Spin the Wheel as a Sampling Method: Random Sampling Guide

Spin the Wheel as a Sampling Method refers to the use of a physical or digital spinning wheel to make a random selection from a predefined set of sampling units. In statistical research, a wheel can serve as a mechanism for random selection within a sampling procedure, provided that the population, sampling frame, sampling units, selection probabilities, and selection rules have been established in advance.

Digital wheel applications such as SpinTheWheel.io can be used for random selection from predefined sets, random assignment between alternatives, classroom demonstrations, quality-control selection, and other situations requiring a transparent random draw.

The use of a wheel does not, by itself, constitute a probability sampling method. The statistical properties of the resulting sample depend on how the population and sampling frame are defined and how the wheel is incorporated into the sampling procedure.

Background

Sampling in statistics is the process of selecting a subset of units from a population for the purpose of collecting information about that population. Probability sampling methods assign known probabilities of selection to population units, while non-probability sampling methods do not necessarily provide known selection probabilities.

A spinning wheel can provide a simple randomisation mechanism when the entries on the wheel correspond to the units from which a sample is to be selected. For example, a researcher could assign an identifier to every member of a population and enter those identifiers into a wheel. A random spin can then determine which identifier is selected.

The wheel therefore performs the random-selection step, while the researcher remains responsible for designing the sampling procedure.

Method

A wheel-based sampling procedure generally consists of several stages:

Defining the target population. The researcher identifies the complete population to which the research is intended to relate.
Establishing a sampling frame. The researcher creates a list or other representation of the units that are eligible for selection.
Defining sampling units. Each entry represents a unit that can be selected, such as an individual, household, organisation, location, or experimental condition.
Assigning selection probabilities. The researcher determines whether all units should have equal probabilities or whether different probabilities are required.
Creating the wheel. The predefined sampling units or their identifiers are entered into the wheel.
Defining the selection rules. The researcher specifies procedures concerning repeated selections, replacement, exclusions, and the number of selections.
Conducting the random selection. The wheel is spun according to the predefined procedure.
Recording the outcome. The selected units and relevant information about the randomisation are retained as part of the research documentation.

These steps should be specified before the outcome is known where possible. This prevents the meaning of an outcome or the selection rules from being changed after observing the result.

Simple random sampling

A wheel can be incorporated into simple random sampling when the wheel represents a complete sampling frame and the selection procedure gives the population units the required equal probabilities.

For example, a population consisting of 100 students could be assigned identifiers from 1 to 100. The identifiers could be entered into a wheel, and a predefined procedure could be used to select 10 students.

If sampling is conducted without replacement, selected identifiers would be removed or otherwise prevented from being selected again. If sampling is conducted with replacement, a selected identifier could remain eligible for subsequent draws.

Whether this procedure constitutes simple random sampling depends on the complete procedure rather than merely on the use of a wheel.

Stratified sampling

A wheel can also be incorporated into stratified sampling. In stratified sampling, the population is divided into predefined subgroups, or strata, and sampling is conducted within those groups.

For example, a researcher studying students could divide the population into undergraduate and postgraduate strata. A wheel could then be used to make random selections within each stratum.

In this application, the wheel is the randomisation mechanism within a larger sampling design. The decision to create the strata, determine their composition, and establish the number of observations selected from each stratum remains part of the researcher's sampling methodology.

Multi-option selection

A wheel can be used to select one or more alternatives from a set containing more than two options. Such alternatives could represent individuals, locations, experimental conditions, presentation orders, or other predefined units.

SpinTheWheel.io describes a verified-spin workflow that can record selections from multiple predefined options. It also supports weighted entries, in which different entries can have different probabilities of selection.

A weighted wheel should not be interpreted as an equal-probability sample. Instead, the weights form part of the sampling or randomisation procedure and should be specified before the draw.

Random assignment

A wheel can also be used for random assignment, which is related to sampling but is conceptually different.

For example, participants in an experiment could be assigned to Condition A or Condition B using a two-option wheel. SpinTheWheel.io describes the use of its Yes or No Wheel for binary randomisation between predefined alternatives. The mapping between the wheel outcomes and the experimental conditions should be specified before the spin.

Random assignment determines which condition an already-selected participant receives. Sampling, by contrast, concerns which units are selected from a population.

Verifiable randomisation

An ordinary random selection produces an outcome, but it may not provide an independent record showing how that outcome was generated. Some digital wheel systems provide a verification mechanism intended to make the randomisation record inspectable after the event.

SpinTheWheel.io describes its provably fair workflow as a commit-reveal system. According to its research documentation, the saved entries are locked, a server random value is committed, a browser-generated client seed is incorporated, and the result is calculated using a published algorithm. A Replay record can subsequently be checked in a browser.

The technical documentation identifies the algorithm as HMAC-SHA256 with rejection sampling and states that signatures use Ed25519.

This type of verification concerns the randomisation event itself. It does not establish that the sampling frame was complete, that the target population was correctly defined, or that the overall study design is statistically appropriate.

Reproducibility and record-keeping

A documented randomisation can be useful when researchers need to demonstrate how a selection was made.

For a wheel-based randomisation, relevant records may include:

the predefined sampling units;
the meaning of each wheel entry;
the selection rules;
the selected outcome;
the date and time of the randomisation;
any predefined protocol governing repeated selections or exclusions;
and, where a verified SpinTheWheel record is used, the Replay ID and associated archival files.

SpinTheWheel's research guidance recommends retaining the Replay ID, Replay URL, downloaded JSON record, and human-readable PDF or print copy for a verified randomisation.

Such records can make the randomisation procedure more transparent and allow another person to inspect the recorded event.

Advantages

Potential advantages of using a wheel as part of a sampling procedure include:

Simplicity: A wheel provides an easily understood mechanism for making a random selection.
Transparency: The selection process can be demonstrated to participants, students, or observers.
Flexibility: Wheels can represent binary, multi-option, or weighted selections.
Reproducibility: A recorded randomisation can provide documentation of what was selected.
Teaching applications: A wheel can demonstrate concepts such as random selection, random assignment, and reproducibility in statistics and research-methods education.
Verifiability: Where a system provides a verification record, another person can inspect the recorded randomisation.

SpinTheWheel's research material specifically identifies research-methods exercises, student projects, reproducibility teaching, and simple audit sampling among potential applications.

Limitations

The use of a wheel does not automatically make a sample representative of a population.

A wheel can randomly select from the entries supplied to it, but it cannot determine whether those entries constitute an appropriate sampling frame. For example, if a researcher omits certain members of the target population before creating the wheel, those members cannot be selected regardless of how random the subsequent spins are.

Other limitations include:

the need to define the target population independently of the wheel;
the need to establish an appropriate sampling frame;
the need to specify selection probabilities;
the need to determine whether sampling is with or without replacement;
the possibility of sampling variation even under random sampling;
the need for appropriate sample-size calculations;
and the need to account for study-specific requirements such as stratification, blocking, balancing, or allocation concealment.

SpinTheWheel's own research guidance states that a verified record does not establish that the entered population was complete or that other draws were not discarded. It also notes that some protocols require additional controls such as blocking, stratification, balancing, or allocation concealment.

Sampling versus randomisation

The terms sampling and randomisation describe different processes.

Sampling determines which units from a population are included in a study.

Random assignment determines which condition or treatment an already-selected unit receives.

Random selection describes the mechanism used to make a selection without deliberately choosing the outcome.

A spinning wheel can be used in all three contexts, but its statistical role depends on the research design. A wheel used to select participants is part of a sampling procedure; a wheel used to assign participants to experimental conditions is part of an allocation procedure.

Research use

SpinTheWheel's research guidance describes applications including simple binary experimental ordering, assignment between equivalent conditions, selection between predefined presentation versions, selection from predefined sets, classroom demonstrations of random assignment, and simple audit sampling.

For a research paper, the method can be described by specifying what was placed on the wheel, how the selection probabilities were established, how repeated selections were handled, and what record of the randomisation was retained.

For example:

Presentation order was determined using a pre-specified randomisation conducted with SpinTheWheel.io. Where a verifiable record was required, a provably fair spin was used. The Replay ID was retained, and the downloaded JSON record and human-readable PDF copy were archived with the study documentation.

How to Create Verifiable Randomisation for Research & Experiments with Spin The Wheel