定量分析_大百科全书条款.doc

Quantitative Research- An Entry for the Encyclopedia of Social Work, 20th Edition(New York: The Oxford University Press)Shenyang Guo, Ph.D.AbstractThis entry describes the definition, history, theories, and applications of quantitative methods in social work research. Unlike qualitative research, quantitative research emphasizes precise, objective, and generalizable findings. Quantitative methods are based on numerous probability and statistical theories with rigorous proofs and support from both simulated and empirical data. Regression analysis plays a paramount important role in contemporary statistical methods, which include event history analysis, generalized linear modeling, hierarchical linear modeling, propensity score matching, and structural equation modeling. Quantitative methods can be employed in all stages of a scientific inquiry ranging from sample selection to final data analysis.Key words: Event history analysis, generalized linear modeling, hierarchical linear modeling, propensity score matching, regression, structural equation modelingQuantitative research is the systematic examination of social phenomena using statistical models and mathematical theories to develop, accumulate, and refine the scientific knowledge base. Unlike qualitative research, quantitative research emphasizes precise, objective, and generalizable findings (Rubin and Babbie 2001), and is characterized by hypothesis testing using large samples, standardized measures, a deductive approach, and rigorously structured data collection instruments (Marlow 1993). Examining the relationship of one, two, or multiple variables, quantitative analysis can be either descriptive (i.e., delineating the interrelation of factors influencing the study phenomena) or explanatory (i.e., defining the mechanisms generating the phenomena). Whereas the results of qualitative research usually cannot be generalized beyond the study sample, the results of quantitative research on tested practices can be applied to whole population, and provide evidence to support policy development promoting social justice. Quantitative research emerged from the positivist tradition developed in the 1820s by French philosopher Auguste Comte, who applied principles of the Scientific Revolution to practical social purposes. In contemporary social sciences, logical positivism is often narrowly defined by equating it with the hypothetic-deductive approach (Grinnell 1997). The recent philosophical shift among the helping professions emphasizing evidence-based practices has propelled the use of quantitative methods in social work research (Gambrill 2003).Theories and Applications Quantitative methods are based on numerous probability and statistical theories. These theories are derived analytically with rigorous proofs, and supported by both simulated and empirical data. For instance, the central limit theorem forms the foundation of probability-sampling techniques. Three proven relationships form the theorems core: (a) between the mean of a sampling distribution and the mean of a population; (b) between the standard deviation of a sampling distribution (i.e., standard error) and the standard deviation of a population; and (c) between the normal sampling distribution and the possible non-normal population distribution (Guo and Hussey 2004).Quantitative methods can be employed in all stages of a scientific inquiry ranging from sample selection to final data analysis. Various methods can be applied to the different stages of research and project development. To develop valid and reliable measurement instruments, researchers use Cronbachs alpha, the generalizability theory, exploratory factor analysis, confirmatory factor analysis, item response theory, and other psychometric approaches (Cronbach et al. 1972; Lord 1980; Thompson 2004). Probability sampling methods, such as simple random sampling, systematic sampling, stratified sampling, clustered sampling, and multistage clustered sampling (Cochran 1977), are used to select a sample representative of the study population. However, researchers also use nonprobability methods of sample selection (i.e., sample selection is not based on a predetermined probability, rather on a variety of non-statistical reasons such as research purpose, convenience, or subjective judgment) with a caveat about statistical inferences (Guo and Hussey 2004). A meta-analysis may be used by researchers in reviewing prior studies of a topic: this approach allows the mean effect size (i.e., the average strength of association between variables) to be calculated across the previous studies (Hunter and Schmidt 2004). Researchers looking to increase the internal validity of a study evaluating the effectiveness of a treatment program, may chose a randomized clinical trial, or quasi-experimental design, to control for extraneous factors (Shadish, Cook, and Campbell 2002). Quasi-experimental designs are typically used in conjunction with analytical strategies such as statistical control, ex post matching, and propensity score matching that enhance internal validity (Guo, Barth, and Gibbons 2006). After data is collected, numerous analytical methods are applied to describe data and to test/confirm research hypotheses, including (a) univariate methods (i.e., measures depicting central tendency and dispersion); (b) bivariate methods (e.g., cross-tabulation with chi-square or nonparametric tests, mean comparisons with independent t test or analysis of variance, and product-moment correlation analysis Kiess 2002); and (c) multivariate methods (e.g., analysis of covariance, multivariate analysis of variance, multivariate analysis of covariance, multiple regression analysis Neter et al. 1996, generalized linear modeling Long 1997, event history analysis Allison 1995, hierarchical linear modeling Raudenbush and Bryk 2002, structural equation modeling Bollen 1989, single-subject time series analysis Nugent, Sieppert, and Hudson 2001). Furthermore, in multivariate analysis of data with missing values, researchers use expectation-maximization or multiple-imputation approach to impute missing data. Such procedures often assume that missing data are missing at random or are missing at completely random (Little and Rubin 2002). In evaluating a studys statistical power, researchers conduct power analysis that essentially focuses on the balance of four elements: statistical power or the ability of rejecting a false hypothesis, statistical significance or fixing the probability of making a type I error at a low level, sample size, and effect size (Cohen 1988). Among all statistical approaches, the ordinary-least-square (OLS) regression model is perhaps most important because it serves as the foundation for advanced models and is the key to understanding multivariate analysis (Neter et al. 1996). OLS is a technique used to characterize the relationship between a dependent variable (i.e., outcome or response variable) and a set of independent variables (i.e., explanatory variables). When applying the OLS regression model, a user makes five basic assumptions about the way in which observations are generated: (a) the dependent variable is a linear function of a specific set of independent variables, plus a disturbance; (b) mean value of the disturbance term is zero; (c) the disturbance terms all have the same variance and are not correlated with one another; (d) the observations on the independent variable are considered fixed in repeated samples; and (e) the number of observations is greater than the number of independent variables, and there are no perfect linear relationships between the independent variables (Kennedy 2003). These assumptions are crucial to a consistent and unbiased estimation of regression model. In practice, researchers often conduct statistical tests to detect violations of these assumptions, and take remedial measures if harmful violations exist. A regression coefficient estimated by such a model reveals the net relationship between an independent variable and the dependent variable: the value of a regression coefficient indicates the amount of change in the dependent variable that is produced by a one-unit increase in the independent variable, while holding all other independent variables constant. An R-square statistic is a measure of explanatory power of the regression model, indicating the proportion of variation in the dependent variable that is accounted for or explained by the independent variables included in the model. Advanced Statistical MethodsOver the course of the past 25 years, quantitative methods in social work research have undergone a significant change driven primarily by the development of user-friendly software that enabled practical application of new statistical methods. The quantitative methods have been further refined by the proliferation of studies that apply these methods to solving challenging problems in social behavioral research. The following provides an overview of advanced statistical models that have been increasingly adopted by social work researchers. Event history analysis (EHA, i.e., survival analysis) is a class of statistical methods for studying the occurrence and timing of events. A key feature of event-history data is censoring, which refers to nonoccurrence of the event under study by the end of a study period (i.e., right censoring), or occurrence of an event that differs from the study event before the end of a study period (i.e., random censoring under the non-informative assumption), or the time origin of event is unknown (i.e., left censoring). The life-table and Kaplan-Meier methods are descriptive approaches to event-history data. The Cox proportional hazards model (i.e., Cox regression) is the most popular model in EHA that tests influences of multiple covariates on timing of event occurrence. The Cox regression analyzes an unobserved variable, commonly called a hazard rate, as the dependent variable. This rate is posited as the instantaneous probability of an event occurring, which translates the length of time it takes an event to occur into a rate expressing the speed at which it occurs within a prespecified period. The hazard rate can be linked to a set of independent variables in the Cox regression. When all other variables are held constant, this allows an assessment of the association between each variable and the hazard rate and of whether this association is statistically significant. The model allows the inclusion of time-varying covariates, that is, covariates that may change in value over the course of the study period. Other EHA models include parametric regression models that assume certain type of probability distribution about survival times, discrete-time model that applies a binary logistic regression to “person-time” data, and discrete-time model that applies a multinomial logit model to “person-time” and multiple-event data (Allison 1995). Recent advances in EHA center on statistical methods handling multivariate failure time data (Lin 1994). Two types of such models (i.e., frailty models and marginal models) are developed to correct for bias in significance testing induced by clustering of event times. Therefore, these models may be viewed as EHA of multilevel data (Guo and Wells 2003). EHA has been widely employed in social work research, particularly in the fields of child welfare, welfare policy, evaluation of welfare-to-work programs, marriage and family, and mental health. Hierarchical linear modeling (HLM, i.e., random effects model or mixed effects model) is a method for analyzing nested or clustered data. OLS regression is inappropriate for such analysis because of the correlation of outcome variables among individuals within the same group. However, HLM uses random effect (i.e., random intercept or random slope), a lump sum of unobserved variables measuring extra heterogeneity for each high-level unit, to correct for bias in significant testing induced by data clustering (Raudenbush and Bryk 2002). Thus, HLM models are extremely useful in testing hypotheses about multilevel influences of study variables on the outcome variable, or testing hypotheses regarding the multilevel influences of individual and group characteristics on change trajectories of an outcome. For instance, to model the change of students outcome over time, an analyst may employ a 3-level hierarchical model. At Level 1, each students change is represented by an individual growth trajectory based on a unique set of predictors (i.e., mean at baseline, linear or curvilinear terms measuring rate of change, and time-varying covariates). These individual growth parameters then become a set of outcome variables in a Level 2 model that are regressed on time-fixed individual characteristics. The Level 2 parameters (i.e., impacts of individual characteristics) become a set of outcome variables in the Level 3 model, which examines the interaction of classroom characteristics and individual characteristics. HLM has several advantages for analysis of longitudinal data. First, responses on any outcome variable from the same individual over time will be correlated, which violates the assumption of independent observations embedded in most statistical models dealing with cross-sectional data. However, HLM accounts for this correlation. Second, when applying conventional linear models to longitudinal data, analysts generally underestimate the standard errors of the impacts, and may erroneously assume statistical significance. HLM not only effectively handles this problem but also others inherent in longitudinal data, such as time-varying predictors, unequal groups at data points over time, and the need to control for the effects of potentially confounding independent variables (Raudenbush and Bryk 2002; Diggle, Liang, and Zeger 1994; Lindsey 1993). Social work research often involves grouped data (e.g., sibling groups, mother-child dyads, neighborhoods) and longitudinal data; therefore, it is important to use HLM to perform rigorous tests of research hypotheses (Guo 2005).Multiple regression models for categorical and limited dependent variables are designed to analyze dependent variables that are binary, multicategorical, ordinal, counted, censored, or from truncated populations (Long 1997). A fundamental difference of these models from OLS regression is that they are nonlinear. Typically, in such models researchers use a link function to transform the original dependent variable. Although the dependent variable is not a linear function of independent variables, the transformed variable through the link function is. For this reason, such models are also known as generalized linear models. Depending on the distribution of the original dependent variable, the analyst may choose different link functions. Hence, there are six models defined by the type of dependent variable and the nature of link function: (a) binary logit and probit models; (b) multinomial logit and probit models; (c) ordered logit and probit models; (d) negative binomial and Poisson models; (e) tobit model; and (f) truncated model. Categorical and limited dependent variables are common in social work research because outcome variables are typically binary (e.g., presence or absence), ordinal (e.g., disagree, neutral, or agree), multicategorical (e.g., multiple reasons for exiting from foster care: reunification, adoption, guardianship), and counted (e.g., number of times using services). A review of social work applications of these models from 1990 through 1999 shows the importance of (a) recognizing the nonlinear nature of models to interpret a nonlinear regression coefficient with caution; (b) understanding the difference between maximum likelihood approach and OLS approach to use appropriate sample size; (c) understanding statistics analogous to F tests (e.g., Wald, likelihood ratio, and Lagrange multiplier tests) to perform significance testing promptly; and (d) understanding pseudo R-square measures and debates concerning their merit (Orme and Buehler 2001).Propensity Score Matching (PSM) is an approach to controlling for selection bias. When experimental designs are infeasible, researchers must rely on observational data to discern differential impacts of social services on treated and untreated clients. More generally, when assignment to conditions is nonrandom, analyses of services data require special procedures to correct biased selection into conditions, and to obtain an accurate estimation of counterfactuals (i.e., outcomes that would have been observed for participants had they not participated). The PSM approach is essentially a two-stage analysis that includes (a) the creation of a matched sample using logistic regression and matching procedures (such as nearest-neighbor matching within caliper, Mahalanobis metric matching, or other approaches), and (b) a follow-up multivariate analysis based on the matched sample (Rosenbaum and Rubin 1983). Recently, economists developed propensity score analysis using nonparametric regression (i.e., kernel or local linear matching) that analyzes pre- and post-intervention data (Heckman, Ichimura, and Todd 1997), and matching estimators that impute the missing counterfactual by using average outcome for individuals with “similar” values on observed covariates (Abadie et al. 2004). Increasingly, the PSM approach has been applied in social work evaluations, particularly in studies using observational data to assess service effectiveness (Guo, Barth, and Gibbons 2006). Structural equation modeling (SEM, i.e., covariance structure analysis, or analysis of moment structures) is a class of methodologies that seeks to represent hypotheses about the means, variances, and covariances of observed data in terms of a smaller number of “structural” parameters defined by a hy