CASRAI Dictionary

Category: Guides & Explainers

Practical how-to guides, templates, checklists, and career pathways for research administrators, authors, and institutional teams.

  • What Is Psychology? Scope, Methods and the Scientific Discipline

    Psychology is the scientific study of mind and behaviour, using systematic observation, measurement and experiment to build and test theories. As an empirical discipline it spans the biological, cognitive, developmental, social and individual aspects of how people and animals perceive, think, feel and act. The American Psychological Association (APA) frames it as a science grounded in evidence rather than intuition or anecdote.

    The scope of the discipline

    Psychology sits at the intersection of the natural and social sciences. It draws on biology and neuroscience to understand the brain, on statistics to quantify behaviour, and on social science to study groups and culture. Its defining commitment is methodological: claims about the mind are evaluated against data gathered under controlled, reproducible conditions rather than accepted on authority. That commitment distinguishes scientific psychology from folk or popular psychology, which may offer intuitively appealing explanations that have never been tested. The discipline’s value lies in its willingness to discard attractive ideas when evidence contradicts them, and to quantify uncertainty rather than asserting confident conclusions about complex human behaviour.

    Major subfields

    Subfield Central question
    Cognitive psychology How do attention, memory, language and reasoning work?
    Developmental psychology How do mind and behaviour change across the lifespan?
    Social psychology How do others influence thought, feeling and action?
    Biological psychology How do brain and body underpin behaviour?
    Personality & individual differences How and why do people differ in stable ways?
    Clinical & counselling How are psychological difficulties understood and supported?

    Research methods

    Psychology relies on a toolkit of complementary methods. Experiments manipulate one variable while holding others constant to test cause and effect, ideally with random assignment to conditions. Observational and correlational studies measure variables as they naturally occur, describing associations without claiming causation. Psychometrics is the science of building and evaluating measures—questionnaires, ability tests and rating scales—so that scores are consistent and meaningful. Underpinning all of these is careful attention to reliability and validity, the twin pillars of sound measurement.

    Quantitative and qualitative approaches

    Psychological research is often divided into quantitative and qualitative traditions, and mature programmes frequently combine them. Quantitative work expresses phenomena as numbers and analyses them statistically, prioritising measurement, comparison and generalisation across large samples. Qualitative work—interviews, focus groups, thematic analysis of text—seeks rich, contextual understanding of how people make meaning, and is well suited to generating hypotheses or studying experiences that resist tidy quantification. Neither is inherently superior; the appropriate method depends on the question. A study estimating how common an attitude is needs quantitative survey methods, whereas one exploring why people hold that attitude may begin qualitatively. Mixed-methods designs deliberately pair the two so that numerical breadth and interpretive depth inform each other.

    The scientific method in psychology

    Psychological research follows the general cycle of the scientific method: observe a phenomenon, derive a testable hypothesis, design a study, collect and analyse data, and revise theory in light of results. Because human behaviour is variable, psychologists lean heavily on statistics to separate genuine effects from chance. The discipline has also become more reflective about its own methods following the replication crisis, adopting practices such as preregistration and data sharing to strengthen the reliability of published findings.

    Measurement and assessment

    Much of psychology depends on turning abstract constructs—intelligence, anxiety, conscientiousness—into numbers. This is harder than it looks, and the field has a long tradition of scrutinising its instruments. Popular tools are not automatically trustworthy: assessments such as the Myers-Briggs Type Indicator illustrate how an instrument can be widely used yet fall short on psychometric grounds. Responsible practice means reporting how a measure was validated, a discipline reflected in CASRAI’s work on responsible assessment.

    A short history of the discipline

    Psychology emerged as a distinct experimental science in the late nineteenth century, conventionally dated to Wilhelm Wundt’s establishment of a dedicated laboratory in Leipzig in 1879. Early schools—structuralism, functionalism and later behaviourism—debated whether psychology should study inner experience or only observable behaviour. The mid-twentieth-century cognitive revolution restored the study of mental processes such as memory and attention using rigorous experimental methods, and the subsequent rise of neuroscience linked those processes to brain function. This trajectory matters because it shows the field repeatedly tightening its methods, a self-correcting tendency that continues in today’s reforms.

    Statistics and inference

    Because behaviour varies between people and occasions, psychology cannot rely on single observations. It uses inferential statistics to ask whether a pattern in a sample is likely to hold in the wider population. Two ideas are central: effect size, which expresses how large a difference or relationship is, and statistical power, the probability that a study will detect a real effect if one exists. Underpowered studies—those with samples too small to reliably find the effects they seek—produce unstable, often exaggerated results. Understanding these concepts is essential to reading psychological research critically, and their neglect contributed directly to the field’s reproducibility problems.

    Distinguishing good evidence from popular myth

    A practical skill the discipline cultivates is separating well-supported findings from appealing but shaky claims. Many ideas that circulate as “psychology” in popular media—rigid personality types, single-study effects presented as laws, or memorable graphs taken at face value—rest on weaker foundations than their fame suggests. Sound practice asks how a finding was measured, whether it has replicated, and how large the effect actually is. This is why the field places such weight on reproducibility and on transparent reporting: a claim is only as good as the method behind it.

    Ethics in psychological research

    Because psychology studies people, it is bound by strong ethical standards. Core principles include informed consent, the right to withdraw, minimisation of harm, confidentiality and, where deception is unavoidable, careful debriefing. Institutional ethics committees, often called institutional review boards, review proposals before data collection begins, and professional bodies such as the APA publish detailed ethics codes. These safeguards became more formalised after historical cases in which participants were exposed to undue stress, and they now shape study design from the outset. Such governance is part of the wider research lifecycle that good metadata and clear terminology, recorded in resources like the research dictionary, are designed to support.

    Frequently asked questions

    Is psychology a science?

    Yes. Psychology uses the scientific method—systematic observation, hypothesis testing, controlled experiments and statistical analysis—to study mind and behaviour, and it revises its theories in light of replicable evidence.

    What are the main branches of psychology?

    Major subfields include cognitive, developmental, social, biological, personality and clinical psychology. They share common methods but differ in the questions they ask and the populations and processes they study.

    What methods do psychologists use?

    Psychologists use experiments, observational and correlational studies, and psychometric testing, supported by statistics. Method choice depends on whether the goal is to establish causation, describe associations or measure an attribute reliably.

    Why does measurement matter so much in psychology?

    Because psychological constructs are abstract, conclusions are only as good as the instruments used. Reliable, valid measures are essential, which is why the field scrutinises its tests and encourages transparent reporting for authors.

  • What Is Statistics? The Discipline and Its Role in Research

    Statistics is the discipline concerned with collecting, organising, analysing, interpreting and presenting data. At its core it is the science of reasoning under uncertainty: it provides methods for drawing conclusions about a whole population from a limited sample, and for quantifying how much confidence those conclusions deserve. Statistics underpins quantitative research across every field, from medicine and economics to ecology and the social sciences.

    Descriptive versus inferential statistics

    The discipline divides into two broad branches. Descriptive statistics summarise and describe the features of a dataset without claiming anything beyond it. Measures of central tendency such as the mean, median and mode, measures of spread such as the range and standard deviation, and visual summaries such as histograms all belong here. Descriptive statistics tell you what the data at hand look like.

    Inferential statistics go further: they use a sample to make estimates or test claims about a larger population that has not been fully observed. Estimation, hypothesis testing, confidence intervals and regression modelling are all inferential tools. The defining feature of inference is that it carries uncertainty, and statistics provides the machinery to measure that uncertainty rather than ignore it.

    Branch Purpose Typical tools
    Descriptive Summarise observed data Mean, median, standard deviation, charts
    Inferential Draw conclusions about a population Confidence intervals, hypothesis tests, regression

    Populations and samples

    The distinction between a population and a sample is fundamental. A population is the entire set of units a researcher wishes to understand: all adults in a country, every transaction in a year, all stars in a galaxy. A sample is a subset of that population actually measured. Because studying an entire population is usually impractical, researchers work from samples and infer to the whole. A numerical fact about a population is a parameter; the corresponding figure calculated from a sample is a statistic, and statistics as a discipline is largely the study of how well sample statistics estimate population parameters.

    Estimation and hypothesis testing

    Two complementary tasks dominate inferential work. Estimation asks how large a quantity is and how precisely we know it, producing point estimates and interval estimates such as confidence intervals. Hypothesis testing asks whether the data are compatible with a specific claim, typically a null hypothesis of no effect, and summarises that compatibility with measures such as p-values. Both rest on the idea that random sampling produces variation, and that this variation can be modelled probabilistically.

    Variability and probability

    Underlying all of statistics is the recognition that data vary. Two samples from the same population will rarely give identical results, and statistics describes this sampling variation using probability. Measures such as the standard deviation quantify spread within data, while probability distributions describe how estimates would behave across repeated sampling. This probabilistic foundation is what allows statisticians to attach honest measures of uncertainty to their conclusions.

    Why statistics is central to research

    Statistics is not an optional add-on to research; it shapes how studies are designed, how large samples need to be, how data are analysed and how findings are reported. Sound statistical practice is essential for reproducibility, because it disciplines researchers against over-interpreting noise and helps others judge whether a result is robust. Poor statistical practice, by contrast, is a recognised driver of irreproducible findings. CASRAI’s work on standardised reporting and the CASRAI dictionary supports clearer, more comparable statistical reporting across the scholarly record, and the reproducibility category tracks developments in this area.

    Frequently asked questions

    Is statistics a branch of mathematics?

    Statistics uses mathematics, particularly probability theory, but it is usually regarded as a distinct discipline. Its focus is on data, inference and the practical business of learning from observation under uncertainty, not on abstract mathematical structure alone.

    What is the difference between a parameter and a statistic?

    A parameter is a fixed numerical characteristic of a population, such as the population mean. A statistic is the corresponding figure computed from a sample, such as the sample mean. Statistics as a discipline studies how to estimate parameters from statistics.

    Why does statistics matter for reproducibility?

    Reproducibility depends on whether a reported result reflects a genuine effect or random variation. Statistical methods quantify that uncertainty and guard against over-claiming, so transparent statistical reporting is one foundation of a trustworthy scholarly record. See the CASRAI author guidance for reporting practices.

  • The Normal Distribution Explained

    The normal distribution, also called the Gaussian distribution, is a continuous probability distribution that is symmetric about its mean and forms a bell-shaped curve. It is fully described by two parameters: the mean, which locates the centre of the curve, and the standard deviation, which controls its width. Most values lie near the mean, and values become increasingly rare as they move further away in either direction.

    Shape, symmetry and parameters

    A normal curve is perfectly symmetric, so its mean, median and mode coincide at the centre. The two tails extend infinitely in both directions, approaching but never touching the horizontal axis. Changing the mean shifts the curve left or right; changing the standard deviation stretches or compresses it. A larger standard deviation produces a flatter, wider bell; a smaller one produces a taller, narrower peak.

    The 68-95-99.7 rule

    For any normal distribution, a fixed proportion of values falls within a given number of standard deviations of the mean. This is known as the empirical rule, or the 68-95-99.7 rule.

    Within Approximate proportion
    ±1 standard deviation 68%
    ±2 standard deviations 95%
    ±3 standard deviations 99.7%

    This rule underpins the interpretation of confidence intervals and the identification of outliers, since values beyond about three standard deviations are unusual under normality.

    The central limit theorem

    The normal distribution is central to statistics largely because of the central limit theorem. This theorem states that the sampling distribution of the mean of a sufficiently large number of independent observations is approximately normal, regardless of the shape of the underlying population, provided the population has a finite variance. In practice, sample means tend towards normality as sample size increases, often by around n = 30 for moderately skewed data. This is why many tests that compare means, such as the t-test, can be applied even when the raw data are not perfectly normal.

    Why it matters for inference

    Because the behaviour of the normal distribution is exactly known, it provides the mathematical basis for many inferential procedures, including the calculation of p-values and significance tests. Standardising a value into a z-score, by subtracting the mean and dividing by the standard deviation, lets researchers compare observations on a common scale and look up exact probabilities.

    What is and is not normally distributed

    Many measurements approximate a normal distribution, including heights, blood pressure and measurement errors. However, normality should never be assumed. Reaction times, incomes and counts of rare events are typically skewed, and some variables are bounded or bimodal. Always check the distribution using histograms or quantile-quantile plots before applying methods that assume normality. Defining variables and their distributions clearly supports the reproducibility standards set out in the CASRAI dictionary and our guidance for authors.

    Frequently asked questions

    What is the difference between the normal and standard normal distribution?

    The standard normal distribution is a special case with a mean of 0 and a standard deviation of 1. Any normal distribution can be converted to the standard normal by calculating z-scores.

    Does my data have to be normal to use statistics?

    Not always. Thanks to the central limit theorem, tests based on means are robust to non-normality at larger sample sizes. For small samples or strongly skewed data, non-parametric alternatives or transformations may be more appropriate.

    How can I check whether data are normally distributed?

    Use graphical tools such as histograms and quantile-quantile plots, supplemented by formal tests like Shapiro-Wilk. Visual inspection is often the most informative, as formal tests can be over-sensitive in large samples.

  • Regression Analysis: An Introduction for Researchers

    Regression analysis is a statistical method for modelling the relationship between an outcome variable and one or more predictor variables. In its simplest form, linear regression fits a straight line through a scatter of points to describe how the outcome changes, on average, as a predictor changes. It is one of the most widely used tools for prediction and for quantifying associations in research.

    The linear regression equation

    Simple linear regression summarises the relationship between a predictor x and an outcome y with the equation y = a + bx, where a is the intercept and b is the slope. The intercept is the predicted value of y when x is zero, and the slope is the average change in y for a one-unit increase in x. A positive slope indicates that y rises with x; a negative slope indicates that it falls.

    Least squares estimation

    The line is chosen by the method of ordinary least squares, which finds the slope and intercept that minimise the sum of the squared vertical distances between the observed points and the fitted line. These distances are called residuals. Squaring them, as with variance, prevents positive and negative residuals from cancelling and penalises large errors more heavily. The result is the best-fitting line in the least squares sense.

    Interpreting R-squared

    The coefficient of determination, R², measures the proportion of variance in the outcome that is explained by the model. It ranges from 0 to 1: an R² of 0 means the predictors explain none of the variation, while an R² of 1 means they explain all of it. An R² of 0.64, for example, indicates that 64% of the variation in the outcome is accounted for by the predictor. R² alone does not confirm that a model is correct, however; it should be read alongside residual plots and an assessment of the model’s assumptions.

    Multiple regression

    Multiple regression extends the model to include several predictors at once, taking the form y = a + b₁x₁ + b₂x₂ + … + bₖxₖ. Each slope coefficient estimates the effect of its predictor while holding the others constant, which helps to adjust for confounding variables. This makes multiple regression valuable when several factors plausibly influence an outcome.

    Assumptions of linear regression

    Assumption Meaning
    Linearity The relationship between predictor and outcome is linear
    Independence Residuals are independent of one another
    Homoscedasticity Residual variance is constant across the range of predictions
    Normality of residuals Residuals are approximately normally distributed

    When these assumptions are violated, estimates and p-values can be misleading. Diagnostic plots help to detect problems before results are reported.

    Correlation is not causation

    A statistically significant slope shows that two variables are associated, not that one causes the other. Unmeasured confounders, reverse causation or coincidence can all produce a relationship. Causal claims require careful study design, such as randomised experiments, not regression alone. Stating this limitation clearly is part of transparent, reproducible reporting, as encouraged by the CASRAI dictionary and our author guidance.

    Frequently asked questions

    What is the difference between correlation and regression?

    Correlation measures the strength and direction of a linear association with a single number between −1 and 1. Regression goes further, producing an equation that predicts the outcome and quantifies the effect of each predictor.

    What counts as a good R-squared value?

    It depends entirely on the field. In physical sciences an R² above 0.9 may be expected, whereas in social or biological research values of 0.2 to 0.4 can still be meaningful. Always interpret R² in context.

    Can regression prove causation?

    No. Regression quantifies association and can adjust for measured confounders, but it cannot establish causation on its own. Causal inference requires appropriate design, such as randomisation or robust quasi-experimental methods.

  • What Is Artificial Intelligence? Definition and History

    Artificial intelligence (AI) is the branch of computer science concerned with building systems that perform tasks normally requiring human intelligence, such as perception, reasoning, language understanding and decision-making. As a research field it spans both symbolic approaches, which encode knowledge and rules explicitly, and statistical approaches, which learn patterns from data. For the research community, AI is best understood not as a single technology but as a long-standing discipline with a measurable history, contested definitions and evolving documentation standards.

    A working definition of artificial intelligence

    There is no universally agreed definition of artificial intelligence, partly because the goalposts move: tasks once considered to require intelligence, such as optical character recognition, become routine engineering and stop being called AI. A durable, standards-friendly definition treats AI as the study and construction of agents that perceive their environment and take actions to maximise a defined objective. This framing accommodates everything from a rule-based expert system to a modern neural network without privileging any one method.

    Because the term is so elastic, research-standards bodies encourage authors to describe the specific method used, rather than the marketing label. A paper that says it “used AI” tells a reader very little; one that names the model class, training data and evaluation protocol is reproducible. The casrai.org research dictionary exists precisely to stabilise this vocabulary across disciplines.

    Narrow AI versus general AI

    Almost all systems deployed today are examples of narrow AI (also called weak AI): they are built for a single, bounded task such as translating text, recommending content or classifying images. A narrow system that excels at one task has no capacity to transfer that competence to another domain.

    Artificial general intelligence (AGI) refers to a hypothetical system with the broad, flexible competence of a human across arbitrary tasks. AGI remains a research aspiration rather than an existing artefact, and claims of its arrival should be treated with scholarly caution. Keeping the narrow/general distinction explicit prevents the overstatement that often clouds reporting on AI in research outputs.

    Symbolic AI versus statistical approaches

    The field has long been organised around two broad paradigms. Symbolic AI (sometimes called “good old-fashioned AI”) represents knowledge as symbols and manipulates them with explicit logical rules; expert systems and classical search and planning belong here. Its strengths are transparency and the ability to explain a decision step by step.

    Statistical or machine-learning approaches instead infer behaviour from data. Rather than hand-coding rules, an engineer specifies a model and an objective, and the system learns parameters that fit observed examples. This paradigm now dominates practical AI, and it underpins the techniques discussed in our companion piece on machine learning concepts and methods. The two paradigms are increasingly combined in neuro-symbolic systems that pair learned perception with explicit reasoning.

    A brief history: Dartmouth 1956 to the deep-learning era

    The field was named at the Dartmouth Summer Research Project on Artificial Intelligence in 1956, a workshop organised by John McCarthy, Marvin Minsky, Nathaniel Rochester and Claude Shannon. Early optimism produced symbolic reasoning programs and the first neural-network models, but progress stalled when problems proved harder than expected, producing the so-called AI winters of reduced funding and interest in the 1970s and again in the late 1980s.

    The modern resurgence, often dated to the early 2010s, came from the convergence of large datasets, graphics-processing hardware and improved training methods, ushering in the deep-learning era. These advances are explored further in our overview of neural networks and deep learning, and they set the stage for today’s generative models.

    Period Milestone Significance
    1950 Turing’s “Computing Machinery and Intelligence” Proposed the imitation game (Turing test)
    1956 Dartmouth workshop Coined the term “artificial intelligence”
    1970s, late 1980s AI winters Funding and interest contracted
    2010s Deep-learning breakthroughs Data plus GPUs revived neural networks

    The Turing test

    In 1950 Alan Turing proposed what is now called the Turing test: rather than asking whether a machine can “think”, he asked whether a human interrogator, conversing by text, could reliably distinguish the machine from a person. The test reframed an unanswerable philosophical question as an operational one. It remains a touchstone for discussion, though contemporary researchers treat it as a thought experiment rather than a benchmark of genuine understanding, and it does not measure reasoning, safety or factual accuracy.

    Why definitions matter for the research record

    Precise terminology is not pedantry; it is the foundation of reproducibility and credit. When AI methods feature in a study, readers and reviewers need to know exactly what was done. This connects to broader work on contribution transparency captured by the CRediT taxonomy and to the emerging disclosure norms tracked in our AI and ML research outputs coverage.

    Frequently asked questions

    Is artificial intelligence the same as machine learning?

    No. Machine learning is a subfield of artificial intelligence concerned with learning from data. AI is the broader discipline and also includes symbolic reasoning, search and planning that need not learn at all.

    Does any current system count as general AI?

    No. All systems in production are narrow AI, built for specific tasks. Artificial general intelligence remains a research aspiration, and claims of its existence should be treated sceptically.

    What was the significance of the 1956 Dartmouth workshop?

    It is where the term “artificial intelligence” was coined and where the field was effectively founded as a distinct research discipline, setting a shared agenda for the decades that followed.

    Does passing the Turing test prove a machine is intelligent?

    Not in any deep sense. The test measures whether a machine can imitate human conversation convincingly, not whether it understands, reasons soundly or is factually reliable.

  • MRI: The Physics of the Measurement Explained

    Magnetic resonance imaging (MRI) is a measurement technique that produces spatial maps of nuclear magnetic resonance signals, most often from the hydrogen nuclei (protons) abundant in water and fat. An MRI scanner places a sample in a strong static magnetic field, excites the nuclei with radiofrequency pulses, and records the faint signal the nuclei emit as they return to equilibrium. This article describes the physics of how that signal is produced, localised and reconstructed. It is a methods explainer about the instrument and the measurement, not an account of how any individual image should be interpreted.

    The starting point: nuclear spin in a magnetic field

    Certain atomic nuclei, including the single proton of hydrogen-1, possess an intrinsic quantum property called spin, which gives them a small magnetic moment. In the absence of an external field these moments point in random directions and there is no net magnetisation. When the sample is placed inside the scanner’s strong static field, conventionally labelled B0 and measured in tesla, the moments adopt a slight preferential alignment with the field. The result is a small bulk magnetisation along the field direction.

    Within that field the nuclei precess, wobbling like a spinning top, at a characteristic frequency. This is the Larmor frequency, and it is proportional to the field strength: stronger fields produce higher precession frequencies and, all else being equal, a larger signal. The proportionality constant is the gyromagnetic ratio, a fixed property of each nucleus. For hydrogen at clinical and research field strengths the Larmor frequency falls in the radiofrequency band, which is why radio waves are the natural tool for manipulating the spins.

    Excitation: the radiofrequency pulse

    To generate a measurable signal, the scanner transmits a radiofrequency (RF) pulse tuned precisely to the Larmor frequency. Because the pulse matches the precession frequency, energy is transferred efficiently to the spin system, a condition known as resonance. The pulse tips the bulk magnetisation away from the static-field axis and into the transverse plane, where its rotation induces a small oscillating voltage in a nearby receiver coil. That induced voltage is the raw MRI signal.

    Once the pulse is switched off, the magnetisation begins to return to its equilibrium alignment. The way it returns carries information about the local molecular environment, and this is the basis of MRI contrast.

    Relaxation: T1 and T2

    Two largely independent relaxation processes govern the recovery. T1, the longitudinal or spin-lattice relaxation time, describes how quickly the magnetisation re-grows along the static-field axis as the spins release energy to their surroundings. T2, the transverse or spin-spin relaxation time, describes how quickly the rotating magnetisation loses coherence as individual spins drift out of phase with one another. A related quantity, T2*, includes additional dephasing caused by small imperfections in the field.

    Parameter What it describes Physical cause
    T1 Recovery of magnetisation along B0 Energy exchange with the molecular lattice
    T2 Loss of phase coherence in the transverse plane Spin-spin interactions
    T2* Faster transverse decay including field inhomogeneity Local field variations plus spin-spin effects

    Different materials have different T1 and T2 values, so by choosing when to excite and when to measure, an experimenter weights the signal towards one relaxation property or another. This is what produces the visible distinction between tissues in a reconstructed image, and it is a property of the measurement parameters rather than an interpretation of the sample.

    Spatial encoding: turning signal into an image

    A plain RF excitation tells you the total resonance signal but nothing about where in the sample it came from. MRI solves this with gradient coils that superimpose small, controlled, spatially varying magnetic fields on top of B0. Because the Larmor frequency depends on field strength, a gradient makes the precession frequency vary with position. The scanner uses three orthogonal gradients in a carefully timed sequence: a slice-selection gradient applied during the RF pulse so that only one plane is excited, a frequency-encoding gradient that makes frequency map onto one in-plane axis, and a phase-encoding gradient that imprints position onto the signal phase along the other axis.

    The signals collected under these gradients fill a raw data matrix known as k-space, which represents the spatial frequencies of the object rather than the picture itself. Applying an inverse Fourier transform to k-space converts those spatial frequencies into the familiar image. The reconstruction is a mathematical operation on measured data, and understanding it is essential to reporting a study reproducibly; our guide on reporting analytical methods reproducibly covers how acquisition parameters should be documented.

    Why MRI sits alongside other measurement techniques

    MRI is one of several physical techniques researchers use to probe matter without contact. It shares the pulse-and-detect logic of ultrasound, and like time-domain spectroscopy it relies on a Fourier transform to move between a measured signal and an interpretable representation. Standard vocabulary for describing such methods in the research record is maintained in the CASRAI dictionary, and the broader context of where measurement sits in a project appears across our research lifecycle coverage.

    Frequently asked questions

    Why does MRI use hydrogen nuclei?

    Hydrogen is overwhelmingly the most abundant magnetically active nucleus in water- and fat-containing samples, and it has a relatively large gyromagnetic ratio, which together give the strongest signal. Other nuclei such as phosphorus-31 or carbon-13 can be imaged in specialised research spectroscopy, but they produce much weaker signals.

    What does field strength change in the measurement?

    A higher static field raises the Larmor frequency and increases the equilibrium magnetisation, which generally improves signal-to-noise ratio and allows finer spatial detail or faster acquisition. It also changes relaxation behaviour and engineering demands, so field strength is a key parameter to record when reporting a method.

    What is k-space?

    K-space is the raw data domain in which MRI signals are collected. Each point encodes a spatial frequency of the object, and the full image is obtained by an inverse Fourier transform of the completed k-space matrix. It is a representation of the measurement, not the picture itself.

    Is MRI quantitative?

    The underlying parameters, including T1, T2 and proton density, are physical quantities that can in principle be measured numerically. Quantitative MRI sequences aim to recover these values rather than weighted contrasts, which is why precise reporting of acquisition settings is essential for reproducibility, as discussed in our reproducibility coverage and the guidance for authors.

  • What Is Machine Learning? Concepts and Methods

    Machine learning (ML) is the subfield of artificial intelligence concerned with algorithms that learn patterns from data and improve at a task with experience, rather than being explicitly programmed with rules. Instead of an engineer writing the logic, the engineer specifies a model and an objective, and the model adjusts its internal parameters to fit examples. The central scientific question is not whether a model fits the data it has seen, but whether it generalises to data it has not.

    Features, labels and the learning objective

    A machine-learning problem is usually framed in terms of features (the input variables describing each example) and, for supervised tasks, labels (the target output to be predicted). For a model predicting house prices, features might include floor area and location, and the label is the sale price. Learning means searching for model parameters that minimise a loss function measuring the gap between predictions and the truth.

    Machine learning is one paradigm within the broader discipline described in our explainer on artificial intelligence definition and history. Where symbolic AI encodes knowledge by hand, ML infers it statistically from examples.

    The three main paradigms

    Machine learning is conventionally divided into three families, distinguished by what kind of feedback the algorithm receives.

    Type Data used Goal Typical examples
    Supervised learning Labelled examples (features + targets) Predict a label for new inputs Classification, regression
    Unsupervised learning Unlabelled data Discover structure Clustering, dimensionality reduction
    Reinforcement learning Rewards from an environment Learn a policy that maximises long-term reward Control, game playing, sequential decisions

    Supervised learning trains on examples paired with correct answers and learns to predict those answers for unseen inputs; classification predicts categories and regression predicts continuous values. Unsupervised learning works with unlabelled data and seeks hidden structure, for instance grouping similar items (clustering) or compressing many variables into a few (dimensionality reduction). Reinforcement learning learns by trial and error: an agent takes actions, receives rewards or penalties, and gradually improves a policy that maximises cumulative reward.

    The train, validation and test split

    To estimate how well a model will generalise, data is partitioned into three disjoint sets. The training set is used to fit the model’s parameters. The validation set is used to tune choices the algorithm does not learn directly, such as model size or learning rate (the hyperparameters), and to compare candidate models. The test set is held back and used only once, at the end, to give an unbiased estimate of performance on unseen data.

    The cardinal rule is that the test set must not influence training or model selection. Repeatedly peeking at the test set leaks information and inflates reported performance, a subtle but common source of irreproducible results. We discuss safeguards at length in our guide to reproducibility of machine learning research.

    Overfitting and generalisation

    Overfitting occurs when a model learns the noise and idiosyncrasies of its training data rather than the underlying pattern, performing well on training examples but poorly on new ones. The opposite failure, underfitting, occurs when a model is too simple to capture the real structure. The art of machine learning lies in finding the balance, the so-called bias-variance trade-off, that yields the best generalisation to unseen data. Techniques such as regularisation, early stopping and cross-validation all serve this goal.

    Why method reporting matters

    Because performance depends so heavily on the data split, the loss function and the hyperparameters, a machine-learning result is only as credible as its reporting. Standardised vocabulary, captured in the casrai.org research dictionary, helps authors describe their methods consistently, and contribution frameworks such as CRediT help assign credit for the data, software and analysis work involved. Coverage of these issues continues in our AI and ML research outputs category.

    Frequently asked questions

    What is the difference between supervised and unsupervised learning?

    Supervised learning trains on data with known correct answers (labels) and predicts those answers for new inputs. Unsupervised learning works with unlabelled data and instead discovers structure, such as clusters or compressed representations, without a target to predict.

    Why split data into training, validation and test sets?

    The training set fits the model, the validation set tunes hyperparameters and compares models, and the held-out test set gives an unbiased estimate of real-world performance. Mixing these roles inflates results and undermines reproducibility.

    What is overfitting?

    Overfitting is when a model memorises the noise in its training data and therefore performs well on that data but poorly on new examples. The goal of machine learning is generalisation, not memorisation.

    Is machine learning the same as artificial intelligence?

    No. Machine learning is a subfield of artificial intelligence focused on learning from data. AI also includes symbolic reasoning, search and planning that do not learn from examples.

  • DOI vs URL: Why Permanent Links Persist and Web Addresses Decay

    A DOI (Digital Object Identifier) is a persistent identifier that resolves to the current location of a resource, whereas a URL is a direct web address that points to one fixed location. The practical difference is durability: when a publisher reorganises a website, a URL can break (“link rot”), but a DOI continues to resolve because it redirects through the Handle System to wherever the content now lives. For scholarly citation, this is why DOIs are preferred over raw URLs.

    How a URL works and why it rots

    A URL (Uniform Resource Locator) describes where something sits on a particular server at a particular path, for example https://example.org/journal/2024/article-37.html. If the publisher migrates platforms, renames directories, or retires a section, that exact path may no longer exist and the link returns a 404 error. This decay is known as link rot; a related problem, content drift, occurs when a URL still resolves but the content behind it has changed. Both undermine the scholarly record because a citation should point readers to the exact source the author used.

    How a DOI works: the Handle System

    A DOI is an identifier of the form 10.xxxx/suffix assigned to a resource by a registration agency such as Crossref or DataCite. The DOI is not a location; it is a name. Resolution happens through the Handle System, a distributed identifier-resolution infrastructure. When you append a DOI to a resolver, for example https://doi.org/10.xxxx/suffix, the resolver looks up the current target URL registered for that DOI and redirects you. If the publisher moves the content and updates the DOI’s registered target, every existing citation keeps working without change. The identifier stays stable while the underlying location is free to move. The same mechanism underpins our wider work on research outputs and metadata.

    DOI vs URL at a glance

    Property DOI URL
    What it identifies The object (a name) A location (a path)
    Persistence High — survives site moves Low — breaks if path changes
    Resolution Handle System redirect Direct request to a server
    Carries metadata Yes (via registration agency) No
    Best for Articles, datasets, formal records Web pages, blogs, sites without a DOI

    How to cite with a DOI

    Most current style guides ask you to present a DOI as a full, clickable link. The widely recommended display form is https://doi.org/10.xxxx/suffix rather than the bare string “doi:10.xxxx/suffix”. Place it at the end of the reference. You do not normally need to add an access date for a source with a DOI, because the identifier is stable; access dates are reserved for sources likely to change. To understand how the DOI fits into the structure of a complete reference, see our guide to what a citation is and its purpose, and the broader explainer on the DOI and Handle System resolution.

    When to use a URL instead

    Not everything has a DOI. Reports, web pages, blog posts, government documents and many grey-literature items are cited with a URL because no persistent identifier was ever assigned. In those cases, give the most stable URL available, add a retrieval date if the content may change, and consider linking to an archived snapshot in a web-archiving service to guard against future link rot. When a DOI is available, always prefer it. Reference managers and a sound bibliography workflow — covered in our piece on how to compile a bibliography — make it easy to capture the DOI automatically. For terminology, our research-standards dictionary defines persistent-identifier concepts precisely.

    Good practice for durable links

    Prefer the DOI when one exists; use the https://doi.org/ resolver form; keep raw URLs only for sources without identifiers; and archive volatile web sources. A reference manager (see our overview of reference management software) will usually pull the DOI from the source metadata, but you should always verify it resolves before you submit.

    Frequently asked questions

    Is a DOI a type of URL?

    No. A DOI is an identifier — a name for an object. It becomes clickable when you prefix it with a resolver such as https://doi.org/, which turns the name into a link that redirects to the object’s current location.

    Why does my old citation’s DOI still work after the journal changed websites?

    Because the DOI resolves through the Handle System to whatever target URL the publisher has registered. When the site moved, the publisher updated that target, so the DOI keeps pointing at the right place even though the underlying URL changed.

    Should I include both the DOI and the URL?

    Generally no — if a DOI exists, cite the DOI and omit the raw URL, because the DOI is the more durable and authoritative link. Use a plain URL only when the source has no DOI.

    Do DOIs guarantee a source will never disappear?

    A DOI guarantees stable resolution as long as the registrant maintains it, but it cannot stop a publisher from withdrawing content. For volatile or unregistered sources, archiving a snapshot remains good practice.

  • Ultrasound: How the Technique Works

    Ultrasound is a measurement technique that probes a material by transmitting high-frequency sound pulses and timing the echoes that bounce back from internal boundaries. Because the speed of sound in a medium is approximately known, the time an echo takes to return can be converted into a depth, and the strength of the echo into a brightness value. Repeating this across many directions builds a map of acoustic boundaries. This article explains the physics of how the technique produces a measurement; it is not a guide to interpreting any particular image.

    What ultrasound actually is

    Sound is a mechanical pressure wave that travels through a medium by compressing and rarefying the material. Audible sound spans roughly twenty hertz to twenty kilohertz; ultrasound is simply sound above the upper limit of human hearing. Research and imaging systems typically use frequencies of a few megahertz, far higher than audible sound. Frequency matters because it sets the wavelength, and the wavelength sets the finest detail the wave can resolve: higher frequencies give finer resolution but are absorbed more strongly and therefore penetrate less deeply. Choosing a frequency is a trade-off between resolution and penetration, and it is a parameter worth recording in any methods description.

    The piezoelectric transducer

    The heart of an ultrasound system is the transducer, which both transmits and receives sound. It relies on the piezoelectric effect: certain crystals and ceramics change shape when a voltage is applied across them, and conversely generate a voltage when mechanically deformed. To transmit, the system applies a short electrical pulse, the element flexes and pushes on the medium, launching a brief pressure wave. To receive, the same element is left to vibrate when an echo arrives, and its deformation generates a small voltage that the electronics amplify and record. A single transducer therefore acts as both loudspeaker and microphone, switching rapidly between the two roles.

    Modern systems use arrays of many small elements. By firing the elements with carefully staggered timing, the system can steer and focus the beam electronically, sweeping it across the field of view without moving the device. This beam-forming is purely a matter of controlled timing and interference of the emitted waves.

    Pulse-echo and time-of-flight

    The core measurement is pulse-echo. The transducer emits a short pulse, then listens. Whenever the pulse crosses a boundary between materials with different acoustic properties, part of it reflects back. The system measures the time-of-flight, the interval between emission and the return of each echo, and converts it to a distance using the relationship that depth equals the speed of sound multiplied by the round-trip time, divided by two. The division by two accounts for the wave travelling to the boundary and back.

    Quantity measured Derived information Physical basis
    Echo arrival time Depth of the boundary Speed of sound times time, halved
    Echo amplitude Strength of the reflection Acoustic mismatch at the boundary
    Frequency shift of echo Velocity of a moving reflector Doppler effect

    By assigning each echo a position from its timing and a brightness from its amplitude, and repeating across many beam directions, the system assembles a cross-sectional image of acoustic boundaries. The picture is a direct consequence of measured timings and amplitudes, much as an MRI image is a consequence of measured resonance signals.

    The Doppler principle

    Ultrasound can also measure motion. When a sound wave reflects from a moving boundary, the frequency of the returning echo shifts: it rises if the reflector approaches the transducer and falls if it recedes. This is the Doppler effect, the same phenomenon that changes the pitch of a passing siren. By comparing the transmitted and received frequencies, the system calculates the component of the reflector’s velocity along the beam. Doppler ultrasound thus turns a frequency measurement into a velocity measurement, and the geometry between beam and motion must be accounted for in the calculation.

    Reporting an ultrasound measurement

    Because the technique is governed by physical parameters, reproducibility depends on documenting them: transmit frequency, the assumed speed of sound, focal settings and the processing applied to the raw echoes. Our guide on reporting analytical methods reproducibly sets out how such parameters belong in a methods section, and the CASRAI dictionary standardises the vocabulary. The broader place of measurement in a study is covered across our research lifecycle articles.

    Frequently asked questions

    Why does higher frequency give finer detail?

    Higher frequency means shorter wavelength, and a wave can resolve features only down to roughly its own wavelength. Shorter wavelengths therefore distinguish closer boundaries, at the cost of being absorbed more quickly and so penetrating less deeply into the material.

    What makes an echo strong or weak?

    An echo arises wherever the acoustic impedance, a product of density and sound speed, changes between two materials. A large mismatch reflects more of the wave and produces a strong echo; a small mismatch reflects little. The amplitude recorded is a property of the boundary, reported as brightness.

    How does Doppler measure velocity?

    It compares the frequency of the emitted pulse with the frequency of the returning echo. Motion of the reflector shifts the echo frequency, and the size of that shift is proportional to the reflector’s velocity component along the beam, a relationship that follows directly from the Doppler equation.

    Is ultrasound the same idea as radar or sonar?

    The pulse-echo timing logic is shared: emit a pulse, time the return, convert to distance. Sonar uses sound in water, radar uses radio waves, and ultrasound uses high-frequency sound in solids or soft media. The contrasts and reproducibility considerations are discussed further in our reproducibility coverage and the author guidance.

  • Annotated Bibliography: How to Write One (Step-by-Step)

    An annotated bibliography is a list of citations in which each entry is followed by a brief paragraph — the annotation — that describes, evaluates and situates the source. Unlike a plain reference list, it tells the reader not just what you cited but why it matters. A good annotation usually does three jobs: summary (what the source argues), evaluation (how credible or useful it is) and relevance (how it relates to your project).

    What an annotation contains

    Each annotation is typically 100–200 words and follows immediately after a full, correctly formatted citation. Depending on the assignment, annotations may be descriptive (summary only), evaluative (summary plus a judgement of quality), or reflective (how the source informs your own argument). Many tutors ask for all three elements. The citation itself follows whatever style you are using; for the underlying principles, see our explainer on what a citation is.

    How to write an annotated bibliography

    Follow these steps in order.

    1. Define your scope. Decide the topic and the criteria a source must meet to be included — recency, methodology, authority, relevance to your research question.
    2. Find and select sources. Search databases and library catalogues, then choose the works that genuinely advance your argument rather than everything you find.
    3. Record full citations. Capture complete, accurate references in your chosen style as you go. A reference manager makes this much faster.
    4. Read critically. Note the thesis, method, evidence and limitations of each source.
    5. Write the annotation. In a short paragraph, summarise the source, evaluate its strengths and weaknesses, and explain its relevance to your work.
    6. Order the entries. Arrange alphabetically by author (most common), or chronologically or thematically if that suits the project.
    7. Proofread and check. Verify every citation against the source — generated references in particular need checking, as we explain in our guide to citation accuracy.

    Annotation styles compared

    Type Contains Best for
    Descriptive Summary only Surveying a field
    Evaluative Summary + critique Assessing source quality
    Reflective Summary + relevance to your project Planning a dissertation or literature review

    A worked example

    The following illustrates an evaluative annotation. The citation comes first, then the paragraph.

    Smith, J. (2023). Open data practices in clinical research. Journal of Research Standards, 12(2), 45–61. https://doi.org/10.xxxx/example

    Smith surveys data-sharing policies across forty clinical journals and argues that mandatory deposit improves reproducibility. The study’s strength is its breadth; its limitation is a focus on policy text rather than compliance in practice. The article is directly relevant to my project because it frames the gap between stated and enacted open-data norms that my dissertation investigates.

    Note how the example uses a DOI rather than a plain URL for durability. For the difference between an annotated bibliography and other list types, see our overview of bibliographies and how to compile them, and our hub on research outputs.

    Common pitfalls

    Avoid simply abstracting the source without evaluating it, padding annotations to a word count, or copying the publisher’s blurb. Keep your own analytical voice, and make sure every citation is verified against the original — accurate referencing supports the integrity of the wider scholarly record discussed across our dictionary.

    Frequently asked questions

    How long should each annotation be?

    Most annotations run to one short paragraph of roughly 100–200 words. Always follow your assignment brief, which may specify a length or which elements (summary, evaluation, relevance) are required.

    What is the difference between an annotated bibliography and an abstract?

    An abstract is a neutral, author-written summary of a single work. An annotation is written by you and adds evaluation and a statement of relevance to your own project, so it is critical rather than purely descriptive.

    Do annotations need full citations?

    Yes. Each entry begins with a complete, correctly formatted citation in your chosen style, then the annotation follows. The citation must be accurate and verified, just as in a standard reference list.

    Can I use a reference manager to build one?

    Yes. Tools such as Zotero, Mendeley and EndNote store your sources and generate formatted citations; you then write the annotations beneath each entry. Always check the generated citation against the source.