按方法、领域与证据探索科学。

Panel-based correlational research

Panel-based correlational research follows the same individuals, organizations, or units across multiple time points and quantifies associations among variables within that longitudinal structure. Unlike a one-shot correlational survey, the panel design captures temporal ordering and within-unit change, enabling resear

research design

Panel-based Model Testing Research

Panel-based model testing research combines the longitudinal power of panel survey designs with the confirmatory rigor of structural model testing — such as structural equation modeling (SEM), path analysis, or confirmatory factor analysis — applied to data collected from the same units (individuals, firms, countries)

research design

Panel-based Relational Survey

A panel-based relational survey is a quantitative design that recruits the same group of respondents and surveys them at two or more time points to examine how variables relate to, predict, or co-vary with one another over time. By combining the relational goal of uncovering associations among variables with the panel

econometrics

PANIC

PANIC (Panel Analysis of Non-stationarity in Idiosyncratic and Common Components) is a second-generation panel unit root test introduced by Bai and Ng (2004). It decomposes each panel series into common factors and idiosyncratic components, then tests for unit roots in each part separately, making it robust to cross-se

statistics

Parametric Bootstrap

The parametric bootstrap is a resampling method that estimates standard errors and confidence intervals by drawing repeated samples from a parametric model that has been fitted to the data. Developed in the bootstrap literature of Efron and Tibshirani (1993) and Davison and Hinkley (1997), it replaces analytic derivati

statistics

Partial Correlation

Partial correlation measures the linear relationship between two continuous variables after removing the shared influence of one or more control variables. The technique was formalised by R. A. Fisher in 1924 and is the standard approach whenever a researcher suspects that a third variable inflates or suppresses the ob

psychometrics

Partial Least Squares Structural Equation Modeling

PLS-SEM is a variance-based approach to structural equation modeling developed by Herman Wold (1985) that estimates latent variable models by maximizing the variance explained in dependent variables. Unlike covariance-based SEM, PLS-SEM is particularly useful for exploratory research, small to medium samples, complex m

research design

Participatory Multilevel Mixed Methods

Participatory multilevel mixed methods is a research design that combines the collaborative ethos of participatory research with the analytical depth of multilevel data collection and the complementary power of mixed quantitative and qualitative methods. It is widely applied in community health, education, and social i

bayesian

Particle Filter

The particle filter, introduced by Gordon, Salmond, and Smith in 1993, is a sequential Monte Carlo algorithm that approximates the Bayesian filtering distribution for nonlinear and non-Gaussian state-space models. Rather than tracking a single best estimate, it maintains a cloud of N weighted random samples — particles

bayesian

Particle Filter with Measurement Error

A particle filter with explicit measurement error is a Sequential Monte Carlo algorithm that tracks the hidden state of a nonlinear, non-Gaussian dynamic system while formally modelling noise in the observations. A population of weighted random samples (particles) represents the posterior state distribution at each tim

bayesian

Particle Filter with Missing Data

A particle filter adapted for state-space models in which some observations are absent. The algorithm tracks a hidden state over time using a cloud of weighted random samples (particles); when a time step has no observed value, the weight-update step is simply skipped, so the particles propagate forward using only the

statistics

Path Analysis

Path analysis tests a researcher-specified causal diagram among observed variables by decomposing their intercorrelations into direct effects, indirect (mediated) effects, and spurious associations. Developed by Sewall Wright in 1921, it is the observed-variable special case of structural equation modeling and remains

statistics

Pearson Correlation

The Pearson product-moment correlation coefficient (r) is a parametric measure of the direction and strength of the linear association between two continuous variables. Introduced by Karl Pearson in 1895, it remains the most widely used bivariate correlation statistic in the social, health, and natural sciences. The co

statistics

Perceptual and Preference Mapping

Perceptual and preference mapping is a family of multivariate techniques that simultaneously positions competing objects—brands, products, or stimuli—and respondent preferences within a common low-dimensional space. Introduced systematically by Hauser and Koppelman (1979), the approach lets researchers visualize how co

statistics

Permutation Test

The permutation test is a nonparametric resampling procedure that builds the sampling distribution of a test statistic directly from the data by repeatedly shuffling the group labels. Developed in the resampling tradition and treated systematically by Good (2005) and Edgington & Onghena (2007), it requires no parametri

econometrics

Pesaran CD Test

The Pesaran CD test is a general diagnostic procedure for detecting cross-sectional dependence in panel data models. Developed by M. Hashem Pesaran (2021), it is applicable to both balanced and unbalanced panels with large N and T, and retains validity under heterogeneous slope coefficients. The test is widely adopted

econometrics

Pesaran-Timmermann Test

Introduced by Pesaran and Timmermann (1992), the PT test is a nonparametric procedure that evaluates whether a forecasting model correctly predicts the direction (sign) of a target variable more often than would be expected by chance. It is widely used in financial econometrics and macroeconomic forecasting to assess t

econometrics

Phillips-Ouliaris Test

The Phillips-Ouliaris test, introduced by Phillips and Ouliaris in their 1990 Econometrica article, is a residual-based nonparametric procedure for testing the null hypothesis of no cointegration among a set of integrated I(1) time series. It corrects OLS residuals from a cointegrating regression for serial correlation

econometrics

Phillips-Perron Test

The Phillips-Perron test, proposed by Peter Phillips and Pierre Perron in 1988, tests for a unit root in a time series, like the Augmented Dickey-Fuller test, but corrects for autocorrelation and heteroskedasticity in the errors non-parametrically rather than by adding lagged differences. It runs a simple Dickey-Fuller

econometrics

Phillips-Perron unit root test

The Phillips-Perron (PP) test is a nonparametric unit root test for time series that corrects for serial correlation and heteroscedasticity in the error term without adding lagged differences. Introduced by Phillips and Perron (1988), it applies a kernel-based long-run variance estimator to adjust the Dickey-Fuller sta

experimental design

Pilot A/B Test

A Pilot A/B test is a small-scale, preliminary split-test experiment run before a full A/B test to assess feasibility, estimate effect sizes, detect operational problems, and validate measurement instruments. Participants are randomly assigned to a control condition (A) and a treatment condition (B), but the study is e

survey methodology

Pilot Multistage Sampling

Pilot multistage sampling applies a small-scale trial run of a multistage sampling design before committing to the full fieldwork. The researcher draws a mini-version of the hierarchical sample — typically spanning the same stages (e.g., regions, then clusters, then individuals) — to test frame quality, stage-transitio

survey methodology

Pilot-tested API-based data collection

Pilot-tested API-based data collection is a structured digital data-gathering approach in which a researcher designs an API query or harvesting script and then runs a small-scale trial before executing the full collection. The pilot phase exposes authentication issues, rate-limit constraints, schema inconsistencies, an

survey methodology

Pilot-tested experiment log

A pilot-tested experiment log is a structured research instrument — a systematic journal of experimental procedures, observations, and results — that has been trialed with a small representative sample before full deployment. The pilot phase identifies ambiguous recording fields, impractical time demands, or inconsiste

survey methodology

Pilot-tested field notes

Pilot-tested field notes combine the classical ethnographic practice of systematic observational recording with a deliberate pre-validation phase. Before the main data collection begins, the researcher conducts one or more trial observation sessions to test and refine the note-taking protocol — assessing categories, fo

survey methodology

Pilot-tested In-depth Interview

A pilot-tested in-depth interview is a qualitative data collection approach in which the interview guide is administered to a small number of participants before the main study, specifically to identify ambiguous questions, refine probes, estimate session duration, and verify that the protocol elicits rich, relevant na

survey methodology

Pilot-tested mobile experience sampling

Pilot-tested mobile experience sampling (mESM) is a data collection approach that combines smartphone-delivered, real-time self-report prompts — the Experience Sampling Method — with a structured pilot phase to validate the instrument, signal timing, burden level, and response quality before full deployment. The pilot

survey methodology

Pilot-tested Semi-structured Interview

A pilot-tested semi-structured interview combines the flexibility of semi-structured interviewing — a guide of open-ended questions allowing conversational depth — with a mandatory pre-study pilot phase in which the guide is trialled on a small subset of participants or informants. The pilot reveals ambiguous questions

survey methodology

Pilot-tested Sensor Data Collection

Pilot-tested sensor data collection is a structured data gathering approach in which sensor instruments — hardware or software-based devices that measure physical, environmental, physiological, or behavioral signals — are deployed in a small-scale trial before the main study. The pilot phase verifies sensor accuracy, c

survey methodology

Pilot-tested Survey

A pilot-tested survey is a structured questionnaire that has been administered to a small, representative sample before the main data-collection phase. The purpose is to detect problems with wording, response options, skip logic, or timing, allowing the researcher to refine the instrument before it reaches the full sam

causal inference

Placebo Test in Education Research

A placebo test is a falsification check used in quasi-experimental education research to validate a causal design. By applying the same estimator to a time period, group, or outcome where no real effect should exist, researchers verify that their identification strategy is not picking up spurious patterns. A statistica

statistics

Point-Biserial Correlation

The point-biserial correlation coefficient (r_pb) measures the strength and direction of the linear association between one naturally dichotomous variable (coded 0/1) and one continuous variable. It is a special case of the Pearson product-moment correlation formally derived by Tate (1954) in the Annals of Mathematical

econometrics

Poisson Regression

Poisson regression is a generalized linear model for count outcomes — events tallied as non-negative integers such as hospital admissions, accidents, or article counts. It models the log of the expected count as a linear function of the predictors, and is developed in the standard count-data treatment of Cameron and Tr

causal inference

Policy Evaluation Causal Impact Analysis

Policy Evaluation Causal Impact Analysis applies the Bayesian structural time-series (BSTS) framework of Brodersen et al. (2015) to estimate the causal effect of a policy intervention on aggregate outcomes. By constructing a synthetic counterfactual from pre-policy data and control covariates, it asks: what would have

causal inference

Policy Evaluation Placebo Test

A policy evaluation placebo test is a falsification check used in quasi-experimental research to validate a causal identification strategy. The researcher applies the same estimation method to a pseudo-treatment — a time period, group, or outcome where the real policy could not have had an effect — and checks that no s

statistics

Polynomial Regression

Polynomial regression is a regression method that models non-linear relationships by including squared and higher-degree terms of an explanatory variable, and it is a core tool of response surface analysis. As developed in Montgomery, Peck and Vining's Introduction to Linear Regression Analysis (2012), it remains linea

psychometrics

Polytomous Confirmatory Factor Analysis

Polytomous confirmatory factor analysis (CFA) tests a pre-specified factor structure when items have three or more ordered response categories (e.g., Likert scales). By working with polychoric correlations and robust estimators such as WLSMV, it avoids the distortions that arise when ordered categorical data are treate

psychometrics

Polytomous EFA

Polytomous exploratory factor analysis extends standard EFA to ordered categorical (Likert-type) response data by replacing the Pearson correlation matrix with a polychoric correlation matrix. It recovers the latent continuous variable that each polytomous item is assumed to reflect, yielding more accurate factor loadi

econometrics

Pooled Mean Group (PMG)

The Pooled Mean Group (PMG) estimator, introduced by Pesaran, Shin, and Smith (1999), is a panel data technique designed for dynamic heterogeneous panels where the long-run equilibrium relationship is common across groups but short-run dynamics and error variances are allowed to differ. It is particularly suited for ma

econometrics

Pooled OLS

Pooled OLS applies standard ordinary least squares to panel data by stacking all cross-sectional and time observations into a single dataset and ignoring the panel structure during estimation. It is the most transparent starting point for panel data analysis, widely used in economics, finance, and social sciences when

pharmacometrics

Population Pharmacokinetics

Population Pharmacokinetics (PopPK) is a nonlinear mixed-effects modeling framework that characterizes how drugs are absorbed, distributed, metabolized, and eliminated across a patient population, estimating both typical population parameters and the magnitude of between-subject variability. Introduced by Sheiner, Rose

statistics

Power analysis

Power analysis is a planning and evaluation technique that quantifies the probability of detecting a real effect of a given magnitude at a chosen significance level. It links four quantities — sample size, effect size, significance level (alpha), and statistical power (1 minus beta) — so that researchers can determine

statistics

Power Analysis for ANOVA

Power analysis for ANOVA is a prospective statistical technique that determines the minimum sample size needed to detect a specified group mean difference with a chosen probability. Formalized by Jacob Cohen in his 1988 monograph, it translates a researcher's effect size expectation — expressed as Cohen's f — along wit

statistics

Power Analysis for Proportions

Power analysis for proportion tests is a prospective sample-size planning method used to determine how many participants are needed to detect a meaningful difference between two (or one) proportions with a specified probability. Formalised by Jacob Cohen in his 1988 landmark text, it applies the arcsine transformation

statistics

Power Analysis for Regression

Power analysis for multiple regression is a pre-study procedure, formalised by Jacob Cohen (1988), that calculates the minimum sample size needed to detect a regression effect of a given size with adequate statistical power. It uses the anticipated R² (or the equivalent Cohen's f² effect size) and the number of predict

statistics

Power Analysis for t-test

Power analysis for the t-test is a sample size planning procedure that determines how many participants are required to detect a mean difference of a given magnitude with acceptable probability. Formalised by Jacob Cohen in his 1969 and 1988 editions of Statistical Power Analysis for the Behavioral Sciences, it links f

experimental design

Pragmatic A/B Test

A pragmatic A/B test is a randomized comparative experiment that evaluates two alternatives — a control (A) and a treatment (B) — under real-world operating conditions rather than tightly controlled laboratory settings. Rooted in the pragmatic-versus-explanatory trial distinction introduced by Schwartz and Lellouch in

epidemiology

Pragmatic Kaplan-Meier analysis

Pragmatic Kaplan-Meier analysis applies the non-parametric Kaplan-Meier product-limit estimator to time-to-event data collected under real-world or pragmatic conditions — diverse populations, routine clinical care, minimal exclusions, and standard-of-care comparators. Unlike explanatory trials designed to isolate a tre

finance

Principal Component Risk Factors

Risk Factor PCA is a dimension-reduction method that decomposes the return covariance matrix of many assets into a small set of orthogonal principal components interpreted as systematic risk factors. Litterman and Scheinkman (1991) used it to show that bond returns are driven by a few common factors, and Connor and Kor

econometrics

Probit Model

The probit model is a regression method for a binary (0/1) outcome that maps a linear index of the predictors through the standard normal cumulative distribution function to produce a probability. It is a classical discrete-choice alternative to logistic regression, developed in standard econometrics treatments such as

statistics

Process Capability Analysis

Process Capability Analysis quantifies how well a manufacturing or business process produces output within specified tolerance limits. Introduced formally by Victor Kane in 1986, it summarises process spread and centering into dimensionless indices — most notably Cp and Cpk — allowing engineers and quality managers to

econometrics

Prophet

Prophet is a Bayesian structural time series model introduced by Taylor and Letham at Facebook/Meta in 2018. It forecasts a continuous series by decomposing it into separate, interpretable trend, seasonality, and holiday components, and is designed to be approachable for analysts working at scale.

statistics

Proportion Test

The proportion test (z-test for proportions) is a parametric hypothesis test that compares one or two sample proportions against a reference value or each other. Grounded in the large-sample normal approximation formalized by Fleiss, Levin, and Paik (2003), it is the standard tool for binary outcome comparisons when sa

epidemiology

Prospective Competing Risks Analysis

Prospective competing risks analysis is an observational study design that follows participants forward in time from a well-defined starting point, recording all events — including those that prevent the primary event from occurring — and then estimates cause-specific incidence while correctly accounting for competing

epidemiology

Prospective Cox proportional hazards

Prospective Cox proportional hazards regression combines a forward-looking cohort design — in which participants are enrolled before outcomes occur and followed over time — with Cox's semi-parametric survival model. The method estimates how baseline covariates measured at enrollment influence the rate at which particip

research statistics

Publication Bias

Publication bias occurs when the results of a study influence whether the study is published. Typically, studies with statistically significant or positive results are more likely to be published than studies with non-significant or negative results, even if both are scientifically valid. This bias distorts the publish

econometrics

QARDL

QARDL (Quantile Autoregressive Distributed Lag) combines quantile regression with ARDL modeling to estimate conditional relationships at different points of the distribution, revealing heterogeneous short-run and long-run effects. Introduced by Koenker and Xiao (2006) and refined by Cho et al. (2015), it captures how t

research design

Qualitative-dominant multilevel mixed methods

Qualitative-dominant multilevel mixed methods design addresses research questions nested across two or more social levels — such as individuals within classrooms within schools — while assigning primary inferential weight to the qualitative strand. Quantitative data collected at one or more levels serve a supporting ro

econometrics

Quandt-Andrews Test

The Quandt-Andrews test, formalized by Andrews (1993), detects structural breaks in regression parameters when the breakpoint date is unknown a priori. It sweeps all candidate break dates within a trimmed interior of the sample, computes a Wald (or LM/LR) statistic at each candidate, and reports the supremum of those s

econometrics

Quantile Regression

Quantile regression models conditional quantiles of an outcome - the median, the 25th or 75th percentile, and so on - rather than the conditional mean that OLS targets. Introduced by Koenker and Bassett in 1978, it reveals how predictors act across the whole distribution, including its tails.