eduKateSG Learning Node Series · 0276
You open an education dataset expecting a column called score. Instead, you find several columns with nearly identical names. Each row appears to give the same student several different proficiency values.
The obvious response is to average them. One student, one number. The spreadsheet becomes easier to understand.
Unfortunately, that convenient move can destroy part of the information the dataset was designed to preserve. Plausible values are not ordinary repeated examination marks. They are a device for estimating population characteristics when each learner’s proficiency is only incompletely observed.
The essential sequence runs in the opposite direction from the tempting shortcut: perform the intended analysis using each plausible-value set, then combine the resulting estimates and their uncertainty appropriately. Do not first collapse every learner’s values into one supposedly definitive mark.
The extra columns are not clutter. They carry uncertainty that the final conclusion needs.
The question behind the unfamiliar columns
Large-scale assessment often asks a population question: what is the distribution of proficiency, how do groups differ, and how does the picture change across time? It may deliberately give each learner only a subset of the complete assessment so the programme can cover a broad domain without imposing an enormous individual test.
This creates a mismatch between the shape of the data file and its intended use. The file has one row per learner, but its primary purpose may be population estimation rather than producing a comprehensive individual score for every row.
Mislevy, Beaton, Kaplan and Sheehan’s foundational 1992 paper explains this problem for sparse matrix samples of item responses. Designs efficient for population characteristics can provide too little information for precise individual proficiency estimates. Plausible-value files support approximations to the relevant population analyses.
The conceptual shift is therefore not from an observed score to a better personal score. It is from incomplete individual observations to a method designed for specified group-level conclusions.
Where this article sits in the assessment map
This guide concerns the interpretation and analysis of plausible values in large-scale educational assessment. It does not provide a formula for awarding individual grades, filling missing school marks or deciding which child should enter a programme.
For the institutional setting, use National Learning Assessment Systems. For the broader treatment of uncertainty and incomplete observations, use Missing Data and Standard Errors.
All numerical datasets below are invented teaching examples. They are not results from an actual school, country or assessment cycle. The formulas illustrate general pooling logic; operational analysis must follow the technical documentation for the particular programme, cycle, domain and statistic.
A latent proficiency is not directly observed
We observe responses to tasks. We do not directly observe a learner’s complete reading proficiency, mathematical proficiency or scientific reasoning capacity as a physical quantity sitting in a cell.
A measurement model relates the observed responses to an underlying proficiency representation. When the learner answers only a limited subset of items, several proficiency values may remain compatible with the evidence under the model.
The uncertainty is not an embarrassing defect to hide. It follows from the amount and kind of information collected. A short set of observations should not be made to look as definitive as an extensive assessment merely because both can be converted into numbers.
A useful mental distinction is between the response record and the proficiency model. “The learner answered these items in these ways” describes observations. “These latent values are compatible with the observations and modelling assumptions” describes inference.
Plausible-value analysis depends on preserving that distinction. Once the draw is relabelled as an ordinary personal mark, the uncertainty it represents becomes difficult to see.
What the values represent
In programmes such as PISA, plausible values are draws from a distribution of proficiency conditional on the available response information and variables used in the population or conditioning model. They represent uncertainty within that modelling system rather than repeated observed performances.
The OECD’s analysis guidance explicitly warns against averaging plausible values within each student’s row and then analysing the resulting number once. The intended workflow combines statistics calculated across the plausible-value sets.
This does not mean the values are arbitrary. They are produced by a documented measurement and population-modelling procedure. Nor does it mean they reveal the exact unobserved truth about an individual. Their validity depends on the model, data and intended analysis.
Think of each full set as one model-compatible representation of the proficiency data used for a particular analysis. The same learners remain in the dataset; the proficiency draw changes. Repeating the analysis lets the uncertainty affect the result rather than disappear before calculation begins.
They are not answers invented for unasked questions
A learner may never have received several items in a matrix-sampled assessment. Plausible values should not be described casually as the programme guessing those missing answers and awarding marks for them.
The relevant draws concern a latent proficiency representation. That is a different object from a completed response vector for every unadministered question.
The distinction matters because the language of “filling in marks” suggests an individual administrative decision. A population-estimation procedure is not an authorised replacement for a child’s missing examination result.
For the same reason, an analyst should not use plausible values to tell a parent which particular unobserved question their child would have answered correctly. The model may support population-level estimates involving proficiency, but it does not create an observed personal performance history.
The appropriate question is not “Which of these values is the student’s real mark?” It is “How should this set of draws be used to estimate the population quantity the programme was designed to measure?”
Why a single best-looking number is not enough
Suppose an analyst replaces every distribution of possible proficiency with its centre. The resulting dataset may look clean. But the spread of uncertainty within each learner’s representation has been compressed.
For some calculations, that compression can change the quantity being estimated. A threshold, percentile, variance or other nonlinear function does not generally behave the same way when applied after averaging as when applied before averaging.
This is a mathematical issue, not merely a software convention. The order of operations can alter the answer. Even where a point estimate happens to agree, an uncertainty calculation that treats the compressed numbers as fully observed values can still be wrong.
The TIMSS 2023 technical notes distinguish plausible values from conventional individual test scores and caution that individual use can misrepresent proficiency. The file’s row structure should not override the instrument’s reporting purpose.
The next example makes the order-of-operations problem visible without requiring an actual assessment dataset.
An invented two-row counterexample
Consider two hypothetical rows, each with five values. Row A contains 470, 490, 510, 530 and 550. Row B contains 550, 530, 510, 490 and 470. Use equal weights, and ask for the proportion above 500.
If we average each row first, both row means are 510. Both exceed 500. The shortcut therefore reports 100% above the threshold.
Now analyse each value column first. In the first column, one of two values exceeds 500, so the proportion is 50%. The second column also gives 50%. The third gives 100%. The fourth and fifth each give 50%.
Averaging those five proportions gives (50 + 50 + 100 + 50 + 50) ÷ 5 = 60%, not 100%.
This tiny dataset is not a usable population estimate. It is a demonstration that classification and averaging do not commute. The sequence of operations changes the statistic.
It should also not be interpreted as establishing a particular child’s probability of passing an examination. The example illustrates an aggregate calculation under hypothetical draws. It does not justify using population-assessment plausible values for individual pass/fail decisions.
The important exception for a simple mean
Precision requires admitting an exception. For a simple weighted mean with the same respondents and fixed weights across plausible-value sets, averaging within rows and then calculating the mean can give the same point estimate as calculating each weighted mean and then averaging.
That follows from the linearity of the mean. It does not rescue the general shortcut. The within-row averaging still removes information needed for the plausible-value component of uncertainty, and the equivalence does not extend automatically to nonlinear statistics or changing analysis samples.
This exception explains why an incorrect analysis can appear to work during a superficial check. The analyst reproduces a published average and concludes that the method is sound. A threshold percentage, standard error or regression analysis can then reveal the problem.
A good validation therefore tests more than one convenient point estimate. It checks the entire workflow against the intended statistic and uncertainty calculation.
The lesson is not “the shortcut always changes the mean.” The lesson is “a coincidentally correct mean is insufficient evidence that the procedure preserves the information needed for inference.”
The two uncertainties you must not collapse
There is uncertainty because the programme sampled learners rather than observing the whole population under all conditions. There is also uncertainty because proficiency is latent and only incompletely measured for each learner.
These are different sources. A large sample can reduce some sampling uncertainty while each learner still provides relatively limited item evidence. Conversely, a detailed individual assessment does not make an unrepresentative population sample representative.
NAEP’s technical account of variance components explicitly distinguishes uncertainty in estimating a population statistic from the variance of the population proficiency distribution itself.
That last distinction is easy to miss. The standard error of an estimated mean is not the same as the spread of proficiency among students. A population can be diverse while its average is estimated precisely. It can also have a narrow proficiency distribution but a poorly estimated average if the evidence is inadequate.
Use labels that preserve these meanings. “Variance” without identifying what varies can make a technically sophisticated report surprisingly hard to interpret.
General pooling logic for one scalar estimate
Let M be the number of plausible-value sets used. For each set m, calculate the statistic of interest, Q_m, and its appropriate design-based sampling variance, U_m.
The combined point estimate is Q_bar, the average of the Q_m estimates. The average sampling variance is U_bar, the average of the U_m values. The between-estimate variance B is the sample variance of the Q_m estimates across the M sets.
A standard multiple-imputation-style expression for total variance is T = U_bar + (1 + 1/M)B. The corresponding standard error is the square root of T.
This general scalar logic is set out in NAEP’s documentation on using plausible values for group statistics. Programme-specific procedures can include particular replication methods and approved approximations. Use the relevant technical guide rather than treating this paragraph as a universal software specification.
For joint tests, vectors of coefficients, nonlinear transformations or complex contrasts, covariance and pooling rules require additional care. A formula for one scalar estimate is not a complete recipe for every model an analyst might fit.
An original worked pooling example
Imagine that five separate analyses produce estimated population means of 498, 500, 502, 499 and 501. These are five estimates from the same sample under five plausible-value sets, not five different student scores.
The combined mean is 500. The deviations from 500 are −2, 0, 2, −1 and 1. Squaring them gives 4, 0, 4, 1 and 1, for a total of 10.
The between-estimate sample variance is therefore B = 10 ÷ (5 − 1) = 2.5.
Suppose the appropriate sampling variance from each of the five analyses is 4. The average sampling variance is then U_bar = 4.
Using the general expression, T = 4 + (1 + 1/5) × 2.5 = 4 + 3 = 7. The standard error is √7, approximately 2.65.
If we ignored the between-estimate component, we would report √4 = 2 instead. The point estimate would still be 500, but the uncertainty would be understated in this invented example.
The numbers make the workflow visible. They are not a published assessment result, and they do not determine which confidence-interval or hypothesis-testing procedure is appropriate for a real programme. Degrees of freedom and survey design can matter as well.
What the between-estimate variance is—and is not
In the worked example, B is calculated from the five population-mean estimates. It is not the average variance of the five values within each student’s row.
This distinction matters because the target statistic changes how uncertainty propagates. A mean, a threshold proportion and a regression coefficient respond differently to the same underlying draws. Their between-estimate variability must therefore be calculated from the relevant repeated analyses.
Nor is B a count of measurement mistakes. It is part of an estimation procedure reflecting the latent and incompletely observed nature of proficiency under the model.
A low B for one statistic does not prove that every individual is precisely measured. Aggregation can stabilise a population estimate while individual uncertainty remains substantial.
When explaining results to non-specialists, say what was repeated: “We estimated the same population quantity under each supplied proficiency draw and combined the resulting estimates.” That description is more informative than saying only that a correction was applied.
Survey weights answer another part of the problem
Plausible values do not replace survey weights. If some students or schools have different selection probabilities, the population estimate needs the appropriate design treatment.
Similarly, using a final student weight does not by itself produce a correct standard error. Complex sampling can include clustering, stratification and other features that ordinary independent-observation formulas do not represent.
The TIMSS 2023 technical notes describe analysis using plausible values together with sampling weights and replication procedures. They illustrate why a correct proficiency variable is only one component of a correct analysis.
Keep the functions separate. The weighting and replication scheme addresses the survey design. The plausible-value analysis addresses incomplete latent measurement for the intended statistic. The final inference needs both where the programme requires them.
A weighted analysis with only one arbitrary plausible-value column is incomplete. An analysis using every plausible-value column but ignoring the survey design is also incomplete. Sophistication in one half of the workflow cannot compensate for omitting the other.
Replicate weights are not additional people
A dataset may contain many replicate-weight columns. They can look as mysterious as plausible values, but they serve a different role.
Replication methods alter the weights according to a specified design so the variation in repeated estimates can support a sampling-variance calculation. The programme’s method determines the replication factors and rules.
The learner rows remain the same observed sample. An analyst must not append replicate-weight results as though they were independent observations. Nor should the number of replicate columns be treated as a multiplier of the sample size.
The same warning applies to plausible values. Five values for each of 1,000 learners do not create 5,000 independently tested learners. They create repeated model-compatible representations for analysing the same sample.
This is a general computational habit worth building: identify whether a repeated column represents another observed unit, another measurement occasion, another model draw or another weighting scheme. These objects can look similar in a table while requiring completely different analysis.
A transparent analysis workflow
Begin with the research question and target population. Decide whether the required statistic is a mean, group difference, proportion, percentile or model coefficient. Identify the instrument cycle, domain and variables before selecting software options.
Then read the relevant technical documentation. Confirm the plausible-value columns, final weight, replicate weights, variance method, missing-value conventions and any restrictions on combining domains or cycles.
Validate the analysis dataset. Check identifiers, merges, row counts and unexpected missingness. If a school-level file is joined incorrectly, the resulting duplication can damage the estimate before the plausible-value procedure even begins.
For each supplied plausible-value set, run the same specified analysis and retain both the estimate and the required variance information. Combine those outputs according to the programme’s rules. Preserve the individual results so another analyst can inspect how the final number was formed.
Finally, check the result against a known published statistic where a matching calculation is available. Agreement is useful but not conclusive: verify that the sample, filters and uncertainty method match, not merely the rounded headline mean.
Why averaging standard errors is not the pooling rule
Standard errors are square roots of variances. Combining them by simple averaging does not generally reproduce the combined variance calculation, and it ignores between-estimate uncertainty if that component is omitted.
In the worked example, each separate sampling standard error was 2. Their average remains 2. The correctly illustrated total standard error was approximately 2.65 because the repeated estimates also varied across plausible-value sets.
Do not average p-values either. A collection of p-values is not a substitute for combining estimates and variance information using the appropriate inferential procedure.
The practical safeguard is to store the necessary intermediate quantities, not only presentation-ready output. Once an analysis retains only a coefficient, a star and a rounded p-value, important information may already have been discarded.
Good reporting can be simple because the underlying analysis was careful. It should not be simple because the calculations removed the very uncertainty they were meant to carry.
Threshold percentages require the threshold inside the repeated analysis
Suppose the question is what proportion of a population is above a specified proficiency threshold. The threshold operation belongs within each plausible-value analysis, followed by appropriate combination of the resulting proportions and uncertainty.
The two-row example showed why. A threshold is discontinuous: a small movement across the boundary changes classification completely. Compressing the draws before applying the threshold can therefore change the aggregate proportion materially.
The threshold itself needs a justified interpretation. A reporting level in an international assessment is not automatically an individual pass mark, a curriculum grade or a placement boundary in a local school.
The related guide How Standard Setting Works examines how performance descriptions become cut scores. Plausible-value analysis does not supply that substantive judgement; it estimates quantities relative to a threshold whose meaning must already be established.
Keep the statistical operation and the educational interpretation separate enough that both can be reviewed.
Group differences need the uncertainty of the difference
An analyst may estimate two group means correctly and still calculate their difference’s uncertainty incorrectly. The relationship between the estimates matters.
A useful approach is to treat the group difference as the statistic of interest within each plausible-value analysis. The survey procedure should then provide the appropriate variance for that contrast, including relevant design relationships.
Do not automatically add squared standard errors as though every pair of estimates were independent. Groups can be represented within a common complex survey design, and other contrasts can involve overlapping populations or correlated estimates.
The same principle applies to a change across time, though linking and cross-cycle design introduce further complications. Follow the programme’s trend procedures rather than arbitrarily pairing plausible-value columns from separate files and assuming that the resulting contrast has the intended meaning.
The desired inference should drive the repeated calculation. Compute the thing you intend to discuss, together with its uncertainty, rather than assemble a new conclusion afterwards from rounded pieces whose dependence has been forgotten.
Regression is not one extra button
Researchers often move from descriptive means to models relating proficiency to background variables. That move introduces new choices: outcome definition, predictors, functional form, missing covariates, survey design and the compatibility of the analysis with the conditioning model.
The broad repeated-analysis principle remains useful, but implementation should follow established methods for the statistic and programme. Multiple coefficients, joint tests and nonlinear models can require more than independently averaging each displayed number.
For relationships involving several proficiency domains, check how the plausible values were jointly generated and how the technical guide permits them to be combined. Do not randomly mix draws from different domains or treat every cross-combination as a new observation.
Missing predictor data also remain a separate problem. The existence of plausible values for proficiency does not mean all background variables have been imputed or that deleting incomplete cases is automatically harmless.
A reproducible model specification should state these choices before the analyst interprets coefficients. A sophisticated outcome representation does not make an otherwise poorly specified regression trustworthy.
Background variables are not bonus marks
Readers sometimes react strongly to the idea that background information enters a proficiency-conditioning model. It can sound as though a student receives extra marks for belonging to a particular group.
That is not a helpful description of the population-estimation task. The model uses available information to represent distributions and relationships under specified assumptions; it is not an ordinary classroom grading rule.
The legitimate questions are about modelling adequacy. Which variables were included? How were they represented? Are important relationships omitted or misspecified? Does the analysis of interest rely on assumptions the supplied plausible values do not adequately preserve?
These are technical and substantive questions worth asking. Rejecting the method as “invented marks” misses its purpose. Treating the model as automatically correct misses its limitations.
The balanced position is to understand the procedure, inspect its assumptions and retain the population-level interpretation for which it was designed.
A correct plausible-value analysis does not prove causation
Suppose a correctly analysed dataset shows that a learning practice is associated with higher proficiency. The plausible-value procedure may help estimate that relationship appropriately. It does not establish that adopting the practice causes the higher proficiency.
Selection, prior attainment, resources, reverse direction and other explanations may remain. Students who are already strong may choose the practice more often. Schools may adopt it alongside several other changes. A background measure may represent a broader advantage rather than the isolated mechanism named in the report.
The measurement problem and the causal-identification problem are different. Solving one does not solve the other.
This distinction is especially important when results become advice to parents or policy proposals. A carefully estimated association can inform a question worth investigating without justifying a confident promise of improvement.
Responsible reporting states what the study design can support. The presence of weights, plausible values and sophisticated software should make the explanation more disciplined, not more expansive.
Comparability still has to be earned
Two groups can have plausible-value columns with the same names while important measurement questions remain. Does the scale represent sufficiently comparable proficiency? Are translations, item functioning and linking adequate for the intended comparison?
The repeated-analysis procedure does not independently validate the underlying scale. It carries uncertainty within a modelling system. If the system is poorly aligned with the construct or comparison, correct pooling does not remove that problem.
Use Measurement Invariance and Differential Item Functioning for related comparability questions. They are connected checks, not synonyms for plausible-value analysis.
For changes across assessment cycles, also ask what changed in the population, instrument, delivery mode and scaling. A trend line can mix these influences unless the programme has a defensible way to connect the measurements.
The final number should therefore travel with its scale definition and comparison conditions, not only with a standard error.
Why country ranks need more than sorted means
Sorting estimated means creates an exact-looking order. The estimates themselves are uncertain. Two populations with nearby means may not be distinguishable at the level implied by the ranking.
Plausible-value analysis contributes to the uncertainty calculation, but ranking introduces its own communication problem. A small numerical difference can become a large narrative difference when one system is called fifth and another eighth.
Report the estimates, uncertainty and appropriate comparisons rather than treating the sorted position as a direct observation. Consider the educational size of differences as well as their statistical detectability.
A tiny but precisely estimated difference need not imply a practically important distinction. A large but uncertain estimate may justify further investigation rather than a definitive league-table story.
The analyst’s job is not complete when the spreadsheet sorts correctly. The interpretation should preserve what the model and design allow the reader to know.
An original audit of a flawed analysis
Imagine an analyst asked to estimate the proportion of learners above a reporting threshold. They average all plausible-value columns within each row, classify the row mean, apply a final weight and calculate a standard error using an ordinary independent-observation formula.
The output is polished. It contains a percentage, a confidence interval and a chart. Four questions expose the weaknesses.
First, was the threshold applied before or after collapsing the draws? The two-row counterexample shows why that order can alter the proportion.
Second, does the variance calculation reflect the survey design? Applying a final weight to the point estimate is not the same as using an appropriate sampling-variance procedure.
Third, where is the between-estimate component? It has disappeared because only one collapsed analysis was performed.
Fourth, what does the threshold mean? The chart title calls it a pass rate, although the assessment documentation describes a population proficiency level rather than an individual qualification decision.
The repair is not a cosmetic footnote. The analyst must rerun the repeated analysis, use the appropriate variance procedure, combine uncertainty and correct the interpretation. A chart can be beautifully formatted while representing the wrong calculation and the wrong educational claim.
What to retain for a reproducible result
Retain the source dataset release, technical documentation version and analysis code. Record the population filters, selected domain, plausible-value columns, weight variables and missing-data treatment.
Keep row counts before and after every merge and filter. A many-to-many merge can multiply records without an obvious error message. A language or school-type filter can silently change the population being described.
Store each repeated estimate and its relevant variance information. This allows a reviewer to see whether one plausible-value set behaves unexpectedly, whether an analysis failed in one iteration and whether the final pooling used the intended number of valid results.
Retain warnings, convergence information and sensitivity checks. Do not simply average the successful iterations when some failed without investigating why. The missing iteration may signal a model or data problem rather than an inconvenient computational detail.
Finally, preserve the exact statistic described in the report. “Mean proficiency among participating learners after these exclusions” and “mean proficiency in the target population” are not automatically the same estimand.
The wrong kind of precision
Suppose a report gives a mean of 501.347829. The additional digits can make the estimate feel authoritative. They do not increase the information collected from learners or repair a misspecified model.
Appropriate reporting precision should reflect the scale, uncertainty and intended use. Rounding is not the main issue; the issue is whether the presentation invites a stronger conclusion than the evidence supports.
The same principle applies to individual rows. A plausible value reported to several decimal places is still a draw within a population-estimation method. Numerical detail does not convert it into an exact personal trait.
For an educator, the useful question is often substantive: which part of the population distribution changed, how large is the change, what uncertainty remains and what further evidence would inform action? Those questions are not answered by adding more decimal places.
Three comparisons that clarify the method
Imagine estimating a city’s traffic conditions from incomplete observations. Several model-compatible traffic maps may imply similar average congestion but different proportions of roads above a severe-delay threshold. Collapsing every road to its average state before calculating the threshold can alter the result. This resembles the order-of-operations issue, though traffic models and educational measurement are not interchangeable.
Imagine evaluating several plausible project-cost scenarios. Calculating whether the project exceeds a budget within each scenario differs from comparing the average cost with the budget once. The threshold makes the distinction visible. The example illustrates nonlinear calculation, not financial advice or a claim that all scenario analysis uses the same pooling rules.
Imagine several possible reconstructions of a damaged historical map. Averaging the coordinates first may blur the routes whose connectivity you wanted to study. Asking the connectivity question within each reconstruction can preserve a different kind of uncertainty.
The shared lesson is to carry uncertainty through the operation that matters. The domain-specific model, sampling design and interpretation still require their own evidence.
What teachers and parents should take from this
Most teachers and parents do not need to calculate plausible values themselves. They do need to recognise when a published result belongs to a population rather than to an individual child.
A large-scale assessment can provide valuable information about an education system while offering little direct guidance about which misconception one learner should repair tomorrow. That is not a contradiction. The instrument was built for a different resolution of the question.
Use population results to ask informed questions about curriculum, opportunity and broad patterns. Use classroom evidence, work samples and appropriate diagnostic assessment to understand an individual learner.
Do not take a national average as a description of every child in the country. Do not take one learner’s plausible-value row as a complete personal profile. The move from group to individual is an inference that needs its own evidence.
The wider Diagnostics & Recovery Hub offers the learner-level route. It complements population measurement without pretending to be the same task.
A final analyst’s checkpoint
Can you state the target population and statistic in one sentence? Can you identify the exact data release and the appropriate technical guide? Are the plausible-value columns and survey design variables correct for that cycle and domain?
Did you repeat the intended analysis rather than average the learner rows first? Did you retain both estimates and variance information? Does the uncertainty procedure include the required sampling and plausible-value components?
Have you checked merges, filters, missing covariates and failed iterations? Are group contrasts, thresholds and nonlinear quantities analysed as the quantities actually discussed in the report?
Finally, does the conclusion remain at the population level the instrument supports? Are associations being distinguished from causes, and reporting thresholds from personal pass marks?
A “yes” to these questions is not a universal validity certificate. It is a strong starting point for a review that can examine the actual evidence rather than merely admire the output.
Back to the unfamiliar columns
The dataset still contains several values for each learner. They now look less like a formatting problem and more like a reminder of what was not completely observed.
The analysis asks its question repeatedly, under each supplied proficiency representation, and combines the resulting estimates with an appropriate account of uncertainty. It does not pretend that the extra columns can be discarded without consequence.
This is a useful principle beyond psychometrics: when uncertainty affects the operation you care about, carry it through that operation before compressing the result.
Plausible-value analysis works when it helps us describe population learning without manufacturing certainty about each individual. Analyse the draws, combine the evidence and keep the interpretation within the design.
Research and connected reading
Foundational research: Mislevy, Beaton, Kaplan & Sheehan, Estimating Population Characteristics From Sparse Matrix Samples of Item Responses. Further methodological reading is listed in von Davier, Gonzalez & Mislevy, What Are Plausible Values and Why Are They Useful?
Official analysis guidance: OECD, Preparing and Analysing the PISA Database; NAEP, Using Plausible Values to Estimate Group Statistics and Their Variances; NAEP, Sampling and Measurement Components of Estimation Variance; and TIMSS 2023 Methodology and Technical Notes. Use the documentation corresponding to the actual dataset rather than transferring settings between programmes.
Connected eduKateSG reading: National Learning Assessment Systems, Standard Setting and Measurement Invariance.
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