Brian S. Everitt A Handbook of Statistical Analyses using SPSS

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Display 11.8 Requesting descriptive statistics via the Factor Analysis dialogue box. these data, we shall use exploratory factor analysis to investigate the underlying structure of the associations between the 14 questionnaire items. Largely as an exercise in illustrating more of the factor analysis options in SPSS, we shall use the formal test for the number of factors provided by the maximum likelihood approach (see Box 11.2) to estimate the number of factors, but then use principal factor analysis to estimate the loadings and specific variances corresponding to this number of factors. As for principal component analysis, the 14 manifest variables to be factor-analyzed can be declared in the Factor Analysis box (see Display 11.2). Simple descriptive summaries for each of the items can be requested via the Factor Analysis box by using the Descriptives… button (Display 11.8). Here we request univariate descriptive summaries and the observed correlation matrix. (Checking Initial solution affects the factor analysis output; we will discuss this later.) The resulting descriptive output is shown in Display 11.9. Each item has been rated on the same Likert scale (1 to 5) and the standard deviations of the item ratings did not vary a lot. It seems therefore reasonable, on this occasion, to model the covariance matrix. We also note that the correlations between the item ratings are all positive. First, we will consider maximum likelihood (ML) factor analysis. This is a method that assumes multivariate normality and then estimates the factor model parameters by maximizing the likelihood function. We leave it as an exercise for the reader to undertake the full factor analysis with this method (see Exercise 11.4.2) and here concentrate only on its goodness-of-fit test, which assesses the null hypothesis that a model with a given number of factors explains the covariance or correlation structure of the manifest variables. The test is generally applied by successively © 2004 by Chapman & Hall/CRC Press LLC
Correlatic friendly manner doubts about ability cold and impersonal reassurance examines me carefully not enough respect doubt about the treatment competent and well trained interest in me unanswered questions jargon confidence confide not free to ask questions Descriptive Statistics Mean Std. Deviation Analysis N friendly manner 1.66 .781 64 doubts about ability 1.92 .997 64 cold and impersonal 1.77 .868 64 reassurance 2.09 1.019 64 examines me carefully 1.94 .852 64 not enough respect 2.02 .934 64 doubt about the treatment 2.27 1.043 64 competent and well trained 1.67 .757 64 interest in me 1.91 .955 64 unanswered questions 2.27 1.144 64 jargon 2.48 1.141 64 confidence 1.94 .941 64 confide 1.88 .864 64 not free to ask questions 1.81 .941 64 Correlation Matrix friendly manner doubts about ability cold and impersonal 1.000 .556 .628 .639 .516 .704 .445 .611 .786 .315 .554 .688 .624 .556 1.000 .584 .460 .443 .513 .478 .681 .576 .631 .271 .723 .505 .424 .628 .584 1.000 .348 .495 .494 .280 .437 .662 .399 .325 .507 .595 .334 .639 .460 .348 1.000 .519 .515 .335 .431 .547 .550 .206 .486 .536 .466 .516 .443 .495 .519 1.000 .540 .376 .558 .656 .538 .130 .629 .507 .381 .704 .513 .494 .515 .540 1.000 .631 .636 .642 .575 .261 .615 .730 .581 .445 .478 .280 .335 .376 .631 1.000 .494 .344 .645 .224 .470 .443 .505 .611 .681 .437 .431 .558 .636 .494 1.000 .703 .615 .242 .751 .495 .492 .786 .576 .662 .547 .656 .642 .344 .703 1.000 .619 .174 .700 .659 .528 .566 .631 .399 .550 .538 .575 .645 .615 .619 1.000 .253 .665 .532 .563 .315 .271 .325 .206 .130 .261 .224 .242 .174 .253 1.000 .310 .240 .234 .554 .723 .507 .486 .629 .615 .470 .751 .700 .665 .310 1.000 .654 .507 .688 .505 .595 .536 .507 .730 .443 .495 .659 .532 .240 .654 1.000 .557 .624 .424 .334 .466 .381 .581 .505 .492 .528 .563 .234 .507 .557 1.000 reassurance examines me carefully not enough respect doubt about competent the and well treatment trained interest in me unanswered questions jargon confidence confide not free to ask questions .566 Display 11.9 Descriptive statistics for questionnaire variables. increasing the number of factors by one until the test yields an insignificant result. However, like all tests for model assumptions, the procedure is not without difficulties. For small samples, too few factors might be indicated and for large samples, too many. In addition, it is not clear what single test level should be chosen and the test has been shown very sensitive to departures from normality. Here we demonstrate the test procedure in the spirit of an explorative tool rather than a formal test. Parameter estimation via maximum likelihood is specified via the Extraction sub-dialogue box (see Display 11.3). As soon as ML is selected from the Method list, it is no longer possible to choose the covariance matrix since SPSS automatically models the correlation matrix. Although our later analysis will concentrate on the former, given the small differences in standard deviations for the questionnaire variables, this should not present a real problem. By fixing the Number of factors, we can fit a series of factor model with one, two, and three factors. The resulting series of tests for model fit is shown in Display 11.10. We detect significant lack of model fit for the one- and two-factor solutions with the three-factor model failing to detect departure from the model at the 5% level (X 2 (1) = 69, p = 0.058). So, according to the ML test criterion, a three-factor model seems reasonable for these data. © 2004 by Chapman & Hall/CRC Press LLC
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A Handbook of Statistical Analyses
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Preface SPSS, standing for Statisti
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Distributors The distributor for SP
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3 Simple Inference for Categorical
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10 Survival Analysis: Sexual Milest
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1. SPSS Base (Manual: SPSS Base 11.
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Display 1.1 Initial SPSS for Window
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Display 1.3 Variable View window of
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three-periods symbol and filling in
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Display 1.6 Opening an existing SPS
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Display 1.8 Typical dialogue box. s
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Transpose… opens a dialogue for s
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Display 1.11 Selecting subsets of c
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A large number of functions are sup
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Display 1.15 Graph procedures demon
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More than one Output Viewer can be
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The Chart Editor facilities are des
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Display 1.19 Syntax Editor showing
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Table 2.1 Lifespans of Rats (in Day
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The test-statistic is where - y 1 a
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For small samples, p-values for the
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Display 2.1 Data View spreadsheet f
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lifespan in days diet Restricted di
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Lifespan in days 1600 1400 1200 100
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Display 2.6 Settings for controllin
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Display 2.8 Generating an independe
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Display 2.10 Generating a Mann-Whit
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Display 2.13 Generating descriptive
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simply because ages were measured o
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Display 2.18 Generating a Wilcoxon
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Husbands' ages (years) 80 70 60 50
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Display 2.24 Generating correlation
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Display 2.26 Fitting a simple linea
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Table 2.4 Motor Vehicle Theft in th
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2.4.5 More on Husbands and Wives: E
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Table 3.1 Belief in the Afterlife B
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make up the table. Most commonly, a
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This is known as a hypergeometric d
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(2) Odds ratio The odds of Variabl
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Display 3.2 Cross-classifying two c
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Odds Ratio for diet (Restricted die
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Display 3.7 Data View spreadsheet f
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Display 3.10 Generating a chi-squar
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20 10 Observed number 30 0 Psychoti
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Chi-Square Tests Value McNemar Test
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Pearson Chi-Square Likelihood Ratio
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Race of defendant found guilty of m
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Estimate ln(Estimate) Std. Error of
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treatment are independent. Estimate
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Table 4.1 Cleaning Cars Sex (1 = ma
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Table 4.2 (continued) Minimum Tempe
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A measure of the fit of the model i
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Display 4.2 Generating the partial
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We specify the dependent variable a
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for the coefficient is given by [0.
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Display 4.7 Setting inclusion and e
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Model 1 2 Model 1 2 Variables Enter
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proportion of variance of the varia
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The final graph shown in Display 4.
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Display 4.12 Generating a scatterpl
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Model 1 Model 1 Model Summary .973a
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Display 4.15 Blocking explanatory v
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1. Residual plot: This is a scatter
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8 6 4 Frequency 10 2 0 2.25 1.75 1.
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a) Latitude January minimum tempera
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Display 4.22 Extending a spreadshee
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Table 4.4 Sulfur Dioxide and Indica
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Table 4.5 Body Fat Content and Age
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Table 5.1 Fecundity of Fruit Flies
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Table 5.3 Female Social Skills Anxi
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There are some advantages (and, unf
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Display 5.1 SPSS spreadsheet contai
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Display 5.3 Defining a one-way desi
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Dependent Variable: FECUNDIT Tukey
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Click Simple in the resulting Error
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finger taps per minute Between Grou
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Display 5.13 Defining a one-way des
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5.0 4.0 Mean score 6.0 3.0 2.0 B. r
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the data to assess whether the assu
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Chapter 6 Analysis of Variance II:
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Table 6.2 Data from Slimming Clinic
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When the cells of the design have d
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Dependent Variable: reaction time p
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Display 6.5 Requesting a line chart
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Display 6.8 Confidence intervals fo
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MANUAL Total manual no manual MANUA
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In a balanced design, the type I, I
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6.4 Exercises 6.4.1 Headache Treatm
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ANCOVA assumes that there is no int
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Table 7.1 Field Independence and a
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or error term. The u i are assumed
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To convey this design to SPSS, the
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LN_FN LN_FC LN_FI LN_CN LN_CC LN_CI
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Within-Subjects Factors Measure: ME
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Measure: MEASURE_1 Within Subjects
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e used, or for a conservative appro
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Table 7.2 Visual Acuity and Lens St
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Chapter 8 Analysis of Repeated Meas
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Table 8.1 A Subset of the Data from
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Table 8.1 (continued) A Subset of t
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Box 8.1 Random Effects Models Supp
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0 10 20 30 Response Average group 1
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95% CI for mean score 30 20 10 0 N
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a) TAU group Baseline depression sc
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Display 8.6 Part of Data View sprea
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Display 8.7 Defining the variables
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variables; and the variance paramet
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Fixed Effects Random Effects Residu
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different post-treatment time point
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Iteration 0 1 2 3 4 5 6 7 8 Update
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a) Estimates of error term (residua
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Table 8.3 Depression Ratings for Su
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Constant error variance across repe
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Display 9.1 Characteristics of 21 T
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Competing models in a logistic regr
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Survived? Total Survived? Total no
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Display 9.4 Defining a five-way tab
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Display 9.6 Defining a logistic reg
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Step 1 a Step 1 PCLASS PCLASS(1) PC
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Table 9.1 Unadjusted Effects of Cat
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of all explanatory variables simult
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Step 1 a Table 9.2 LR Test Results
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log-odds of survival log-odds of su
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Page 286 and 287: that need to be considered. If the
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Page 296 and 297: Display 11.6 Saving factor scores.
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Page 306 and 307: Display 11.16 Reproduced covariance
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Page 316 and 317: Display 12.2 Declaring a discrimina
Page 318 and 319: Box's M F Display 12.4 (continued)
Page 320 and 321: Display 12.6 (continued) Functions
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Page 326 and 327: * * * * * * H I E R A R C H I C A L
Page 328 and 329: Display 12.14 Declaring a k-means c
Page 330 and 331: 12.4 Exercises Cluster Number of Ca
Page 332 and 333: Table 12.2 (continued) SIDS Data Gr
Page 334 and 335: References Agresti, A. (1996) Intro
Page 336 and 337: Greenhouse, S. W. and Geisser, S. (
Page 338: Stevens, J. (1992) Applied Multivar
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Brian S. Everitt A Handbook of Statistical Analyses using SPSS

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