during each phase of sampling.

Saves time and money Arrangements made with small number sampling units Characteristics of clusters or population can be estimated.

Causes a larger sampling error Requires each member assignment of population to cluster Uses a more complicated statistic analysis

Systematic Random Sampling
Type of probability sampling Every kth element is selected. Process Obtain a listing of population Determine the sample size Determine the sampling interval (k = N/n) Select random starting point Select every kth element

Easy to draw sample Economical Time-saving technique

Samples may be biased. After first sample is chosen, no longer equal chance

Learning Objective Five Compare Three Methods Of Nonprobability Sampling
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Nonprobability Sampling
Sample elements are chosen nonrandomly. Produces biased sample Each element of the population may not be included in the sample. Restricts generalizations made about study findings

Nonprobability Sampling
Convenience Quota Purposive

Convenience Sampling Chooses the most readily available subject or object Does not guarantee that the subject or object is typical of the population

Snowball Sampling Type of convenience sampling method
Study subjects recruit other potential subjects. May be called network sampling May find people reluctant to volunteer

Quota Sampling Type of nonprobability sampling
Researcher selects sample to reflect characteristics. Examples of stratum

Quota Sampling Age Gender Educational background
Number of elements in each stratum Number is in proportion to size of total population.

Purposive Sampling Type of nonprobability sampling
Researcher uses personal judgment in subject selection. Each subject chosen is considered representative of population. Many qualitative studies use this technique.

Nonprobability Sampling Procedures

Learning Objective Six Determine Which Sampling Technique To Use In Various Types Of Research Studies 46

Research Studies Use voluntary subjects Follow the ethics of research
Subjects must voluntarily agree. Subjects may refuse to participate.

Research Data Based on voluntary responses from subjects
Biased sample occurs if subjects do not participate.

Volunteers As Subjects
Sample selection varies. Subjects volunteer for a study. Researcher approaches subjects.

Random Sampling or Random Assignment
Each subject has equal probability of being included. Random assignment Procedure to ensure that each subject has equal chance

Threefold Randomization Process
Used for experimental studies Helps represent the ideal study procedure Steps to ensure the process Subjects randomly selected from population Subjects randomly assigned to groups Experimental treatments randomly assigned to groups

Learning Objective Seven Compare Longitudinal And Cross-Sectional Studies
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Classification of Research Studies
Longitudinal Cross-sectional

Longitudinal Research Study
Subjects are followed over time. A cohort study is one example. Subjects are studied based on Similar age group Similar background

Longitudinal Research Study (cont’d)
Data are gathered. Same subjects Several times Tells influence of time

Cross-Sectional Study
Subjects checked at one point in time Data collected from groups of people Data may represent differences in Ages Time periods Developmental states Important considerations

Longitudinal Versus Cross-Sectional Studies
Longitudinal studies Accurate means of studying changes over time Studies take a long time to perform. Cross-sectional studies Less expensive Take less time Easier to conduct

Learning Objective Eight Enumerate Factors To Be Considered In Deciding The Size Of The Sample
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Sample Size No simple rules
Qualitative studies use much smaller samples than quantitative studies. Factors to consider for sample sizes in quantitative studies Homogeneity of population Degree of precision desired by the researcher Type of sampling procedure that is used

Sample Size (cont’d) Central limit theorem
Sampling distribution of the mean

Larger Sample Sizes Many uncontrolled variables are present.
Small differences are expected in members. Population must be divided into subgroups. Dropout rate among subjects is expected to be high. Statistical tests are used that require a minimum sample size.

Power Analysis Helps to determine sample size
May prevent type II error Helps to detect statistical significance

Power Analysis (cont’d)
Low power; type II error high External funding sources require it. Helps determine the optimum sample size

Nursing Research Studies
Usually limited to small convenience samples Generalizations to total population difficult Small sample sizes warrant replication studies. Similar results from replication help with generalization.

Learning Objective Nine Discuss Sampling Error And Sampling Bias
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Sampling Error Random fluctuations in data
Not under the control of the researcher Chance variations occur when sample is chosen.

Sampling Bias Bias when samples are not carefully selected
All nonprobability sampling methods have it. May occur in probability sampling methods Subjects decide not to participate when chosen. Final sample is now not representative of population.

Learning Objective Ten Critique The Sampling Procedure Described In Research Reports And Articles
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Critiquing the Population and Samples
Is the target population identified? Is the accessible population identified? Was a probability or nonprobability sampling method used? Is the specific sampling method named? Is the sampling method described? Is the sampling method appropriate for the study?

Critiquing the Population and Samples (cont’d)
Are the demographic characteristics of the sample presented? Is the sample size adequate? Was power analysis used to determine the sample size? Is the sample representative of the population?

Critiquing the Population and Samples (cont’d)
Are potential sampling biases identified? Is subject dropout discussed?

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