USP Classroom · Research Methods

Sampling Methods

Choose cases that can answer your question. Learn how researchers move from a population to a sample, organise selection, plan sample size, and explain what their findings can support.

Start learning Watch Dr. USP’s lecture

What you will learn

Distinguish a population, sampling frame, selected sample, and respondents.
Compare probability and non-probability approaches.
Work through random, systematic, stratified, and cluster selection.
Plan sample size and interpret sampling uncertainty.
Calculate simple design weights and write a transparent sampling plan.

Learn by building a sampling plan

Define: Use Sections 1–2 to establish the population and basis of selection.

Choose: Compare the methods in Sections 3–7 against your question and resources.

Calculate and report: Work through Sections 8–12, then use the glossary and readings.

Your working case: A fictional college has 1,200 undergraduate students: 600 in Commerce, 360 in Arts, and 240 in Science. A study examines their news-verification practices. All numbers, allocations, and results in this case are invented for learning.

01 · Establish the reach of the inquiry

Define the population before drawing the sample

Sampling selects a part of a larger set for study. Researchers use it to estimate population characteristics, compare groups, explore experiences, or examine information-rich cases.

A population is the complete set of units relevant to the research question. Its boundaries need a place, period, and eligibility rule. “Young people” leaves much undecided. “All undergraduate students enrolled at this college on 1 August” gives selection a workable starting point.

A sample is the set selected for study. A census attempts to include every eligible unit. Sampling can reduce cost and allow closer attention to each case. A census may suit a small accessible population, while still requiring accurate coverage, participation, and measurement.

Target populationThe people, texts, organisations, or events the question concerns.
Sampling frameThe operational list or system through which units can be identified and selected.
Selected sampleThe units chosen through the specified procedure.
Respondents or observed casesThe selected units from which usable information is actually obtained.

Follow each link. Missing names affect coverage; missed contacts and refusals affect participation. The selected sample and the achieved sample can therefore differ.

Identify the units at each step

A sampling unit is a unit selected at a particular stage. The unit of analysis is the entity about which the analysis draws conclusions. A household survey may first select neighbourhoods, then households, then one adult in each household. If the question concerns adults, the final selection within households matters.

Apply it to the college study

Target population: the 1,200 enrolled undergraduates at the reference date.

Frame: a checked enrolment register with one record per eligible student and a faculty identifier.

Final sampling unit and unit of analysis: the individual student.

Check for duplicate names, students who have left, recent entrants, and missing contact details before selection.

Write your boundaries: Complete “My population consists of all ______ in ______ during ______, who meet ______.” Then name the frame and one group it might miss.

02 · Connect selection with inference

Compare probability and non-probability sampling

Probability sampling uses a defined random mechanism with known, non-zero inclusion probabilities for units in the covered population. Non-probability sampling selects cases through processes such as access, volunteering, judgment, quotas, or referrals.

An inclusion probability is the chance that a unit enters the selected sample under the design. Probability methods can support population estimation and estimates of sampling uncertainty when the design and analysis are properly implemented. The probabilities can differ across units.

Begin with the question and the available frameChoose the selection logic that can support the intended claim.

Probability selection

A specified chance mechanismSimple random · systematic with random start · stratified random · cluster and multistage designs.

A design-based basis for estimationRecord selection probabilities and carry the design into estimates and uncertainty.

Non-probability selection

A specified recruitment rationaleConvenience · volunteer · purposive · quota · snowball recruitment.

A basis that needs explanationState which cases were reached, why they were selected, and what assumptions a broader claim requires.

Both families need deliberate design and transparent reporting. Their routes from selected cases to wider claims differ.

Separate equal probability from known probability

In a simple random sample of 300 from 1,200 students, each student has an inclusion probability of 300 ÷ 1,200 = 0.25. A design that oversamples a smaller faculty can give its students a higher probability while remaining a probability design. Statistics Canada’s probability-sampling guide explains these alternatives.

Describe representation through the design

Ask which population the frame covers, how selection operates, who participates, and how the analysis accounts for those decisions. Similarity on a few demographic characteristics provides useful information, but the full argument also concerns characteristics related to the research outcome.

Keep two random processes distinct: Random sampling concerns entry into a study. Random assignment concerns allocation to conditions within an experiment. A study may use either, both, or neither; each supports a different part of the research argument.

03 · Use a recorded chance procedure

Draw simple random and systematic samples

Simple random sampling gives every possible sample of a fixed size the same chance of selection. Systematic sampling selects units at a regular interval after a random start.

Simple random sampling: select from the whole frame

Clean and freeze the college’s register of 1,200 eligible students.
Assign each student a unique ID from 1 to 1,200.
Use a random-number procedure to select 300 distinct IDs without replacement.
Save the frame version, procedure, selected IDs, and the random seed where available.
Contact those selected through a planned protocol and record the outcomes.

Without replacement means a unit can enter the sample only once. A lottery can also implement random selection if every unit is represented once and the draw is properly mixed. A reproducible electronic draw is usually easier to audit for a large register.

Implement a simple random draw in a spreadsheet

Keep one row per eligible unit and its unique ID. Generate an independent random number beside every row, then freeze those generated values so they cannot change during selection. Sort the complete rows by the random-number column and take the first n distinct IDs. Specify a random tie-break rule if ties occur. Save the frozen values, original frame, selected IDs, and steps. Check that the sort moved whole rows together and preserved the ID-to-person link.

Simple random sampling offers a clear selection rule and straightforward estimation. It requires a usable frame and may scatter respondents across many locations. Small subgroups can also yield too few cases for the comparisons a researcher wants.

Systematic sampling: calculate an interval

For a separate illustration, suppose the college selects 100 students from the same 1,200-name list. The sampling interval is:

Intervalk = N ÷ n = 1,200 ÷ 100 = 12

Randomly choose a starting position from 1 to 12. If the start is 7, select 7, 19, 31, 43, …, 1,195. This yields 100 positions. Each position in this particular design has a 1-in-12 chance of selection.

Check how the list is ordered. Sorting by a useful characteristic can spread the sample across that characteristic. A repeating pattern aligned with the interval can produce a poorly balanced sample and increase sampling variability. For example, a list that repeats the same staff role every twelfth entry creates a problem when k = 12.

Preserve the random start: Starting with a favourite name and then taking every twelfth person changes the design. When N ÷ n is not an integer, use an appropriate fractional-interval or other specified procedure rather than improvising the rounding.

Try the sequence: A list contains 800 items and you need 80. Calculate the interval, give the permitted starting positions, and write the first five selections for a start of 4.

04 · Plan the contribution of each subgroup

Stratify the population and allocate the sample

Stratified random sampling divides the population into non-overlapping groups, called strata, and draws a probability sample within every stratum.

Strata should together cover the population. Choose a characteristic available on the frame and relevant to precision, comparison, or the study’s reporting needs. In the college case, faculty provides three strata.

Proportional allocation

Allocate the sample in the same proportions as the population. For stratum h, use n_h = n × N_h ÷ N. Here N_h is the stratum population size and n_h is its selected sample size.

On a narrow screen, scroll the table sideways.

Fictional allocation of 300 selected students
Faculty	Population N_h	Population share	Selected n_h
Commerce	600	50%	150
Arts	360	30%	90
Science	240	20%	60
Total	1,200	100%	300

Draw the allocated number randomly within each faculty. Each student then has an inclusion probability of 0.25. If everyone selected responds, all students receive the same base weight of 4.

Disproportionate allocation

A study focused on faculty comparisons might select 100 from each faculty. This gives Science more observations than proportional allocation would provide. The design can improve the basis for that subgroup’s analysis, while creating unequal inclusion probabilities. Use suitable weights for a college-wide estimate.

Allocation can also account for differences in variability, costs, and the importance of particular estimates. A design should explain which estimates it seeks to improve and how the allocation serves that purpose.

Read the word “proportional” literally: Equal numbers from unequal-sized strata produce disproportionate allocation. Quota recruitment also sets group counts, but its usual selection within groups follows a non-random recruitment process. The selection procedure distinguishes these designs.

Choose an allocation: Would you prefer 150–90–60 or 100–100–100 if the main objective were to compare faculties? Explain the benefit, the cost, and the implication for a college-wide percentage.

05 · Organise selection across locations and levels

Use clusters and multiple stages

Cluster sampling selects groups of units, such as colleges, villages, schools, or neighbourhood blocks. Multistage sampling then selects further units within the groups already chosen.

Imagine a different study covering undergraduates across 20 colleges. The researcher could randomly select five colleges and then randomly select 30 students from each selected college’s register. This produces 150 selected students through a two-stage design.

Separate one-stage and multistage designs

One-stage cluster sample

Select colleges and include every eligible student in those selected colleges. The cluster is the college.

Two-stage cluster sample

Select colleges, then sample students within each selected college. The first-stage unit is the college; the final unit is the student.

Stratified selection

Sample within every defined stratum.

CommerceDraw a sample here.

ArtsDraw a sample here.

ScienceDraw a sample here.

Cluster selection

Select some groups from the group frame.

College A · selectedInclude all or sample within it.

College B · unselectedNo students selected here.

College C · selectedInclude all or sample within it.

College D · unselectedNo students selected here.

The core distinction concerns which groups contribute: every stratum contributes a sample, while a cluster design selects a subset of groups. This diagram simplifies the designs to show that relationship.

Balance fieldwork efficiency and precision

Clustering can reduce travel, administration, and the need for a complete individual-level frame at the outset. However, people within a college or neighbourhood may share experiences. For outcomes showing this similarity, a clustered sample usually contains less independent information than the same number of widely dispersed individuals.

When feasible, selecting more clusters with fewer observations per cluster can improve precision relative to concentrating the same total in very few clusters. Preserve cluster identifiers and use analysis that reflects the design.

Go further: calculate a two-stage inclusion probability

Assume five of 20 colleges are selected by simple random sampling, followed by 30 students selected randomly within each chosen college. A student in a college with N_i eligible students has probability:

π = (5 ÷ 20) × (30 ÷ N_i)

For a college with 300 students, π = 0.025 and the base weight is 40. For one with 600 students, π = 0.0125 and the base weight is 80. Equal numbers selected per college therefore give different student-level probabilities when college sizes differ.

Another design option: Probability-proportional-to-size selection gives larger first-stage units higher selection probabilities, using a measure such as enrolment. In suitable multistage designs, it can help control final-unit probabilities. It needs an accurate size measure and a specified selection procedure.

Describe every stage: If colleges are chosen for convenience, subsequent random selection of students supports a narrower argument about those colleges. To establish a probability sample of the full covered student population, specify the chance-based selection at each relevant stage.

06 · Make the recruitment rationale visible

Choose non-probability methods deliberately

Non-probability methods can recruit accessible participants, locate specialised experience, investigate difficult-to-reach networks, or develop an exploratory account. Their value rests on how well the selected cases serve the question.

On a narrow screen, scroll the table sideways.

Five common recruitment approaches
Method	How recruitment works	Example and consideration
Convenience	Select cases that are readily accessible.	Interview students leaving the library. The location and time shape who is available.
Volunteer / self-selection	People respond to an open invitation.	Post a survey link on a channel. Exposure, interest, and willingness shape participation.
Purposive / purposeful	Select cases using explicit criteria relevant to the question.	Recruit journalists who have handled election-related verification. Justify the criteria and sought variation.
Quota	Recruit until specified subgroup counts are filled, usually through non-random selection.	Obtain 100 students from each faculty through available contacts. Group counts are controlled; selection within groups still matters.
Snowball / chain referral	Initial participants suggest other eligible participants.	Begin with freelance fact-checkers and follow referrals. Different starting points may reach different networks.

Strengthen purposive selection

Specify the experience or position each case should contribute. You might seek maximum variation across language, newsroom type, or professional role; select criterion-based cases that meet a defined experience requirement; or investigate a case that challenges an emerging explanation.

For a study of verification practices, recruit reporters, editors, and verification specialists whose work directly addresses the question. Record how each was identified, who declined, and which perspectives remain difficult to reach. Palinkas and colleagues discuss purposeful strategies and their relationship to mixed-method designs.

Understand the referral network

Snowball recruitment can open doors where a useful list is unavailable. Start from varied entry points when the question requires different networks. Keep a recruitment record and protect the choice to participate. People with many connections, or connections to the initial contacts, may become easier to reach.

Match the claim to recruitment: These methods can support rich accounts and bounded comparisons. A wider population estimate requires an explicit inferential argument. An ordinary probability-sample margin of sampling error cannot be attached automatically to an open-link or convenience sample.

07 · Sample communication as well as people

Choose a design for the media question

Media research samples people, organisations, texts, images, programmes, interactions, and time periods. Define the relevant population of material with the same care you would bring to a population of respondents.

Estimate student practices

A checked enrolment register supports probability selection. Stratification can secure planned faculty comparisons.

Investigate newsroom decisions

Purposively select people with relevant responsibilities and seek contrasting roles or settings. Explain the experience each case contributes.

Study a year of news coverage

Define outlets, dates, topics, and eligible items. Build an archive-based frame and consider stratifying by outlet or period.

Explore an online controversy

Define platforms, search terms, languages, dates, and retrievable material. Record what the collection route makes visible or leaves inaccessible.

Separate the mode from the sample design

“Online survey” describes a mode of data collection. A researcher can invite randomly selected students through email or distribute an unrestricted link to anyone who encounters it. Both use the internet; their recruitment designs differ.

The same applies to online panels. Ask how members entered the panel, how the study selected them, and who actually responded. A sample vendor’s panel size alone provides little information about the quality of a particular population estimate.

Define the accessible text population

A set of posts returned by a platform search is shaped by retrieval, ranking, access rules, deletion, and the search terms. Randomly selecting from that retrieved set can create a probability sample of the defined set. Extending the findings to every post on the platform needs a separate coverage argument.

Choose through the claim: Write one question about prevalence and another about professional experience. For each, identify the population, frame or recruitment route, selection method, and intended reach of the conclusion.

08 · Plan for the estimate or comparison

Justify the sample size

Sample size follows the research objective, the variation in the outcome, the desired precision or power, the design, and the expected participation. Begin with the result the study needs to estimate or compare.

For a survey, ask whether the priority is one overall percentage, separate subgroup estimates, a difference between groups, or a model with several predictors. Each objective can require a different calculation. Resources and earlier studies inform the plan; the justification should also explain why the proposed size serves this question.

A starting calculation for one proportion

For a large population under simple random sampling, a common normal-approximation planning formula is:

Required sample size before adjustmentsn₀ = z² × p × (1 − p) ÷ e²

z: the normal critical value; approximately 1.96 for 95% confidence.
p: the expected population proportion. Using 0.50 gives the largest variance for a binary outcome.
e: the desired margin in proportion units; 0.05 means five percentage points.

Worked planning example

For 95% confidence, p = 0.50, and e = 0.05:

n₀ = 1.96² × 0.50 × 0.50 ÷ 0.05² = 384.16

Round upward to 385 completed observations under these planning assumptions. This calculation concerns one proportion and does not by itself plan a subgroup comparison or repair a coverage problem.

Adjust for a small finite population

When sampling without replacement from a fixed population of known size N, the finite population adjustment can reduce the required size for that finite-population estimate:

n = n₀ ÷ [1 + (n₀ − 1) ÷ N]

With N = 1,000 and the unrounded n₀ = 384.16, n ≈ 277.74. Round upward to 278. Retain the stated confidence, precision, and sampling assumptions. The adjustment does not enlarge the population to which the estimate applies.

The Penn State sampling lesson develops confidence intervals and sample-size calculations in greater detail.

Allow for the design and nonresponse

A design effect compares the variance of a particular estimate under the planned design with its variance under a relevant simple-random-sampling benchmark. It depends on the outcome, estimator, and design. Clustering and unequal weights can increase it; effective stratification can reduce it.

A separate planning illustration

Suppose a large-population calculation requires an SRS-equivalent sample of 400, and a justified planning design effect is 1.5:

Required completed interviews ≈ 400 × 1.5 = 600
Invitations at an expected 60% completion rate = 600 ÷ 0.60 = 1,000

This assumes all invited units are eligible. Adjust further if eligibility is uncertain, and allow for different participation patterns across subgroups. The resulting count is a planning expectation, rather than a guaranteed fieldwork yield.

Plan separately for other objectives

For hypothesis tests, use a power calculation based on a meaningful effect, significance level, design, and intended analysis. For qualitative work, justify the relevance, depth, variation, and adequacy of the cases. If you use a stopping criterion such as saturation, define how it will be assessed within the chosen approach.

Keep the assumptions beside the number: “385” belongs to a particular calculation. Small subgroups, rare outcomes, complex designs, and different analytical goals can require a different plan. Qualitative studies also need a question-specific rationale rather than a fixed universal count.

09 · Distinguish precision from other sources of error

Interpret sampling uncertainty and assess bias

Sampling uncertainty arises because different samples drawn through the same design can produce different estimates. A standard error describes this variation for an estimator.

The actual difference between a sample estimate and the population value is usually unknown. A probability design allows researchers to estimate sampling variability and construct suitable uncertainty intervals. The calculation should reflect stratification, clustering, weights, and other relevant design features.

Read a margin of sampling error

For a large-population simple random sample, an approximate 95% margin for a proportion is:

Margin ≈ 1.96 × √[p̂ × (1 − p̂) ÷ n]

Here p̂ is the observed sample proportion. Near 50%, the margin is about 9.8 percentage points for n = 100, 4.9 for n = 400, and 2.45 for n = 1,600. Under these assumptions, halving the margin requires roughly four times as many observations.

These figures omit a finite population correction and assume the simple-random-sampling setting. Other interval methods can be more suitable for small counts or proportions near zero or one. A 95% confidence procedure is designed to cover the fixed population value in about 95% of repeated samples under its assumptions.

Examine errors beyond sampling variation

Coverage

A register omits eligible students or includes duplicates. Some units then have missing or distorted routes into selection.

Nonresponse

Selected students who participate may differ from those who do not on the outcome being estimated.

Measurement

Ambiguous wording, recall, or pressure to give an acceptable answer can distort the recorded response.

Processing

Coding, duplicate handling, data entry, or scoring decisions can change the result after collection.

A larger sample generally improves sampling precision when the other conditions remain comparable. Its effect on bias depends on the source of the bias. Adding more respondents through the same narrow recruitment channel can reproduce the same selection problem.

Track participation and compare respondents with the frame on relevant available characteristics. A response rate informs the assessment, while the risk of nonresponse bias also depends on how participation relates to the outcome.

Label uncertainty correctly: A margin of sampling error covers sampling variation under its stated design assumptions. It leaves other errors to be assessed separately. Model-based precision measures for non-probability samples require an explanation of the model, assumptions, validation, and calculation, as AAPOR’s disclosure guidance specifies.

10 · Connect selection probabilities with estimation

Work through sampling weights

A base sampling weight is the inverse of a unit’s inclusion probability. It records how much population representation that unit receives under the design.

Base weightwᵢ = 1 ÷ πᵢ

For a simple random sample of n units from N, the weight is N ÷ n. In a stratified sample with simple random selection within each stratum, it is N_h ÷ n_h.

Return to the equal-faculty allocation

Select 100 students randomly from each faculty. For this worked calculation, assume every selected student responds and that the register fully covers the defined population.

On a narrow screen, scroll the table sideways.

Fictional disproportionate stratified sample
Faculty	Population	Selected	Inclusion probability	Base weight
Commerce	600	100	100 ÷ 600 = 1/6	6.0
Arts	360	100	100 ÷ 360 = 5/18	3.6
Science	240	100	100 ÷ 240 = 5/12	2.4

Suppose 60 Commerce respondents, 40 Arts respondents, and 20 Science respondents report checking the original source before sharing news. These are invented responses.

Unweighted percentage(60 + 40 + 20) ÷ 300 = 40%

Each faculty contributes one-third of the unweighted sample. To estimate the college-wide proportion under this design, restore the faculties’ population contributions:

Weighted percentageWeighted “yes” total = (60 × 6) + (40 × 3.6) + (20 × 2.4) = 552
Total weight = (100 × 6) + (100 × 3.6) + (100 × 2.4) = 1,200
Estimated college-wide proportion = 552 ÷ 1,200 = 46%

The change from 40% to 46% follows from the allocation: the faculty with the highest observed proportion also contains half the college population. The result illustrates why sampling and estimation must be planned together.

Carry the full design into analysis

Practical survey weights may include further adjustments for nonresponse and known population totals. State how each adjustment was calculated and what assumptions it needs. Statistics Canada’s estimation guidance explains the relationship between weights, auxiliary information, and survey design.

Use suitable survey-analysis procedures for standard errors and intervals, specifying the relevant strata, clusters, and weights. Entering a weight as though each record were a set of independent duplicate observations can misstate uncertainty.

Distinguish base weights from later adjustments: Base weights follow the actual draw. Nonresponse adjustments address a different process and rely on additional assumptions. Matching a few known population totals cannot, by itself, resolve every difference between participants and non-participants.

11 · Make the selection reproducible in practice

Conduct and report the sampling plan

A sampling protocol turns the design into actions that researchers can follow and readers can assess. Specify selection before recruitment begins, then record what happened.

Define: state the population, eligibility criteria, reference period, and unit of analysis.
Check the frame: record its source, date, coverage, duplicates, and known gaps.
Specify selection: name the method, strata, clusters, stages, allocation, and random procedure where applicable.
Justify size: identify the main estimate or comparison, assumptions, subgroup requirements, and expected losses.
Recruit consistently: plan contact modes, reminders, contact attempts, consent, and eligibility checks.
Record outcomes: distinguish selected, contacted, eligible, completed, refused, unavailable, and unusable cases as appropriate.
Analyse through the design: retain identifiers for strata and clusters, calculate suitable weights, and use justified uncertainty methods.
Explain scope: report departures, inaccessible groups, participation, and the population to which the claims apply.

Preserve selection during fieldwork

For a randomly selected student who does not respond, follow the contact protocol and record the outcome. Pre-specify any reserve-sample procedure through the same design. Substituting an available friend changes the route into the achieved sample and can distort the original selection probabilities.

Separate contact details from response records where practical. Collect only the identifiers needed for recruitment, follow-up, and analysis. This keeps the sampling process workable while protecting participants’ information.

Report the achieved sample clearly

Give the number selected and the number contributing to each main analysis. Explain eligibility and missing outcomes. For a survey response rate, use a stated definition suited to the recruitment design; AAPOR provides reporting resources for survey transparency.

Adapt this methods paragraph

“The target population comprised [eligible units, place, and period]. The sampling frame was [source and date], with [known coverage limitations]. We used [design], selecting [numbers] through [procedure]. The sample-size plan reflected [precision, power, or qualitative rationale]. Recruitment involved [contact protocol]. Of [number selected], [number] contributed usable data. Analysis used [weights and design information, where applicable]. The findings concern [specified population or cases], with limitations arising from [coverage, participation, or other constraints].”

Check your description: Could another researcher identify the eligible units, reconstruct the selection, and explain why the analysis gives each observation its contribution?

12 · Watch, calculate, and decide

Use the lecture as a sampling workshop

Watch Dr. Uma Shankar Pandey’s lecture with a sampling-plan draft beside you. Pause after each method and explain how you would implement it for your own question.

If the player does not load, watch the lecture on YouTube. These links provide approximate starting points from the supplied transcript. Use the chapter’s detailed procedures alongside the overview.

00:01 · Why researchers sampleConnect the selection with the study’s purpose.01:13 · The sampling frameIdentify the operational list or selection system.01:51 · Probability and random samplesRecord how the inclusion probabilities arise.03:06 · Systematic and stratified approachesPlan the random start or subgroup allocation.04:18 · Multiple stagesList the units selected at each level.04:51 · Non-probability recruitmentConsider access, participation, and referral routes.06:01 · Purposive and volunteer samplesExplain the criteria or invitation process.06:37 · Sample-size considerationsState the objective and assumptions behind your number.

Attempt each question before opening the response

1. A survey link is posted openly in student groups. Which design does this suggest?

It suggests volunteer or self-selection recruitment through those groups, with coverage shaped by who belongs to them and sees the link. Describe the distribution route and screening. An online questionnaire can also be used with a probability sample when access is directed to previously selected units.

2. For N = 800 and n = 80, what does systematic selection require?

The interval is 10. Select the start randomly from positions 1–10. For a start of 4, the first five selected positions are 4, 14, 24, 34, and 44. Check for a repeating list pattern aligned with the interval.

3. Does selecting 100 students from each faculty give proportional allocation?

In the fictional college, it gives disproportionate allocation because the faculties contain 600, 360, and 240 students. Proportional allocation of 300 is 150, 90, and 60. Either allocation can be used in a stratified random design if selection within each faculty follows the specified probability procedure.

4. What distinguishes strata from clusters?

A stratified design draws a sample within every defined stratum. A cluster design selects some groups from a group frame, then includes all eligible units or samples further within the chosen groups. Designs may combine stratification and clustering.

5. Why does the weighting example change 40% to 46%?

The unweighted sample gives equal influence to three unequal-sized faculties. Design weights restore their population contributions: (60 × 6 + 40 × 3.6 + 20 × 2.4) ÷ 1,200 = 46%. The example assumes complete response within the selected stratified sample.

6. Can a researcher use 385 as the sample size for every survey?

The figure comes from a particular large-population proportion calculation: 95% confidence, expected proportion 0.50, five-percentage-point margin, and an SRS planning basis. Other objectives, subgroups, designs, participation rates, and finite populations change the calculation.

7. Why might 5,000 volunteers still leave a population estimate uncertain?

Their recruitment may miss people whose experiences differ, and willingness to participate may relate to the outcome. The large count reduces some random variability but does not establish coverage or resolve selection differences. Examine the recruitment and the assumptions supporting any wider inference.

8. How should an interview study justify purposive selection?

Explain which experiences, roles, settings, or contrasting cases can answer the question. Describe how cases were identified and recruited, what variation was sought, and how the adequacy of the material was assessed. Connect the size to the study’s depth and analytical purpose.

Your independent learning project

Prepare a one-page sampling plan for a study of news use, media trust, verification, or newsroom practice.

Define the question, population, and units.
Identify the frame or recruitment route and its coverage.
Choose a method and explain one plausible alternative.
Specify the selection procedure and any allocation or stages.
Justify size through the main analytical objective.
Plan contacts, nonresponse records, and any reserve selection.
State the estimation or qualitative interpretation strategy.
Write a scope statement and name the main unresolved limitation.

Completion check: Ask a peer to describe exactly how a unit enters your study. Revise the plan wherever that route remains unclear.

13 · Keep a working reference beside the plan

Glossary and further learning

Return to these terms while designing a study or reading a published methods section. Use the sources below to develop the calculations and design choices further.

Target population: The complete set of units the research question concerns, bounded by explicit criteria.
Sampling frame: The operational list or system through which units can be identified and selected.
Inclusion probability: A unit’s probability of entering the selected sample under the design.
Stratum: A non-overlapping population subgroup within which a sample is drawn.
Cluster: A group of units selected as part of the sampling design.
Allocation: The distribution of the selected sample across strata or other design components.
Sampling variability: Variation in an estimate across possible samples drawn through a specified design.
Standard error: The standard deviation of an estimator’s sampling distribution, usually estimated from data and design information.
Bias: A systematic difference between an estimator’s expected value and the quantity it aims to estimate.
Base weight: The inverse of the inclusion probability.
Design effect: The ratio of an estimator’s variance under a design to its variance under a relevant SRS benchmark.
Effective sample size: A size expressing precision relative to a reference design; approximately n ÷ design effect for the specified estimate.
Purposive selection: Selection through explicit criteria intended to secure cases relevant to the research question.

References and learning resources

Pandey, U. S. Sampling methods in research: Learn probability and non-probability sampling methods. Dr. USP [Video].
https://www.youtube.com/watch?v=BzlqpKQh8v0The companion lecture and supplied transcript provide the starting overview.
Statistics Canada. 3.2.2 Probability sampling. Statistics: Power from Data!
Read the probability-sampling guideIntroduces simple random, systematic, stratified, cluster, and unequal-probability approaches.
Statistics Canada. 3.2.3 Non-probability sampling. Statistics: Power from Data!
Read the non-probability-sampling guideExplains recruitment approaches and their implications for wider inference.
Penn State Department of Statistics. Confidence intervals and sample size. STAT 506: Sampling Theory and Methods.
Study estimation and sample-size calculationsFurther work on proportions, confidence intervals, and finite-population sample-size planning.
United Nations Statistics Division. (2008). Designing household survey samples: Practical guidelines.
Find the handbook in the UN household-survey collectionDevelops frames, sample design, weights, survey implementation, and sampling errors.
Statistics Canada. (2020). Considering interviewer and design effects when planning sample sizes: Introduction.
Read the design-effect and sample-size discussionExplains why effective size, design effects, eligibility, and participation belong in planning.
Statistics Canada. Estimation. Data Quality Guidelines [Archived guidance].
Read the estimation guidanceConnects inclusion probabilities, weights, nonresponse adjustments, and variance estimation.
Palinkas, L. A., Horwitz, S. M., Green, C. A., Wisdom, J. P., Duan, N., & Hoagwood, K. (2015). Purposeful sampling for qualitative data collection and analysis in mixed method implementation research. Administration and Policy in Mental Health and Mental Health Services Research, 42, 533–544.
Read the author manuscriptA detailed discussion of purposeful strategies and their use in mixed-method studies.
American Association for Public Opinion Research. Transparency Initiative: Disclosure elements.
Consult the sampling, precision, and weighting disclosure guidanceUse the reporting elements to make recruitment and inference assessable.

Build the next part of the research plan

Place your sampling decisions beside the question, measurement, and analysis. For a study of media messages, carry the same selection logic into the corpus discussed in Content Analysis. Return to Research Methodology to connect the selected cases with the study’s larger design.

Return to the top ↑