Sampling
Understanding the key concepts of sampling theory Sampling involves selecting a group of people, events, objects, or other elements with which to conduct a study. A sampling method or plan de- fines the selection process, and the sample defines the selected group of people (or elements). A sample selected in a study should represent an identified population. The population might be people who have heart failure (HF), patients who were hospital- ized with coronavirus disease 2019 (COVID-19), or persons who received care from a registered nurse (RN). In most cases, however, it would be impos- sible for researchers to study an entire population. Sampling theory was developed to determine the most effective way to acquire a sample that accur- ately reflects the population under study. The key concepts of sampling theory are described in the fol- lowing sections, including relevant examples from published studies.
Population
Populations and elements The population is a particular group of individuals or elements, such as patients with type 2 diabetes or intravenous catheters, to be studied. The target population is the entire set of individuals or elem- ents who meet the sampling criteria (defined in the next section), such as adult men, 50 years of age or older, diagnosed with type 2 diabetes, and hospital ized with a lower extremity infection. An accessible population is the portion of the target population to which the researcher has reasonable access. Fig. 9.1 demonstrates the link of the population, tar- get population, and accessible population in a study. The accessible population might include individ- uals within a state, city, hospital, or nursing units, such as patients with diabetes who are in an acute care hospital in Dallas, Texas. Researchers obtain the sample from the accessible population by using a particular sampling method or plan, such as simple random sampling. The individual units of the popu- lation and sample are called elements. An element can be a person, situation, or any other single unit of study. When elements in a study are persons, they are referred to as participants or subjects. However, the term participant is more commonly used in all types of nursing study.
Generalization
Generalization from the sample to population Generalization extends the findings from the sam- ple under study to the larger population. In quan- titative and outcomes studies, researchers obtain a sample from the accessible population with the goal of generalizing the findings from the sample to the accessible population and then, more abstractly, to the target population (see Fig. 9.1). The quality of the study design and the consistency of the study’s find- ings with those from previous research in this area influence the extent of the generalization (Kazdin, 2017). If a study has a strong design and findings consistent with previous research, then researchers can be more confident in generalizing their findings to the target population and using the findings in practice. For example, the findings from the study of male patients, diagnosed with type 2 diabetes, and hospitalized with an infection in Dallas, may be generalized to the target population of male patients with type 2 diabetes hospitalized in Texas urban hospitals or, more broadly, to urban hospitals in the southern United States.
Ebo
RESEARCH/EBP TIP The generalization of quality findings enables you to decide whether to use this evidence in caring for the same type of patients in your practice, with the goal of moving toward evidence-based practice (EBP) (Melnyk & Fineout-Overholt, 2019).
Sampling criteria
Sampling criteria Sampling criteria include the list of characteristics for eligibility in or exclusion from membership in the target population. Inclusion sampling criteria are the characteristics that the study participant or element must possess to be part of the target population. For example, researchers may choose to study the effect of an internet-based early ambula- tion program on the length of hospital stay for older adults having knee joint replacement surgery. In this example, the inclusion criteria are 60 years or older, able to speak and read English, and undergoing an initial surgical replacement of one knee joint. Exclu- sion sampling criteria are those characteristics that excluded or eliminate potential participants from the target population for safety reasons or specific characteristics that might alter their responses. For example, any study participant with a history of pre- vious joint replacement surgery, diagnosis of demen- tia, or a debilitating chronic muscle disease would be excluded from this example study. Researchers should state a sample criterion only once and should not include it as both an inclusion and an exclusion criterion. For example, researchers should not have an inclusion criterion of no diagnosis of dementia and an exclusion criterion of diagnosis of dementia. When a quantitative study is completed, the goal is to generalize findings from the sample to the tar- get population, designated by the sampling criteria (Gray & Grove, 2021). Researchers may narrowly define the sampling criteria to make the sample as homogeneous (or similar) as possible to control for extraneous variables. Conversely, the researcher may broadly define the criteria to ensure that the study sample is heterogeneous, with a broad range of values or scores on the variables being studied. If the sampling criteria are narrow and restrictive, the generalization of the findings is to a limited group of individuals. When critically appraising a study, examine the sample inclusion and exclusion criteria to determine to whom the study findings can be ap- propriately generalized.
Sampling error
Sampling Error, Bias, Acceptance & Refusal Rates (Study Notes)
📊 Sampling error & bias
Sampling error increases when the sampling method is not random because the researcher may select participants who are similar (e.g., same race, gender, or background). This makes the sample less representative of the target population, leading to bias and reduced generalizability.
Even with random sampling, bias can still occur if participants refuse or drop out, because the final sample may no longer fully represent the original population.
📉 Refusal rate
The refusal rate is the percentage of eligible participants who decline to participate.
Refusal rate
=
(
number who refused
number of eligible participants approached
)
×
100
%
Refusal rate=(
number of eligible participants approached
number who refused
)×100%
✔️ “Eligible participants approached” = people who met inclusion criteria, did not meet exclusion criteria, and were actually invited to participate.
📈 Acceptance rate
The acceptance rate is the percentage of eligible participants who agree to participate.
Acceptance rate
=
(
number who accepted
number of eligible participants approached
)
×
100
%
Acceptance rate=(
number of eligible participants approached
number who accepted
)×100%
🔁 Relationship between rates
Acceptance rate = 100% − refusal rate
Refusal rate = 100% − acceptance rate
✔️ They provide the same information in reverse form
📌 Interpretation
High acceptance rate / low refusal rate → fewer missing participants, less sampling error, and a more representative sample
This increases the likelihood of generalization, but does not guarantee it
🚫 Reporting rule
Researchers should report either acceptance rate or refusal rate, not both, because they are mathematically equivalent and would be redundant.
Refusal rate
representative of the target population. Researchers usually report the refusal rate, and it is best to pro- vide rationales for the individuals who refuse to par- ticipate. In addition, the characteristics of those re- fusing to participate should be compared with those who participated to determine whether they differed in some way.
Sample attrition
Sample attrition and retention rates in studies Sampling error also may occur in studies with high sample attrition. Sample attrition is the withdrawal or loss of participants from a study and can be ex- pressed as either a number or a percentage. The per- centage is the sample attrition rate, and it is best if researchers include both the number of participants withdrawing and the attrition rate. The formula for calculating the sample attrition rate in a study is as follows:
Sample attrition
Sample attrition rate = (number of participants withdrawing from a study ÷ sample size of study) × 100% For example, in the hypothetical study of early am- bulation education (n = 76), 31 participants (12 from the intervention group and 19 from the comparison group) withdrew for various reasons. Loss of 31 par- ticipants means a 41% attrition rate: Page 496 of 1086 48%
Representative
Representativeness of a sample Representativeness means that the sample, access- ible population, and target population are alike in as many ways as possible (see Fig. 9.1). The representa- tiveness of a sample might be evaluated in terms of the setting, characteristics of the participants, and number of participants in a study. Persons seeking care in a particular setting may be different from those who seek care for the same problem in another setting or those who choose to use self-care to man- age their problems. In addition, people who do not have access to health care are excluded from most studies. Sample characteristics are used to provide a picture of the sample, and these characteristics need to be reasonably representative of those in the popu- lation. In studies testing the effects of interventions, the participants in the experimental and control groups need to have similar demographic character- istics to reduce the potential for errors (see Chapters 5 and 11). A larger sample size usually results in a sample that is more representative of the population (Gray & Grove, 2021; Kazdin, 2017).
Arrition rate in diffrent groups
Sample attrition rate = (31 ÷ 76) × 100% = 0.408 × 100% = 40.8% = 41% = In this example, the overall sample attrition rate was high (41%) and would be considered a study weak- ness. Also, the rates differed for the intervention and comparison groups. You can also calculate the at- trition rates for the groups. If the two groups were equal at the start of the study with 38 participants, then the attrition rate for the intervention group was (1238) × 100% = 0.316 100% = 31.6% 32%. The attrition for the comparison group was (19 ÷ 38) × 100% = 0.50 × 100%: = 50%. The potential for sampling error is greatest when a large number of participants withdraw from the study before data collection is completed or when a large number of participants withdraw from one group but not the other(s) in the study. Researchers must ask whether the participants who withdrew were different in some way and whether the remaining participants represent the target population. In studies involv- ing an intervention, participants in the comparison group, who do not receive the intervention, may be more likely to withdraw from the study. However, sometimes the attrition is higher for the interven- tion group if the intervention is complex and/or time-consuming (Gray & Grove, 2021). In this ex- ample with the early ambulation program, there is a strong potential for sampling error because the sam- ple attrition rate was large (41%), and the attrition rate in the comparison group (50%) was larger than the attrition rate in the intervention group (32%). Page 497 of 1086 48%
Retention rate
UNDERSTANDING NURSING RE…
High refusal and attrition rates (>10-15%) increase the potential for sampling error, which may affect the credibility of the study results and findings (Gray & Grove, 2021; Kazdin, 2017).
The opposite of sample attrition is sample reten- tion, which is the number of participants who re- main in and complete a study. You can calculate the sample retention rate in two ways:
Sample retention rate = (number of participants completing study ÷ sample size) × 100%
or
Sample retention rate
=
100%
- sample attrition rate
In the early ambulation study, 45 participants were retained in the study that had an original sample of 76 participants:
Sample retention rate = (45 ÷ 76) × 100% = 0.592 × 100% = 59.2% = 59%
or
Sample retention rate = 100% - 41% = 59%
The higher the retention rate the more represen- tative the sample is of the target population and the
retention sample
UNDERSTANDING NURSING RE…
High refusal and attrition rates (>10-15%) increase the potential for sampling error, which may affect the credibility of the study results and findings (Gray & Grove, 2021; Kazdin, 2017).
The opposite of sample attrition is sample reten- tion, which is the number of participants who re- main in and complete a study. You can calculate the sample retention rate in two ways:
Sample retention rate = (number of participants completing study ÷ sample size) × 100%
or
Sample retention rate
=
100%
- sample attrition rate
In the early ambulation study, 45 participants were retained in the study that had an original sample of 76 participants:
Sample retention rate = (45 ÷ 76) × 100% = 0.592 × 100% = 59.2% = 59%
or
Sample retention rate = 100% - 41% = 59%
The higher the retention rate the more represen- tative the sample is of the target population and the
Higher Attrition rate meaning
Key idea: Attrition vs retention reporting
Researchers should report either attrition rate or retention rate (not both) because they describe the same thing from opposite directions.
📌 Best practice in research reporting
Researchers should include:
A rate (percentage)
attrition OR retention rate
The actual number of participants
e.g., “31 participants withdrew”
🧠 Why both number + rate matter
Percentage (rate): shows how big the loss is relative to sample size
Number: shows the real impact in actual participants
⚠️ Why reasons for withdrawal matter
Researchers should also explain why participants dropped out because it helps determine if bias may have been introduced.
Examples of withdrawal reasons:
severe complications
schedule/work conflicts
moved away
🔍 Why this affects study quality
If many participants withdraw for similar reasons, researchers must ask:
Are the remaining participants still representative of the target population?
If not:
↑ bias
↑ sampling error
↓ accuracy of results
High acceptance rates low attrition rate
Researchers strive to have a sample that is repre- sentative of the target population. When the sam- ple in a study has a high acceptance rate (>90%) and a low attrition rate (<10-15%), the potential for sampling error is less, resulting in more credible findings.
Sampling frames
Sampling frames From a sampling theory perspective, each person or element in the population should have an oppor- tunity to be selected for the sample. One method of providing this opportunity is referred to as random sampling. For everyone in the accessible population to have an opportunity for selection in the sample, each person in the population must be identified. To accomplish this, the researcher must acquire a list of every member of the population, using the sampling criteria to define eligibility. This list is referred to as the sampling frame. In some studies, the complete sampling frame cannot be identified because it is not possible to list all members of the population. The Health Insurance Portability and Accountability Act has made it difficult to obtain a complete sampling frame for some studies because of its requirement to protect individuals’ health information (see Chapter 4). For some studies, a sampling frame could be iden- tified through licensing boards or certification or- ganizations. For example, a sample of RNs might be randomly selected from a list of RNs recognized by the board of nursing in a selected state. Once a sam- pling frame has been identified, researchers select participants for their studies using a sampling plan or method.
Probability sampling
Probability sampling methods In probability sampling, each person or element in a population has an opportunity to be selected for a sample. Probability or random sampling methods in- crease the sample’s representativeness of the target population. All the subsets of the population, which may differ from each other, have a chance to be rep- resented in the sample. To represent a wide range of people in a population, all the subsets need to be included. The opportunity for sampling error is less when participants are selected randomly, but it still can occur (Kazdin, 2017). With nonrandom sampling strategies, researchers might (consciously or unconsciously) select individ- uals whose conditions or behaviors are consistent with the study hypotheses. For example, researchers may exclude participants because they are too sick, too healthy, coping too well, not coping adequately, uncooperative, or noncompliant. By using random sampling, researchers leave the selection to chance, hthereby increasing the validity of their study find- ings. The probability sampling methods included in this text are simple random sampling, stratified random sampling, cluster sampling, and systematic sam- pling. Table 9.1 identifies the common probability sampling methods used in nursing studies, their ap- plications, and their representativeness of the popu- lation. Probability sampling methods are commonly used in quantitative and outcomes studies
Simple random sampling which is a type of probility sample method
Simple random sampling is the most basic of the probability sampling plans. It is achieved by ran- domly selecting elements from the sampling frame. Researchers can accomplish random selection in a variety of ways; it is limited only by the imagination of the researcher. If the sampling frame is small, re- searchers can write names on slips of paper, place them into a container, mix them well, and then draw them out one at a time until they have reached the desired sample size. A computer program is the most common method for randomly selecting study participants. The researcher can enter the sampling frame (list of potential participants) into a computer, which randomly selects participants until the de- sired sample size is achieved. Another method for randomly selecting a study sample is to list potential participants and use a random number generator online. Tables of random numbers can be created online with an option to select a random sample from the table using a pro- gram such as QuickCalcs
Simple random sample
Set eligibility criteria first
Researchers decide:
inclusion criteria (who CAN be in)
exclusion criteria (who CANNOT be in)
2. 📋 Create the sampling frame
They make a list of all eligible people
Example: 350 diabetic patient records
3. 🎲 Simple random sampling
They assign numbers or use the existing list
A computer or random number table picks participants randomly
👉 This is where selection happens
4. ✋ Informed consent AFTER selection
The selected people are contacted
They are asked if they agree to participate
Only those who say “yes” are included in the final sample
Cluster sampling
Cluster sampling In cluster sampling, a researcher develops a sam- pling frame that includes a list of all the states, cities, institutions, or units with which elements of the identified population can be linked. A randomized sample of these states, cities, or institutions can then be used in the study. In some cases, this ran- domized selection continues through several stages and is then referred to as multistage sampling. For example, the researcher may first randomly se- lect states and then randomly select cities within the sampled states. Next, the researcher may ran- domly select hospitals within the randomly selected cities. Within the hospitals, nursing units may be randomly selected. At this level, all patients on the Page nursing unit who fit the criteria for the study may be included, or patients can be randomly selected. Cluster sampling is commonly used in two types of research situation. In the first type of situation, the researcher considers it necessary to obtain a geographically dispersed sample but recognizes that obtaining a simple random sample will require too much travel time and/or expense. In the second, the researcher cannot identify the individual elements making up the population and therefore cannot de- velop a sampling frame. For example, a complete list of all people in the United States who have had open heart surgery does not exist. Nevertheless, it is often possible to obtain lists of institutions or or- ganizations with which the elements of interest are associated-in this example, perhaps large medical centers, university hospitals with cardiac surgery departments, and large cardiac surgery practices— and then randomly select institutions from which the researcher can acquire study participants. Obradors-Rial and colleagues (2020) conducted a predictive correlational study to determine whether school and town factors were predictive of risky al- cohol consumption among rural and urban 10th- grade adolescents. The researchers obtained their sample using cluster and stratified random sampling methods. The data were collected using a computer- ized survey that had an 88.4% response rate. The details of their sampling methods are provided in Research Example 9.4, with aspects of the sample identified in [brackets].
Systematic sampling
Systematic sampling Systematic sampling is used when an ordered list of all members of the population is available. The pro- cess involves selecting every kth individual on the list, using a starting point selected randomly. If the initial starting point is not random, the sample is a nonprobability or nonrandom sample. To use this design, the researcher must know the number of elements in the population and the size of the sam- ple desired. The population size is divided by the desired sample size, giving k, the size of the gap be- tween elements selected from the list. The formula is: k = population size ÷ desired sample size. = 12. For example, if the population size is N = 1200 and the desired sample size is n = 100, then k Thus the researcher would include every 12th per- son on the list in the sample. Some have argued that this procedure does not actually give each element of a population an opportunity to be included in the sample and does not provide as representative a sample as simple random sampling and stratified random sampling. Systematic sampling provides a random, but not equal, chance for inclusion of par- ticipants in a study (see Table 9.1; Gray & Grove, 2021; Kazdin, 2017). Momeni and colleagues (2020) conducted a cross- sectional descriptive study to identify the factors that influence married women to obtain a pap smear screening in South Iran. The researchers noted that women in Iran did not take pap smear screening seriously, which influenced the incidence of cervical cancer. Research Example 9.5 describes the system- atic sampling method implemented in this study.
Convenience sampling
understanding gained in qualitative and mixed methods studies. pants are included in a study because they happen to be in the right place at the right time (Gray & Grove, 2021). A classroom of students, patients attending a selected clinic, individuals in a support group, and patients hospitalized with a specific diagnosis, such as COVID-19, are examples of convenience samples. The researcher simply enters available participants into the study until the desired sample size is reached. Biases exist in the sample, some of which may be subtle and unrecognized. However, conveni- ence sampling is considered acceptable when it is used with reasonable knowledge and care in imple- menting a study (Kazdin, 2017). Convenience samples are inexpensive, accessible, and usually less time-consuming to obtain than other types of samples. This type of sampling pro- vides a means to conduct studies on nursing inter- ventions when researchers cannot obtain a random sample and/or the pool of potential participants is limited. Researchers often think it best to include all individuals who meet sample criteria to increase the sample size. Many nurses and other healthcare researchers conduct quasi-experimental studies and RCTs with convenience samples. The study design is strength- ened when the participants obtained by conveni- ence sampling are randomly assigned to groups (see Chapter 8). However, random assignment to inter- vention and comparison groups is a design strategy, not a sampling method. The random group assign- ment helps strengthen the equivalence of the study groups. For RCTs, researchers usually increase the gsample size to strengthen the sample’s representa- tiveness (Tam et al., 2020). Brauneis et al. (2021) conducted a quasi-experi- mental study to examine the effects of low-fidelity simulation-based experiences (SBEs) on medication administration confidence and medication safety knowledge. The SBE was implemented in a class for graduate prelicensure nursing students. These stu- dents had degrees in other disciplines and were seek- ing preparation as RNs. Research Example 9.6 ad- dresses the sampling method used in this study.
Convenience sampling
understanding gained in qualitative and mixed methods studies. pants are included in a study because they happen to be in the right place at the right time (Gray & Grove, 2021). A classroom of students, patients attending a selected clinic, individuals in a support group, and patients hospitalized with a specific diagnosis, such as COVID-19, are examples of convenience samples. The researcher simply enters available participants into the study until the desired sample size is reached. Biases exist in the sample, some of which may be subtle and unrecognized. However, conveni- ence sampling is considered acceptable when it is used with reasonable knowledge and care in imple- menting a study (Kazdin, 2017). Convenience samples are inexpensive, accessible, and usually less time-consuming to obtain than other types of samples. This type of sampling pro- vides a means to conduct studies on nursing inter- ventions when researchers cannot obtain a random sample and/or the pool of potential participants is limited. Researchers often think it best to include all individuals who meet sample criteria to increase the sample size. Many nurses and other healthcare researchers conduct quasi-experimental studies and RCTs with convenience samples. The study design is strength- ened when the participants obtained by conveni- ence sampling are randomly assigned to groups (see Chapter 8). However, random assignment to inter- vention and comparison groups is a design strategy, not a sampling method. The random group assign- ment helps strengthen the equivalence of the study groups. For RCTs, researchers usually increase the gsample size to strengthen the sample’s representa- tiveness (Tam et al., 2020). Brauneis et al. (2021) conducted a quasi-experi- mental study to examine the effects of low-fidelity simulation-based experiences (SBEs) on medication administration confidence and medication safety knowledge. The SBE was implemented in a class for graduate prelicensure nursing students. These stu- dents had degrees in other disciplines and were seek- ing preparation as RNs. Research Example 9.6 ad- dresses the sampling method used in this study.
Quota sampling
Quota sampling uses a convenience sampling tech- nique with an added feature a strategy to ensure the inclusion of participant types likely to be under- represented in the convenience sample, such as mi- nority groups, children, and those with limited ac- cess to health care. This technique is similar to that used in stratified random sampling. Quota sampling involves stratification by selected subgroups of a population to improve the representativeness of the sample for the problem being studied. Thus quota sampling offers an improvement in representative- ness over using only convenience sampling Ashford and colleagues (2020, Abstract section) conducted a correlational study to examine “if re- cent persistent cough or cytokine levels are related to the Electronic Nicotine Delivery Systems (ENDS) use in college students.” The sample includes 61 under- graduate students from the University of Kentucky, who completed an online survey on a secure website and provided an oral salivary sample for analysis of cytokines. The quota sampling process used in this study is presented in Research Example 9.7.