多元數(shù)據(jù)分析

內(nèi)容概要

　　《多元數(shù)據(jù)分析（英文版）（第7版）》是一本面向應用的經(jīng)典多元數(shù)據(jù)分析教材，自1979年出版第1版至今，深受讀者好評?！抖嘣獢?shù)據(jù)分析（英文版）（第7版）》循序漸進地介紹了各種多元統(tǒng)計分析方法，并通過豐富的實例演示了這些方法的應用。書中不僅涵蓋多元數(shù)據(jù)分析的基本方法，而且還介紹了一些新方法，如結構方程建模和偏最小二乘法等。

作者簡介

作者：（美國）海爾（Joseph F.Hair.Jr.） （美國）William C.Black （美國）Barry J.Babin 等海爾（Joseph F Hair，Jr.），于1971獲得佛羅里達大學市場營銷博士學位.現(xiàn)為肯尼索州立大學市場營銷系教授。他出版了四十多本書，包括《Marketing》、《Marketing Essentials》等。他是美國市場營銷協(xié)會、市場營銷科學學會、西南市場營銷協(xié)會和南方市場營銷學會委員。2004年他被美國市場營銷科學學會授予杰出教育獎，2007年被市場管理協(xié)會授予創(chuàng)新性市場營銷人才。William C.Black，于1980年獲得德州大學奧斯汀分校博士學位，現(xiàn)為路易斯安那州立大學工商管理學院市場營銷系教授。他的研究興趣包括多元統(tǒng)計、應用信息技術，以及與電子商務相關的市場原理的進展。他是《Journal of BusinessResearch》編審委員會成員。Barry J.Babin于1991年獲得路易斯安那州立大學工商管理學博士學位，現(xiàn)為路易斯安那理工大學市場營銷與定量分析學教授、商學院Max P.Watson教授。他主要研究零售的各個方面和服務管理。他還曾被美國市場營銷科學研究院和市場營銷學會評為杰出研究員。Rolph E.Anderson，擁有佛羅里達大學博士學位，現(xiàn)為Drexei大學工商管理學院R0yal H.Gibson Sr教授。他曾兩次獲得Drexel大學優(yōu)秀教師獎，并獲得過《Journal of Personal Selling＆Sales Management》杰出評論獎、Drexel大學商學院科研成就獎等。

書籍目錄

preface iii
about the authors v
　chapter 1 introduction: methods and model building
　　what is multivariate analysis?
　　multivariate analysis in statistical terms
　　some basic concepts of multivariate analysis
　　the variate
　　measurement scales
　　measurement error and multivariate measurement
　　statistical significance versus statistical power
　　types of statistical error and statistical power
　　impacts on statistical power
　　using power with multivariate techniques
　　a classification of multivariate techniques
　　dependence techniques
　　interdependence techniques
　　types of multivariate techniques
　　principal components and common factor analysis
　　multiple regression
　　multiple discriminant analysis and logistic regression
　　canonical correlation
　　multivariate analysis of variance and covariance
　　conjoint analysis
　　cluster analysis
　　perceptual mapping
　　correspondence analysis
　　structural equation modeling and confirmatory factor
analysis
　　guidelines for multivariate analyses and interpretation
　　establish practical significance as well as statistical
　　significance
　　recognize that sample size affects all results
　　know your data
　　strive for model parsimony
　　look at your errors
　　validate your results
　　a structured approach to multivariate model building
　　stage 1: define the research problem, objectives,
　　and multivariate technique to be used
　　stage 2: develop the analysis plan
　　stage 3: evaluate the assumptions underlying the multivariate
technique
　　stage 4: estimate the multivariate model and assess overall model
fit
　　stage 5: interpret the variate(s)
　　stage 6: validate the multivariate model
　　a decision flowchart
　　databases
　　primary database
　　other databases
　　organization of the remaining chapters
section i: understanding and preparing for multivariate
analysis
section ii: analysis using dependence techniques
section iii: interdependence techniques
section iv: structural equations modeling
　　summary 28 . questions 30 . suggested readings
　　references
section i understanding and preparing for multivariate
analysis
　chapter 2 cleaning and transforming data
　　introduction
　　graphical examination of the data
　　univariate profiling: examining the shape of the
distribution
　　bivariate profiling: examining the relationship between
variables
　　bivariate profiling: examining group differences
　　multivariate profiles
　　missing data
　　the impact of missing data
　　a simple example of a missing data analysis
　　a four-step process for identifying missing data and applying
remedies
　　an illustration of missing data diagnosis with the four-step
process
　　outliers
　　detecting and handling outliers
　　an illustrative example of analyzing outliers
　　testing the assumptions of multivariate analysis
　　assessing individual variables versus the variate
　　four important statistical assumptions
　　data transformations
　　an illustration of testing the assumptions underlying
multivariate analysis
　　incorporating nonmetric data with dummy variables
　　summary 88 . questions 89 . suggested readings
　　references
　chapter 3 factor analysis
　　what is factor analysis?
　　a hypothetical example of factor analysis
　　factor analysis decision process
　　stage 1: objectives of factor analysis
　　specifying the unit of analysis
　　achieving data summarization versus data reduction
　　variable selection
　　using factor analysis with other multivariate techniques
　　stage 2: designing a factor analysis
　　correlations among variables or respondents
　　variable selection and measurement issues
　　sample size
　　summary
　　stage 3: assumptions in factor analysis
　　conceptual issues
　　statistical issues
　　summary
　　stage 4: deriving factors and assessing overall fit
　　selecting the factor extraction method
　　criteria for the number of factors to extract
　　stage 5: interpreting the factors
　　the three processes of factor interpretation
　　rotation of factors
　　judging the significance of factor loadings
　　interpreting a factor matrix
　　stage 6: validation of factor analysis
　　use of a confirmatory perspective
　　assessing factor structure stability
　　detecting influential observations
　　stage 7: additional uses of factor analysis results
　　selecting surrogate variables for subsequent analysis
　　creating summated scales
　　computing factor scores
　　selecting among the three methods
　　an illustrative example
　　stage 1: objectives of factor analysis
　　stage 2: designing a factor analysis
　　stage 3: assumptions in factor analysis
　　component factor analysis: stages 4 through 7
　　common factor analysis: stages 4 and 5
　　a managerial overview of the results
　　summary 148 . questions 150 . suggested readings
　　references
section ii analysis using dependence techniques
　chapter 4 simple and multiple regression
　　what is multiple regression analysis?
　　an example of simple and multiple regression
　　prediction using a single independent variable:
　　simple regression
　　prediction using several independent variables:
　　multiple regression
　　summary
　　a decision process for multiple regression analysis
　　stage 1: objectives of multiple regression
　　research problems appropriate for multiple regression
　　specifying a statistical relationship
　　selection of dependent and independent variables
　　stage 2: research design of a multiple regression analysis
　　sample size
　　creating additional variables
　　stage 3: assumptions in multiple regression analysis
　　assessing individual variables versus the variate
　　methods of diagnosis
　　linearity of the phenomenon
　　constant variance of the error term
　　independence of the error terms
　　normality of the error term distribution
　　summary
　　stage 4: estimating the regression model and assessing overall
model fit
　　selecting an estimation technique
　　testing the regression variate for meeting the regression
assumptions
　　examining the statistical significance of our model
　　identifying influential observations
　　stage 5: interpreting the regression variate
　　using the regression coefficients
　　assessing multicollinearity
　　stage 6: validation of the results
　　additional or split samples
　　calculating the press statistic
　　comparing regression models
　　forecasting with the model
　　illustration of a regression analysis
　　stage 1: objectives of multiple regression
　　stage 2: research design of a multiple regression analysis
　　stage 3: assumptions in multiple regression analysis
　　stage 4: estimating the regression model and assessing overall
model fit
　　stage 5: interpreting the regression variate
　　stage 6: validating the results
　　evaluating alternative regression models
　　a managerial overview of the results
　　summary 231 . questions 234 . suggested readings
　　references
　chapter 5 canonical correlation
　　what is canonical correlation?
　　hypothetical example of canonical correlation
　　developing a variate of dependent variables
　　estimating the first canonical function
　　estimating a second canonical function
　　relationships of canonical correlation analysis to other
multivariate techniques
　　stage 1: objectives of canonical correlation analysis
　　selection of variable sets
　　evaluating research objectives
　　stage 2: designing a canonical correlation analysis
　　sample size
　　variables and their conceptual linkage
　　missing data and outliers
　　stage 3: assumptions in canonical correlation
　　linearity
　　normality
　　homoscedasticity and multicollinearity
　　stage 4: deriving the canonical functions and assessing overall
fit
　　deriving canonical functions
　　which canonical functions should be interpreted?
　　stage 5: interpreting the canonical variate
　　canonical weights
　　canonical loadings
　　canonical cross-loadings
　　which interpretation approach to use
　　stage 6: validation and diagnosis
　　an illustrative example
　　stage 1: objectives of canonical correlation analysis
　　stages 2 and 3: designing a canonical correlation analysis and
testing the assumptions
　　stage 4: deriving the canonical functions and assessing overall
fit
　　stage 5: interpreting the canonical variates
　　stage 6: validation and diagnosis
　　a managerial overview of the results
　　summary 258 . questions 259 . references
　chapter 6 conjoint analysis
　　what is conjoint analysis?
　　hypothetical example of conjoint analysis
　　specifying utility, factors, levels, and profiles
　　gathering preferences from respondents
　　estimating part-worths
　　determining attribute importance
　　assessing predictive accuracy
　　the managerial uses of conjoint analysis
　　comparing conjoint analysis with other multivariate methods
　　compositional versus decompositional techniques
　　specifying the conjoint variate
　　separate models for each individual
　　flexibility in types of relationships
　　designing a conjoint analysis experiment
　　stage 1: the objectives of conjoint analysis
　　defining the total utility of the object
　　specifying the determinant factors
　　stage 2: the design of a conjoint analysis
　　selecting a conjoint analysis methodology
　　designing profiles: selecting and defining factors and
levels
　　specifying the basic model form
　　data collection
　　stage 3: assumptions of conjoint analysis
　　stage 4: estimating the conjoint model and assessing overall
fit
　　selecting an estimation technique
　　estimated part-worths
　　evaluating model goodness-of-fit
　　stage 5: interpreting the results
　　examining the estimated part-worths
　　assessing the relative importance of attributes
　　stage 6: validation of the conjoint results
　　managerial applications of conjoint analysis
　　segmentation
　　profitability analysis
　　conjoint simulators
　　alternative conjoint methodologies
　　adaptive/self-explicated conjoint: conjoint with
　　a large number of factors
　　choice-based conjoint: adding another touch of realism
　　overview of the three conjoint methodologies
　　an illustration of conjoint analysis
　　stage 1: objectives of the conjoint analysis
　　stage 2: design of the conjoint analysis
　　stage 3: assumptions in conjoint analysis
　　stage 4: estimating the conjoint model and assessing overall
model fit
　　stage 5: interpreting the results
　　stage 6: validation of the results
　　a managerial application: use of a choice simulator
　　summary 327 . questions 330 . suggested readings
　　references
　chapter 7 multiple discriminant analysis and logistic
regression
　　what are discriminant analysis and logistic regression?
　　discriminant analysis
　　logistic regression
　　analogy with regression and manova
　　hypothetical example of discriminant analysis
　　a two-group discriminant analysis: purchasers versus
nonpurchasers
　　a geometric representation of the two-group discriminant
function
　　a three-group example of discriminant analysis: switching
intentions
　　the decision process for discriminant analysis
　　stage 1: objectives of discriminant analysis
　　stage 2: research design for discriminant analysis
　　selecting dependent and independent variables
　　sample size
　　division of the sample
　　stage 3: assumptions of discriminant analysis
　　impacts on estimation and classification
　　impacts on interpretation
　　stage 4: estimation of the discriminant model and assessing
overall fit
　　selecting an estimation method
　　statistical significance
　　assessing overall model fit
　　casewise diagnostics
　　stage 5: interpretation of the results
　　discriminant weights
　　discriminant loadings
　　partial f values
　　interpretation of two or more functions
　　which interpretive method to use?
　　stage 6: validation of the results
　　validation procedures
　　profiling group differences
　　a two-group illustrative example
　　stage 1: objectives of discriminant analysis
　　stage 2: research design for discriminant analysis
　　stage 3: assumptions of discriminant analysis
　　stage 4: estimation of the discriminant model and assessing
overall fit
　　stage 5: interpretation of the results
　　stage 6: validation of the results
　　a managerial overview
　　a three-group illustrative example
　　stage 1: objectives of discriminant analysis
　　stage 2: research design for discriminant analysis
　　stage 3: assumptions of discriminant analysis
　　stage 4: estimation of the discriminant model and assessing
overall fit
　　stage 5: interpretation of three-group discriminant analysis
results
　　stage 6: validation of the discriminant results
　　a managerial overview
　　logistic regression: regression with a binary dependent
variable
　　representation of the binary dependent variable
　　sample size
　　estimating the logistic regression model
　　assessing the goodness-of-fit of the estimation model
　　testing for significance of the coefficients
　　interpreting the coefficients
　　calculating probabilities for a specific value of the independent
variable
　　overview of interpreting coefficients
　　summary
　　an illustrative example of logistic regression
　　stages 1, 2, and 3: research objectives, research design, and
statistical assumptions
　　stage 4: estimation of the logistic regression model and
assessing overall fit
　　stage 5: interpretation of the results
　　stage 6: validation of the results
　　a managerial overview
　　summary 434 . questions 437 . suggested readings
　　references
　chapter 8 anova and manova
　　manova: extending univariate methods for assessing group
differences
　　multivariate procedures for assessing group differences
　　a hypothetical illustration of manova
　　analysis design
　　differences from discriminant analysis
　　forming the variate and assessing differences
　　a decision process for manova
　　stage 1: objectives of manova
　　when should we use manova?
　　types of multivariate questions suitable for manova
　　selecting the dependent measures
　　stage 2: issues in the research design of manova
　　sample size requirements—overall and by group
　　factorial designs—two or more treatments
　　using covariates—ancova and mancova
　　manova counterparts of other anova designs
　　a special case of manova: repeated measures
　　stage 3: assumptions of anova and manova
　　independence
　　equality of variance–covariance matrices
　　normality
　　linearity and multicollinearity among the dependent
variables
　　sensitivity to outliers
　　stage 4: estimation of the manova model and assessing overall
fit
　　estimation with the general linear model
　　criteria for significance testing
　　statistical power of the multivariate tests
　　stage 5: interpretation of the manova results
　　evaluating covariates
　　assessing effects on the dependent variate
　　identifying differences between individual groups
　　assessing significance for individual dependent variables
　　stage 6: validation of the results
　　summary
　　illustration of a manova analysis
　　example 1: difference between two independent groups
　　stage 1: objectives of the analysis
　　stage 2: research design of the manova
　　stage 3: assumptions in manova
　　stage 4: estimation of the manova model and assessing the overall
fit
　　stage 5: interpretation of the results
　　example 2: difference between k independent groups
　　stage 1: objectives of the manova
　　stage 2: research design of manova
　　stage 3: assumptions in manova
　　stage 4: estimation of the manova model and assessing overall
fit
　　stage 5: interpretation of the results
　　example 3: a factorial design for manova with two independent
variables
　　stage 1: objectives of the manova
　　stage 2: research design of the manova
　　stage 3: assumptions in manova
　　stage 4: estimation of the manova model and assessing overall
fit
　　stage 5: interpretation of the results
　　summary
　　a managerial overview of the results
　　summary 498 . questions 500 . suggested readings
　　references
section iii analysis using interdependence techniques
　chapter 9 grouping data with cluster analysis
　　what is cluster analysis?
　　cluster analysis as a multivariate technique
　　conceptual development with cluster analysis
　　necessity of conceptual support in cluster analysis
　　how does cluster analysis work?
　　a simple example
　　objective versus subjective considerations
　　cluster analysis decision process
　　stage 1: objectives of cluster analysis
　　stage 2: research design in cluster analysis
　　stage 3: assumptions in cluster analysis
　　stage 4: deriving clusters and assessing overall fit
　　stage 5: interpretation of the clusters
　　stage 6: validation and profiling of the clusters
　　an illustrative example
　　stage 1: objectives of the cluster analysis
　　stage 2: research design of the cluster analysis
　　stage 3: assumptions in cluster analysis
　　employing hierarchical and nonhierarchical methods
　　step 1: hierarchical cluster analysis (stage 4)
　　step 2: nonhierarchical cluster analysis (stages 4, 5, and
6)
　　summary 561 . questions 563 . suggested readings
　　references
　chapter 10 mds and correspondence analysis
　　what is multidimensional scaling?
　　comparing objects
　　dimensions: the basis for comparison
　　a simplified look at how mds works
　　gathering similarity judgments
　　creating a perceptual map
　　interpreting the axes
　　comparing mds to other interdependence techniques
　　individual as the unit of analysis
　　lack of a variate
　　a decision framework for perceptual mapping
　　stage 1: objectives of mds
　　key decisions in setting objectives
　　stage 2: research design of mds
　　selection of either a decompositional (attribute-free)
　　or compositional (attribute-based) approach
　　objects: their number and selection
　　nonmetric versus metric methods
　　collection of similarity or preference data
　　stage 3: assumptions of mds analysis
　　stage 4: deriving the mds solution and assessing overall
fit
　　determining an object’s position in the perceptual map
　　selecting the dimensionality of the perceptual map
　　incorporating preferences into mds
　　stage 5: interpreting the mds results
　　identifying the dimensions
　　stage 6: validating the mds results
　　issues in validation
　　approaches to validation
　　overview of multidimensional scaling
　　correspondence analysis
　　distinguishing characteristics
　　differences from other multivariate techniques
　　a simple example of ca
　　a decision framework for correspondence analysis
　　stage 1: objectives of ca
　　stage 2: research design of ca
　　stage 3: assumptions in ca
　　stage 4: deriving ca results and assessing overall fit
　　stage 5: interpretation of the results
　　stage 6: validation of the results
　　overview of correspondence analysis
　　illustrations of mds and correspondence analysis
　　stage 1: objectives of perceptual mapping
　　identifying objects for inclusion
　　basing the analysis on similarity or preference data
　　using a disaggregate or aggregate analysis
　　stage 2: research design of the perceptual mapping study
　　selecting decompositional or compositional methods
　　selecting firms for analysis
　　nonmetric versus metric methods
　　collecting data for mds
　　collecting data for correspondence analysis
　　stage 3: assumptions in perceptual mapping
　　multidimensional scaling: stages 4 and 5
　　stage 4: deriving mds results and assessing overall fit
　　stage 5: interpretation of the results
　　overview of the decompositional results
　　correspondence analysis: stages 4 and 5
　　stage 4: estimating a correspondence analysis
　　stage 5: interpreting ca results
　　overview of ca
　　stage 6: validation of the results
　　a managerial overview of mds results
　　summary 623 . questions 625 . suggested readings
　　references
section iv structural equations modeling
　chapter 11 sem: an introduction
　　what is structural equation modeling?
　　estimation of multiple interrelated dependence
relationships
　　incorporating latent variables not measured directly
　　defining a model
　　sem and other multivariate techniques
　　similarity to dependence techniques
　　similarity to interdependence techniques
　　the emergence of sem
　　the role of theory in structural equation modeling
　　specifying relationships
　　establishing causation
　　developing a modeling strategy
　　a simple example of sem
　　the research question
　　setting up the structural equation model for path analysis
　　the basics of sem estimation and assessment
　　six stages in structural equation modeling
　　stage 1: defining individual constructs
　　operationalizing the construct
　　pretesting
　　stage 2: developing and specifying the measurement model
　　sem notation
　　creating the measurement model
　　stage 3: designing a study to produce empirical results
　　issues in research design
　　issues in model estimation
　　stage 4: assessing measurement model validity
　　the basics of goodness-of-fit
　　absolute fit indices
　　incremental fit indices
　　parsimony fit indices
　　problems associated with using fit indices
　　unacceptable model specification to achieve fit
　　guidelines for establishing acceptable and unacceptable fit
　　stage 5: specifying the structural model
　　stage 6: assessing the structural model validity
　　structural model gof
　　competitive fit
　　comparison to the measurement model
　　testing structural relationships
　　summary 678 . questions 680 . suggested readings
　　appendix 11a: estimating relationships using path analysis
　　appendix 11b: sem abbreviations
　　appendix 11c: detail on selected gof indices
　　references
　chapter 12 applications of sem
　　part 1: confirmatory factor analysis
　　cfa and exploratory factor analysis
　　a simple example of cfa and sem
　　a visual diagram
　　sem stages for testing measurement theory validation with
cfa
　　stage 1: defining individual constructs
　　stage 2: developing the overall measurement model
　　unidimensionality
　　congeneric measurement model
　　items per construct
　　reflective versus formative constructs
　　stage 3: designing a study to produce empirical results
　　measurement scales in cfa
　　sem and sampling
　　specifying the model
　　issues in identification
　　avoiding identification problems
　　problems in estimation
　　stage 4: assessing measurement model validity
　　assessing fit
　　path estimates
　　construct validity
　　model diagnostics
　　summary example
　　cfa illustration
　　stage 1: defining individual constructs
　　stage 2: developing the overall measurement model
　　stage 3: designing a study to produce empirical results
　　stage 4: assessing measurement model validity
　　hbat cfa summary
　　part 2: what is a structural model?
　　a simple example of a structural model
　　an overview of theory testing with sem
　　stages in testing structural theory
　　one-step versus two-step approaches
　　stage 5: specifying the structural model
　　unit of analysis
　　model specification using a path diagram
　　designing the study
　　stage 6: assessing the structural model validity
　　understanding structural model fit from cfa fit
　　examine the model diagnostics
　　sem illustration
　　stage 5: specifying the structural model
　　stage 6: assessing the structural model validity
　　part 3: extensions and applications of sem
　　reflective versus formative measures
　　reflective versus formative measurement theory
　　operationalizing a formative construct
　　distinguishing reflective from formative constructs
　　which to use—reflective or formative?
　　higher-order factor analysis
　　empirical concerns
　　theoretical concerns
　　using second-order measurement theories
　　when to use higher-order factor analysis
　　multiple groups analysis
　　measurement model comparisons
　　structural model comparisons
　　measurement bias
　　model specification
　　model interpretation
　　relationship types: mediation and moderation
　　mediation
　　moderation
　　longitudinal data
　　additional covariance sources: timing
　　using error covariances to represent added covariance
　　partial least squares
　　characteristics of pls
　　advantages and disadvantages of pls
　　choosing pls versus sem
　　summary 778 . questions 781 . suggested readings
references
index

章節(jié)摘錄

版權頁：插圖：Missing data are termed missing at random （MAR） if the missing values of Y depend on X,  but not on Y In other words, the observed Y values represent a random sample of the actual Y  values for each value of X, but the observed data for Ydo not necessarily represent a truly ran-  dom sample of all Y values. Even though the missing data process is random in the sample, its  values are not generalizable to the population. Most often, the data are missing randomly  within subgroups, but differ in levels between subgroups. The researcher must determine the  factors determining the subgroups and the varying levels between groups.For example, assume that we know the gender of respondents （the X variable） and are  asking about household income （the Y variable）. We find that the missing data are random for  both males and females but occur at a much higher frequency for males than females. Even  though the missing data process is operating in a random manner within the gender variable,  any remedy applied to the missing data will still reflect the missing data process because gen-  der affects the ultimate distribution of the household income values.A higher level of randomness is termed missing completely at random （MCAR）. In these  instances the observed values of Y are truly a random sample of all Y values, with no underly-  ing process that lends bias to the observed data. In simple terms, the cases with missing data  are indistinguishable from cases with complete data.From our earlier example, this situation would be shown by the fact that the missing  data for household income were randomly missing in equal proportions for both males and  females. In this missing data process, any of the remedies can be applied without making  allowances for the impact of any other variable or missing data process.Diagnostic Tests for Levels of Randomness. As previously noted, the researcher must ascer-tain whether the missing data process occurs in a completely random manner. When the data set issmall, the researcher may be able to visually see such patterns or perform a set of simple calculations（such as in our simple example at the beginning of the chapter）. However, as sample size and the num-ber of variables increases, so does the need for empirical diagnostic tests. Some statistical programsadd techniques specifically designed for missing data analysis （e.g., Missing Value Analysis in SPSS）,which generally include one or both diagnostic tests.The first diagnostic assesses the missing data process of a single variable Y by forming twogroups: observations with missing data for Y and those with valid values of Y. Statistical testsare then performed to determine whether significant differences exist between the two groupson other variables of interest. Significant differences indicate the possibility of a nonrandommissing data process.Let us use our earlier example of household income and gender. We would first form twogroups of respondents, those with missing data on the household income question and thosewho answered the question. We would then compare the percentages of gender for each group.If one gender （e.g., males） was found in greater proportion in the missing data group, we wouldsuspect a nonrandom missing data process. If the variable being compared is metric （e.g., anattitude or perception） instead of categorical （gender）, then t-tests are performed to determinethe statistical significance of the difference in the variable's mean between the two groups. Theresearcher should examine a number of variables to see whether any consistent patternemerges. Remember that some differences will occur by chance, but either a large number or asystematic pattern of differences may indicate an underlying nonrandom pattern.A second approach is an overall test of randomness that determines whether the missing datacan be classified as MCAR.

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