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What you will learn in Grokking Statistics

A friendly guide for beginners

by Thomas Nield

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Chapter by chapter

Concepts explained in this book

• meanA measure of central tendency calculated as the arithmetic average of numerical observations.
• statisticsThe discipline of collecting, analyzing, interpreting, and reasoning from data to describe phenomena and infer broader conclusions.
• biasModel bias is systematic prediction error arising when a model's rigid assumptions prevent it from adequately representing the data.
• p-valueA p-value is a probability, calculated under the null hypothesis, of obtaining a result at least as extreme as the observed result.
• null hypothesisA hypothesis stating that a claimed population value or relationship represents the status quo to be evaluated.
• hypothesis testingA statistical procedure for evaluating evidence against a specified null hypothesis about a population or data-generating process.
• standard deviationThe nonnegative square root of variance, measuring typical dispersion in the original units of a variable.
• alternative hypothesisA hypothesis that challenges the null hypothesis by asserting a different population value or relationship.
• linear regressionA regression method that models a dependent variable as a linear function of one or more predictors.
• critical z-valueA cutoff value from a reference distribution that determines the boundary of a statistical confidence interval or decision region.
• continuous distributionA continuous distribution is a probability distribution whose variable can take values across a continuous range rather than only distinct countable values.
• Pearson correlation coefficientPearson correlation is the standardized covariance-based measure of linear association between two numerical variables.
• correlationA correlation coefficient is a numerical measure summarizing the strength and direction of association between two variables.
• z-scoreA standardized score expressing how many standard deviations an observation lies above or below a distribution's mean.
• confidence intervalA confidence interval is an interval estimation procedure that expresses uncertainty about an unknown population parameter under a specified confidence level.
• samplingSampling is the process of selecting observations from a population to form a sample for analysis or experimentation.
• class imbalanceAn imbalanced dataset has substantially unequal numbers of observations across its classes.
• logistic regressionA regression method that models the probability of a categorical outcome using a logistic link function.
• sigmoidAn S-curve is a sigmoid-shaped relationship in which growth is initially rapid, then slows toward a plateau.
• one-sided testA one-tailed hypothesis test that treats an unusually large deviation in one specified direction from the null value as evidence against the null hypothesis.
• sample sizeSample size is the number of observations included in a sample.
• standard normal distributionA standard normal distribution is a normal distribution with mean zero and standard deviation one.
• Central Limit TheoremA theorem stating that, under suitable conditions, the distribution of sample means approaches a normal distribution as sample size increases, regardless of the population distribution's shape.
• thresholdA cutoff probability used to convert a predicted probability into a categorical decision.
• hypothesisA hypothesis is a proposed explanation or relationship that can be evaluated with evidence.
• probability distributionA probability function assigns a probability to an event or possible outcome.
• sampling distributionThe probability distribution of a statistic, such as the mean, across repeated samples from a population.
• recallTrue positive rate is the proportion of positive instances correctly classified as positive.
• normal distributionA normal distribution is a continuous probability distribution characterized by a symmetric bell-shaped curve determined by its mean and standard deviation.
• probability densityA probability density function is a function whose values describe the relative likelihood of values of a continuous random variable.
• level of significanceThe significance threshold below which a p-value leads to rejection of the null hypothesis.
• linear relationshipA relationship in which changes in one variable are proportional to changes in another.
• cumulative distribution functionA function that returns the probability that a random variable is less than or equal to a specified value.
• statistical sampleA sample is a subset of observations selected from a larger population for statistical analysis.
• student's t-distributionA t-distribution is a family of continuous probability distributions used for inference about means when population variability is estimated from a small sample.
• probability theoryProbability is the mathematical framework for quantifying the likelihood of possible outcomes under uncertainty.
• interquartile rangeThe difference between the third and first quartiles, representing the spread of the middle half of observations.
• confounderA confounding variable is an unmodeled variable associated with both a predictor and an outcome that can distort their apparent relationship.
• heteroscedasticityHeteroscedasticity is the condition in which the variance of a response changes across the values of an independent variable.
• two-tailed testA two-tailed hypothesis test treats unusually large deviations in either direction from the null value as evidence against the null hypothesis.
• populationA population is the complete set of filament units or production sources about which the analysis seeks to draw conclusions.
• incentive structureAn incentive is a reward, penalty, or motivating condition that encourages a person or group to take a particular action.
• dataData is a collection of recorded observations, measurements, or other information.
• statistical analysisThe practical process of collecting, analyzing, interpreting, and quantifying numerical data.
• p-hackingP-hacking is the selective analysis or threshold manipulation of data to obtain or present a statistically significant result.
• varianceA measure of dispersion equal to the average squared deviation from a distribution's mean.
• PythonPython is a general-purpose, high-level programming language with dynamic typing and extensive support for scientific and data-oriented computing.
• area under the curveThe area under the curve is the area beneath a receiver operating characteristic or precision-recall curve, summarizing performance across thresholds.
• precision-recall curveA precision-recall curve plots a classifier's precision against its recall across decision thresholds.
• receiver operating characteristicA receiver operating characteristic curve plots a classifier's true-positive rate against its false-positive rate across decision thresholds.
• cross-validationCross-validation repeatedly partitions data into complementary training and evaluation folds to assess model performance.
• train_test_splittrain_test_split is a scikit-learn function that randomly partitions arrays or datasets into training and testing subsets.
• binomial distributionA binomial distribution gives the probabilities of obtaining a specified number of successes in a fixed number of independent Bernoulli trials.
• residual errorA residual is the difference between an observed response value and the value predicted by a fitted model.
• proportionThe fraction or percentage of a population possessing a specified categorical attribute.
• false positiveA statistical error in which a null hypothesis is rejected when it is true.
• data miningData mining is the process of discovering patterns or relationships by analyzing data, often before formulating a specific hypothesis.
• data collection coverageData coverage is the extent to which collected data represent the relevant situations and conditions within an operating domain.
• operational design domainAn operating domain is the environment, context, and range of conditions in which an automated system is expected to function effectively.
• predicted valueA predicted value is the outcome estimated by a model for an observation's input values.
• exponential distributionThe exponential distribution is a continuous probability distribution commonly modeling waiting times between events in a constant-rate Poisson process.
• false-positive rateFalse-positive rate is the proportion of negative instances incorrectly classified as positive.
• confusion matrixA confusion matrix is a table that cross-tabulates predicted classes against actual classes and counts correct and incorrect classifications.
• confirmation biasThe tendency to favor, seek, or interpret evidence in ways that support an existing belief or desired conclusion.
• probability mass functionA function that assigns a probability to each possible value of a discrete random variable.
• simulationA simulation is a computational procedure that generates artificial outcomes according to specified rules or probability models.
• extrapolationExtrapolation is the estimation of values outside the observed data range by extending an inferred pattern.
• degree of beliefA belief is a person's degree of credence in a proposition or the likelihood of an event.
• discretizationBinning is the process of grouping continuous or discrete observations into intervals and summarizing each interval.
• alpha regionA tail region of a reference distribution containing the total probability assigned to the rejection rule.
• critical rangeThe interval of test-statistic values that is not sufficiently extreme to reject the null hypothesis.
• critical thinkingDeliberate evaluation of claims, evidence, assumptions, and reasoning before accepting a conclusion.
• beta distributionA continuous probability distribution over probabilities of success, parameterized by the observed numbers of successes and failures.
• medianThe middle value of an ordered set of observations, or the midpoint of the two middle values when the set has even size.
• selection biasSelection bias is systematic distortion caused by including some groups in a sample more readily than others, making those groups overrepresented.
• degree of freedomDegrees of freedom are the number of independent values available to estimate a quantity after accounting for constraints.
• margin of errorA margin of error is the amount added to and subtracted from a point estimate to form an interval estimate.
• binary outcomeA binary outcome is an outcome restricted to two possible categories, such as yes and no.
• floating-point valueA floating-point value is a computer representation of a real number using a significand and an exponent, subject to finite precision.
• artificial intelligenceThe field concerned with building systems that perform tasks associated with human intelligence, such as reasoning, perception, and learning.
• natural numberA whole number is a nonnegative integer, including zero and excluding negative values and fractional values.
• self-selection biasSelf-selection bias is distortion caused when individuals' choice to participate in a study is related to their characteristics or outcomes.
• empirical ruleA rule stating that approximately 68%, 95%, and 99.7% of observations from a normal distribution lie within one, two, and three standard deviations of the mean, respectively.
• uncertaintyThe lack of certainty about a value, outcome, or conclusion inferred from incomplete or variable data.
• black boxA black-box model is a model whose internal decision process is not readily understood or inspected by its users.
• data collectionData collection is the systematic process of obtaining observations, measurements, or records for a defined purpose.
• false negativeA false negative is an incorrect negative classification in which a system fails to indicate that an event is present.
• independent sampleAn independent sample is a sample whose observations are collected separately from those of another sample, typically from a separate population.
• discrete distributionA probability distribution whose possible outcomes form a finite or countably infinite set of distinct values.
• negative correlationA negative correlation is a relationship in which higher values of one variable tend to occur with proportionally lower values of another.
• histogramA histogram is a chart that divides numerical data into equal-width intervals and displays the count in each interval.
• right-skewed distributionRight skew is an asymmetric distribution shape with most observations at lower values and a long tail toward higher values.
• training data biasData bias is systematic distortion in collected or represented data that causes analyses or models to produce unfair or unrepresentative results.
• Law of Truly Large NumbersThe principle that a sufficiently large collection of opportunities makes the occurrence of even extremely unlikely events probable somewhere.
• symmetrySymmetry is a property in which corresponding parts of a distribution mirror one another around a center.
• scipy.stats.norm.cdfA SciPy function that returns the cumulative distribution function value for a normal distribution.
• inverse cumulative density functionA percent-point function returns the value whose cumulative distribution up to that value equals a specified probability.
• missing valueMissing data consists of observations or variable values that are absent from a dataset when they are expected or needed.
• scientific methodThe scientific method is a systematic approach that formulates an objective or question before collecting and analyzing evidence.
• real numberA real number is any number that can be represented as a point on the continuous number line.
• f-scoreThe F-measure is a classification metric that combines precision and recall using their harmonic mean.
• precisionPrecision is the proportion of predicted positive cases that are actually positive.
• labelA categorical value assigned to an observation to represent its class or outcome.
• diminishing returnsDiminishing returns is a pattern in which each additional input produces a progressively smaller increase in output.
• sum of squaresThe sum of squares is a quantity formed by adding squared residuals or deviations to measure model error.
• Monte Carlo simulationA Monte Carlo simulation is a computational simulation method that models uncertain real-world processes by repeatedly generating random outcomes from probability distributions.
• maximum likelihood estimationA parameter-estimation technique that selects parameter values maximizing the likelihood of the observed data.
• scikit-learnscikit-learn is a Python library providing machine-learning algorithms and utilities for data analysis and modeling.
• tensor reshapingA NumPy array operation that changes an array’s dimensions without changing its element values.
• validation setA validation dataset is a held-out dataset used to evaluate model choices after training and iterative testing but before final assessment.
• independent variableAn independent variable is a predictor or input variable whose relationship with an outcome is modeled.
• data torturingRepeated or selective manipulation and analysis of data to obtain a desired finding.
• ethical problemA situation in which statistical practice creates a conflict involving harm, honesty, responsibility, or fairness.
• model torturingRepeated or selective modification of a statistical model until it produces a preferred result.
• process assumptionAn implicit or explicit belief about how a data-generating or analytical process operates.
• statistical abuseThe misleading use or manipulation of statistical analysis to support a preferred conclusion while obscuring weaknesses in the evidence.
• statistical significanceA result property indicating that an observed pattern would be relatively unlikely under a specified null model.
• linear componentThe linear component of a logistic function is the linear predictor whose value equals the outcome's log-odds.
• logitThe logit function maps a probability to the natural logarithm of its odds, log(p/(1-p)).
• odds ratioAn odds ratio is the quotient of two odds, measuring how the relative likelihood of an event changes between conditions.
• SQLiteSQLite is a self-contained, serverless relational database engine that stores an entire database in a single file.
• linregresslinregress is a SciPy statistical function that fits a simple linear regression and returns its estimated statistics.
• machine learningThe field and set of methods for learning predictive or descriptive patterns from data.
• human-in-the-loopHuman in the loop is a system pattern in which people participate in reviewing, labeling, guiding, or validating automated processing.
• Poisson distributionThe Poisson distribution is a discrete probability distribution for the number of events occurring in a fixed interval under a constant-rate independent-event assumption.
• anomalyAn outlier is an observation that differs markedly from most other observations in a dataset.
• slopeA slope is a regression coefficient describing the change in the predicted response for a one-unit change in an input variable.
• analysis-drivenAn analysis-driven approach prioritizes examining data provenance, biases, missingness, and context rather than merely accepting reported values.
• percentileA percentile is a value below which a specified percentage of observations in an ordered dataset falls.
• evaluation datasetA held-out dataset used to evaluate a trained model on observations not used for fitting it.
• classifierA classification model predicts a categorical label or class for an observation rather than a continuous numerical value.
• statistical modelingStatistical modeling is the process of representing relationships or data-generating processes with mathematical or probabilistic models.
• generalizationGeneralization is the ability of a fitted model to perform appropriately on new data beyond the observations used to fit it.
• one-vs-rest strategyA multiclass classification strategy that trains one binary classifier per category against all other categories.
• replicability crisisThe reproducibility crisis is a scientific reliability problem in which published findings cannot be consistently replicated by other researchers.
• outlier removalOutlier removal is the exclusion of observations identified as unusually distant from the rest of a dataset.
• point estimateA single numerical estimate of an unknown population parameter.

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