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#### SPSS for Instruction

SPSS Books and Manuals

Learn how to more productively and efficiently work with SPSS software. A number of SPSS books and manualsfor beginners and expert users alikecan show you how.

Below are descriptions of books and manuals of interest to SPSS users. Use these books to teach yourself SPSS or supplement techniques youve learned in the classroom.

SPSS 13.0 Guide to Data Analysis by Marija Norusis SPSS 13.0 Guide to Data Analysis is a friendly introduction to both data analysis and SPSS software. Easy-to-understand explanations and in-depth content make this guide both an excellent supplement to other statistics texts and an ideal primary text for any introductory data analysis course. With this book, you will learn how to describe data, test simple hypotheses, and examine relationships using real datasets. Exercises at the end of each chapter let you test your skills. SPSS 13.0 Guide to Data Analysis is designed for use with SPSS 13.0 for Windows, including the SPSS Student Version. A data CD is included with this book. To view a description of this book, table of contents, and preface, or to purchase a copy, visit www.prenhall.com. ISBN: 0-13-186535-8

SPSS 13.0 Statistical Procedures Companion by Marija Norusis SPSS 13.0 Statistical Procedures Companion is an introduction to SPSS and its most frequently used statistical procedures. The book takes you from creating, cleaning, and describing data files to analyzing the data using sophisticated statistical procedures such as logistic regression; factor, cluster, and discriminant analysis; log linear models; and general linear models. Youll find discussion of the statistical backgrounds for each procedure and a review of the basics of hypothesis testing. The book offers practical suggestions, emphasizing topics that arise when analyzing real data for presentations, reports, and dissertations. A data CD is included with this book. To view a description of this book, table of contents, and preface, or to purchase a copy, visit www.prenhall.com. ISBN: 0-13-186539-0

SPSS 13.0 Advanced Statistical Procedures Companion by Marija Norusis SPSS 13.0 Advanced Statistical Procedures Companion covers the procedures in two popular SPSS add-on modules, SPSS Advanced Models and SPSS Regression Models. The book provides introductions to and examples for procedures such as loglinear and logit analysis for categorical data; ordinal, multinomial, two-stage, and weighted least squares regression; Kaplan-Meier and Cox regression models for survival analysis; and variance components analysis. A data CD is included with this book. To view a description of this book, table of contents, and preface, or to purchase a copy, visit www.prenhall.com. ISBN: 0-13-186540-4

SPSS 13.0 Brief Guide SPSS 13.0 Brief Guide uses a convenient tutorial system to acquaint beginning users with the components of the SPSS system. Learn how to use the Data Editor, import data into SPSS, work with statistics and output, create and edit charts, modify data values, manage syntax and data files, calculate new data values, and sort and select data. To view a description of this book and table of contents, or to purchase this book, visit www.spss.com/estore/softwaremenu/book.cfm. ISBN: 0-13-154242-7

SPSS Base 13.0 User's Guide SPSS Base 13.0 User's Guide provides a thorough explanation of SPSS features. Topics covered include the Text Wizard,

SPSS Programming and Data Management: A Guide for SPSS and SAS Users, Second Edition by Raynald Levesque SPSS Programming and Data Management: A Guide for SPSS and SAS Users, Second Edition documents the wealth of functionality beneath the SPSS user interface. It includes detailed examples of command syntax, the macro facility, scripting, and the output management system. The accompanying CD-ROM includes the command and data files used in the book. The book also contains a chapter for SAS users, showing equivalent SPSS code for many common data management tasks. With knowledge gained from this book, you will be able to use the many tools available within SPSS to import data from almost any source, clean it, transform it, merge it with other data, and get it into the condition required to produce reliable models and informative results. To view the complete table of contents or to purchase this book, visit www.spss.com/estore/softwaremenu/book.cfm. ISBN: 0-56827-355-X

Database Wizard, Data Editor, scripting, data definition and modification, file and output management (including the SPSS Viewer and report cubes), statistical and graphical procedures (including output examples), production mode operation, and utilities for getting information (including help) and controlling the environment. To view a description of this book and table of contents, or to purchase this book, visit www.spss.com/estore/softwaremenu/book.cfm. ISBN: 0-13-185723-1

Manuals for add-on modules and stand-alone software User manuals are available for all SPSS add-on modules and many stand-alone products, such as Amos. Visit www.spss.com/estore/softwaremenu/book.cfm for a full list of available manuals, or to make a purchase.

To learn more, please visit www.spss.com. For SPSS office locations and telephone numbers, go to www.spss.com/worldwide.

SPSS is a registered trademark and the other SPSS products named are trademarks of SPSS Inc. All other names are trademarks of their respective owners. 2005 SPSS Inc. SB13INS-0405

Complex Samples Descriptives Statistics. 45 Complex Samples Descriptives Missing Values. 46 Complex Samples Options. 46

Complex Samples Crosstabs

Complex Samples Crosstabs Statistics. 51 Complex Samples Missing Values. 53 Complex Samples Options. 53

#### Complex Samples Ratios

Complex Samples Ratios Statistics. 57 Complex Samples Ratios Missing Values. 58 Complex Samples Options. 58

Complex Samples General Linear Model

Complex Samples General Linear Model Statistics. 65 Complex Samples Hypothesis Tests. 66 Complex Samples General Linear Model Estimated Means. 68 Complex Samples General Linear Model Save. 69 Complex Samples General Linear Model Options. 70 CSGLM Command Additional Features. 71

10 Complex Samples Logistic Regression

Complex Samples Logistic Regression Reference Category. 75 Complex Samples Logistic Regression Model. 76 Complex Samples Logistic Regression Statistics. 78 Complex Samples Hypothesis Tests. 80 Complex Samples Logistic Regression Odds Ratios. 81 Complex Samples Logistic Regression Save. 83 Complex Samples Logistic Regression Options. 84 CSLOGISTIC Command Additional Features. 85

Part II: Examples 11 Complex Samples Sampling Wizard

Using the Wizard. Plan Summary. Sampling Summary. Sample Results. Obtaining a Sample from a Partial Sampling Frame...

#### . 89. 121

Obtaining a Sample from a Full Sampling Frame. 89

Using the Wizard to Sample from the First Partial Frame. Sample Results. Using the Wizard to Sample from the Second Partial Frame. Sample Results. Related Procedures.

12 Complex Samples Analysis Preparation Wizard

Using the Complex Samples Analysis Preparation Wizard to Ready NHIS Public Data. 123 Using the Wizard. 123 Summary. 126 Preparing for Analysis When Sampling Weights Are Not in the Data File. 126 Computing Inclusion Probabilities and Sampling Weights Using the Wizard. Summary. Related Procedures. 137 137

13 Complex Samples Frequencies

Using Complex Samples Frequencies to Analyze Nutritional Supplement Usage. 139 Running the Analysis. Frequency Table. Frequency by Subpopulation. Summary. Related Procedures.... 144

14 Complex Samples Descriptives

Using Complex Samples Descriptives to Analyze Activity Levels. 145 Running the Analysis. 145 Univariate Statistics. 148

Univariate Statistics by Subpopulation. 149 Summary. 150 Related Procedures. 150

15 Complex Samples Crosstabs

Using Complex Samples Crosstabs to Measure the Relative Risk of an Event. 151 Running the Analysis. Crosstabulation. Risk Estimate. Risk Estimate by Subpopulation. Summary. Related Procedures.... 157 158

16 Complex Samples Ratios

Running the Analysis. Ratios. Pivoted Ratios Table. Summary. Related Procedures....

output to help identify stagewise information. Note: The source variable list has the same content across steps of the Wizard. In other words, variables removed from the source list in a particular step are removed from the list in all steps. Variables returned to the source list appear in the list in all steps.

Tree Controls for Navigating the Sampling Wizard

On the left side of each step in the Sampling Wizard is an outline of all the steps. You can navigate the Wizard by clicking on the name of an enabled step in the outline. Steps are enabled as long as all previous steps are validthat is, if each previous step has been given the minimum required specifications for that step. See the Help for individual steps for more information on why a given step may be invalid.

9 Sampling from a Complex Design

Sampling Wizard: Sampling Method

Figure 2-3 Sampling Wizard, Method step

This step allows you to specify how to select cases from the working data file.

Method. Controls in this group are used to choose a selection method. Some sampling

types allow you to choose whether to sample with replacement (WR) or without replacement (WOR). See the type descriptions for more information. Note that some probability-proportional-to-size (PPS) types are available only when clusters have been defined and that all PPS types are available only in the first stage of a design. Moreover, WR methods are available only in the last stage of a design.

Simple Random Sampling. Units are selected with equal probability. They can be

selected with or without replacement.

#### 10 Chapter 2

Simple Systematic. Units are selected at a fixed interval throughout the sampling

frame (or strata, if they have been specified) and extracted without replacement. A randomly selected unit within the first interval is chosen as the starting point.

Simple Sequential. Units are selected sequentially with equal probability and

#### without replacement.

PPS. This is a first-stage method that selects units at random with probability

proportional to size. Any units can be selected with replacement; only clusters can be sampled without replacement.

PPS Systematic. This is a first-stage method that systematically selects units with

probability proportional to size. They are selected without replacement.

13 Sampling from a Complex Design

Click Refresh Strata to repopulate the grid with each combination of labeled data values for variables in the grid.

Exclude. To specify sizes for a subset of stratum/cluster combinations, move one or more variables to the Exclude list. These variables are not used to define sample sizes.

Sampling Wizard: Output Variables

Figure 2-6 Sampling Wizard, Output Variables step

This step allows you to choose variables to save when the sample is drawn.

Population size. The estimated number of units in the population for a given stage.

The root name for the saved variable is PopulationSize_.

Sample proportion. The sampling rate at a given stage. The root name for the saved

variable is SamplingRate_.

#### 14 Chapter 2

Sample size. The number of units drawn at a given stage. The root name for the saved variable is SampleSize_. Sample weight. The inverse of the inclusion probabilities. The root name for the saved variable is SampleWeight_.

Some stagewise variables are generated automatically. These include:

Inclusion probabilities. The proportion of units drawn at a given stage. The root name

for the saved variable is InclusionProbability_.

Cumulative weight. The cumulative sample weight over stages previous to and including the current one. The root name for the saved variable is SampleWeightCumulative_. Index. Identifies units selected multiple times within a given stage. The root name for

the saved variable is Index_. Note: Saved variable root names include an integer suffix that reflects the stage numberfor example, PopulationSize_1_ for the saved population size for stage 1.

15 Sampling from a Complex Design

Sampling Wizard: Plan Summary

Figure 2-7 Sampling Wizard, Plan Summary step

This is the last step within each stage, providing a summary of the sample design specifications through the current stage. From here, you can either proceed to the next stage (creating it, if necessary) or set options for drawing the sample.

#### 16 Chapter 2

Sampling Wizard: Draw Sample Selection Options

Figure 2-8 Sampling Wizard, Draw Sample, Selection Options step

This step allows you to choose whether to draw a sample. You can also control other sampling options, such as the random seed and missing-value handling.

Draw sample. In addition to choosing whether to draw a sample, you can also choose to execute part of the sampling design. Stages must be drawn in orderthat is, stage 2 cannot be drawn unless stage 1 is also drawn. When editing or executing a plan, you cannot resample locked stages. Seed. This allows you to choose a seed value for random number generation. Include user-missing values. This determines whether user-missing values are valid. If

Figure 3-3 Analysis Preparation Wizard, Estimation Method step (stage 1)

This step allows you to specify an estimation method for the stage.

WR (sampling with replacement). WR estimation does not include a correction for

sampling from a finite population, since it assumes that the sample was taken from an infinite population. When the population for the stage is much larger than the sample, this is a reasonable assumption. WR estimation can be specified only in the final stage of a design; the Wizard will not allow you to add another stage if you select WR estimation.

Equal WOR (equal probability sampling without replacement). Equal WOR estimation includes the finite population correction and assumes that units are sampled with equal probability. Equal WOR can be specified in any stage of a design.

#### 28 Chapter 3

Unequal WOR (unequal probability sampling without replacement). In addition to using the finite population correction, Unequal WOR accounts for sampling units (usually clusters) selected with unequal probability. This estimation method is available only in the first stage.

Analysis Preparation Wizard: Size

Figure 3-4 Analysis Preparation Wizard, Size step (stage 1)

This step is used to specify inclusion probabilities or population sizes for the current stage. Sizes can be fixed or can vary across strata. For the purpose of specifying sizes, clusters specified in previous stages can be used to define strata.

Units. You can specify exact population sizes or the probabilities with which units

#### were sampled.

29 Preparing a Complex Sample for Analysis

Value. A single value is applied to all strata. If Population Sizes is selected as the

unit metric, you should enter a non-negative integer. If Inclusion Probabilities is selected, you should enter a value between 0 and 1, inclusive.

#### size values for strata.

Figure 3-5 Define Unequal Sizes dialog box

#### 30 Chapter 3

Analysis Preparation Wizard: Stage Summary

Figure 3-6 Analysis Preparation Wizard, Plan Summary step (stage 1)

This is the last step within each stage, providing a summary of the analysis design specifications through the current stage. From here, you can either proceed to the next stage (creating it if necessary) or save the analysis specifications. If you cannot add another stage, it is likely because: No cluster variable was specified in the Design Variables step.

31 Preparing a Complex Sample for Analysis

You selected WR estimation in the Estimation Method step. This is the third stage of the analysis, and the Wizard supports a maximum of three stages.

Analysis Preparation Wizard: Finish

Figure 3-7 Analysis Preparation Wizard, Finish step

This is the final step. You can save the plan file now or paste your selections to a syntax window. When making changes to stages in the existing plan file, you can save the edited plan to a new file or overwrite the existing file. When adding stages without making changes to existing stages, the Wizard automatically overwrites the existing plan file. If you want to save the plan to a new file, choose to Paste the syntax generated by the Wizard into a syntax window and change the filename in the syntax commands.

#### 32 Chapter 3

Modifying an Existing Analysis Plan

E From the menus choose: Analyze Complex Samples Prepare for Analysis. E Select Edit a plan file, and choose a plan filename to which you will save the analysis

E Click Next to continue through the Wizard. E Review the analysis plan in the Plan Summary step, and then click Next.

Subsequent steps are largely the same as for a new design. For more information, see the Help for individual steps.

E Navigate to the Finish step, and specify a new name for the edited plan file, or choose

to overwrite the existing plan file. Optionally, you can: Remove stages from the plan.

33 Preparing a Complex Sample for Analysis

Analysis Preparation Wizard: Plan Summary

Figure 3-8 Analysis Preparation Wizard, Plan Summary step

This step allows you to review the analysis plan and remove stages from the plan.

Remove Stages. You can remove stages 2 and 3 from a multistage design. Since a plan

must have at least one stage, you can edit but not remove stage 1 from the design.

#### Complex Samples Plan

Complex Samples analysis procedures require analysis specifications from an analysis or sample plan file in order to provide valid results.

Figure 4-1 Complex Samples Plan dialog box

Plan. Specify the path of an analysis or sample plan file. Joint Probabilities. In order to use Unequal WOR estimation for clusters drawn

using a PPS WOR method, you need to specify a separate file containing the joint probabilities. This file is created by the Sampling Wizard during sampling.

Complex Samples Frequencies

The Complex Samples Frequencies procedure produces frequency tables for selected variables and displays univariate statistics. Optionally, you can request statistics by subgroups, defined by one or more categorical variables.

Example. Using the Complex Samples Frequencies procedure, you can obtain

algorithm stops after an iteration in which the absolute or relative change in the parameter estimates is less than the value specified, which must be non-negative.

Limit iterations based on change in log-likelihood. When selected, the algorithm

stops after an iteration in which the absolute or relative change in the log-likelihood function is less than the value specified, which must be non-negative.

Check for complete separation of data points. When selected, the algorithm

performs tests to ensure that the parameter estimates have unique values. Separation occurs when the procedure can produce a model that correctly classifies every case.

Display iteration history. Displays parameter estimates and statistics at every n

iterations beginning with the 0th iteration (the initial estimates). If you choose to print the iteration history, the last iteration is always printed regardless of the value of n.

User-Missing Values. All design variables, as well as the dependent variable and any covariates, must have valid data. Cases with invalid data for any of these variables are deleted from the analysis. These controls allow you to decide whether user-missing values are treated as valid among the strata, cluster, subpopulation, and factor variables. Confidence Interval. This is the confidence interval level for coefficient estimates,

exponentiated coefficient estimates, and odds ratios. Specify a value greater than or equal to 50 and less than 100.

CSLOGISTIC Command Additional Features

The SPSS command language also allows you to: Specify custom tests of effects versus a linear combination of effects or a value (using the CUSTOM subcommand). Fix values of other model variables when computing odds ratios for factors and covariates (using the ODDSRATIOS subcommand). Specify a tolerance value for checking singularity (using the CRITERIA subcommand).

#### 86 Chapter 10

Create user-specified names for saved variables (using the SAVE subcommand). Produce a general estimable function table (using the PRINT subcommand). See the SPSS Command Syntax Reference for complete syntax information.

#### Part 2: Examples

Complex Samples Sampling Wizard

Obtaining a Sample from a Full Sampling Frame

A state agency is charged with ensuring fair property taxes from county to county. Taxes are based on the appraised value of the property, so the agency wants to survey a sample of properties by county to be sure that each countys records are equally up-to-date. However, resources for obtaining current appraisals are limited, so its important that what is available is used wisely. The agency decides to employ complex sampling methodology to select a sample of properties. A listing of properties is collected in property_assess_cs.sav, found in the \tutorial\sample_files\ subdirectory of the directory in which you installed SPSS. Use the Complex Samples Sampling Wizard to select a sample.

#### Using the Wizard

E To run the Complex Samples Sampling Wizard, from the menus choose: Analyze Complex Samples Select a Sample.

90 Chapter 11 Figure 11-1 Sampling Wizard, Welcome step

E Select Design a sample and type c:\property_assess.csplan as the name of the plan

#### E Click Next.

91 Complex Samples Sampling Wizard Figure 11-2 Sampling Wizard, Design Variables step (stage 1)

E Select County as a stratification variable. E Select Township as a cluster variable. E Click Next, and then click Next in the Method step.

This design structure means that independent samples are drawn for each county. In this stage, townships are drawn as the primary sampling unit using the default method, simple random sampling.

92 Chapter 11 Figure 11-3 Sampling Wizard, Sample Size step (stage 1)

E Type 4 as the value for the number of clusters to select in this stage. E Click Next, and then click Next in the Output Variables step.

93 Complex Samples Sampling Wizard Figure 11-4 Sampling Wizard, Plan Summary step (stage 1)

E Select Yes, add stage 2 now. E Click Next.

94 Chapter 11 Figure 11-5 Sampling Wizard, Design Variables step (stage 2)

E Select Neighborhood as a stratification variable. E Click Next, and then click Next in the Method step.

117 Complex Samples Sampling Wizard Figure 11-27 Sampling Wizard, Plan Summary step (stage 1)

118 Chapter 11 Figure 11-28 Sampling Wizard, Draw Sample, Selection Options step

E Select Custom value for the type of random seed to use and type 4231946 as the value. E Click Next, and then click Next in the Draw Sample, Output Files step.

119 Complex Samples Sampling Wizard Figure 11-29 Sampling Wizard, Finish step

These selections produce the sampling plan file demo_2.csplan and draw a sample according to that plan.

#### 120 Chapter 11

Figure 11-30 Data Editor with sample results

You can see the sampling results in the Data Editor. Three new variables were saved to the working file, representing the inclusion probabilities and cumulative sampling weights for the third stage, plus the final sampling weights. These new weights take into account the weights computed during the sampling of the first two stages. Units with values for these variables were selected to the sample. Units with system-missing values for the variables were not selected. The company will now use its resources to obtain survey information for the housing units selected in the sample. Once the surveys are collected, you can process the sample with Complex Samples analysis procedures, using the sampling plan demo_2.csplan to provide the sampling specifications.

121 Complex Samples Sampling Wizard

#### Related Procedures

The Complex Samples Sampling Wizard procedure is a useful tool for creating a sampling plan file and drawing a sample. To ready a sample for analysis when you do not have access to the sampling plan file, use the Analysis Preparation Wizard.

Complex Samples Analysis Preparation Wizard

The Analysis Preparation Wizard guides you through the steps for creating or modifying an analysis plan for use with the various Complex Samples analysis procedures. It is most useful when you do not have access to the sampling plan file used to draw the sample.

A researcher wants to study the use of nutritional supplements among U.S. citizens, using the results of the National Health Interview Survey (NHIS) and a previously created analysis plan. For more information, see Using the Complex Samples Analysis Preparation Wizard to Ready NHIS Public Data in Chapter 12 on p. 123. A subset of the 2000 survey is collected in nhis2000_subset.sav, found in the \tutorial\sample_files\ subdirectory of the directory in which you installed SPSS. The analysis plan is stored in nhis2000_subset.csaplan. Use Complex Samples Frequencies to produce statistics for nutritional supplement usage.

#### Running the Analysis

E To run a Complex Samples Frequencies analysis, from the menus choose: Analyze Complex Samples Frequencies.

140 Chapter 13 Figure 13-1 Complex Samples Plan dialog box

E Browse to the \tutorial\sample_files\ subdirectory of the directory in which you

installed SPSS and select nhis2000_subset.csaplan.

#### E Click Continue.

141 Complex Samples Frequencies Figure 13-2 Frequencies dialog box

E Select Vitamin/mineral supplmnts-past 12 m as a frequency variable. E Select Age category as a subpopulation variable. E Click Statistics.

142 Chapter 13 Figure 13-3 Frequencies Statistics dialog box

E Select Table percent in the Cells group. E Select Confidence interval in the Statistics group. E Click Continue. E Click OK in the Frequencies dialog box.

#### Frequency Table

Figure 13-4 Frequency table for variable/situation

143 Complex Samples Frequencies

Each selected statistic is computed for each selected cell measure. The first column contains estimates of the number and percentage of the population that do or do not take vitamin/mineral supplements. The confidence intervals are non-overlapping; thus, you can conclude that, overall, more Americans take vitamin/mineral supplements than not.

Frequency by Subpopulation

Figure 13-5 Frequency table by subpopulation

When computing statistics by subpopulation, each selected statistic is computed for each selected cell measure by value of Age category. The first column contains estimates of the number and percentage of the population of each category that do or do not take vitamin/mineral supplements. The confidence intervals for the table

#### 144 Chapter 13

percentages are all non-overlapping; thus, you can conclude that with increasing age category, greater proportions of Americans take vitamin/mineral supplements.

Using the Complex Samples Frequencies procedure, you have obtained statistics for the use of nutritional supplements among U.S. citizens. Overall, more Americans take vitamin/mineral supplements than not. When broken down by age category, greater proportions of Americans take vitamin/mineral supplements with increasing age.

E To run a Complex Samples Crosstabs analysis, from the menus choose: Analyze Complex Samples Crosstabs.

152 Chapter 15 Figure 15-1 Complex Samples Plan dialog box

installed SPSS and select demo_2.csplan.

153 Complex Samples Crosstabs Figure 15-2 Crosstabs dialog box

E Select Newspaper subscription as a row variable. E Select Response as the column variable. E There is also some interest in seeing the results broken down by income categories, so

select Income category in thousands as a subpopulation variable.

#### E Click Statistics.

154 Chapter 15 Figure 15-3 Crosstabs Statistics dialog box

E Deselect Population size and select Row percent in the Cells group. E Select Odds ratio and Relative risk in the Summaries for 2-by-2 Tables group. E Click Continue. E Click OK in the Complex Samples Crosstabs dialog box.

These selections produce a crosstabulation table and risk estimate for Newspaper subscription by Response. Separate tables with results split by Income category in thousands are also created.

155 Complex Samples Crosstabs

#### Crosstabulation

Figure 15-4 Crosstabulation for newspaper subscription by response

The crosstabulation shows that, overall, not very many people responded to the mailing. However, a greater proportion of newspaper subscribers responded.

#### Risk Estimate

Figure 15-5 Risk estimate for newspaper subscription by response

The relative risk is a ratio of event probabilities. The relative risk of a response to the mailing is the ratio of the probability that a newspaper subscriber responds, to the probability that a nonsubscriber responds. Thus, the estimate of the relative risk is simply 18.6%/10.6% = 1.743. Likewise, the relative risk of nonresponse is the ratio of the probability that a subscriber does not respond, to the probability that a nonsubscriber does not respond. Your estimate of this relative risk is 0.911. Given these results, you can estimate that a newspaper subscriber is 1.743 times as likely to respond to the mailing as a nonsubscriber, or 0.911 times as likely as a nonsubscriber not to respond. The odds ratio is a ratio of event odds. The odds of an event is the ratio of the probability that the event occurs, to the probability that the event does not occur. Thus, the estimate of the odds that a newspaper subscriber responds to the mailing

175 Complex Samples General Linear Model

The usecoup coefficients suggest that spending among customers with dependents at home decreases with decreased coupon usage. There is a moderate amount of uncertainty in the estimates, but the confidence intervals do not include 0. The interaction coefficients suggest that customers who do not use coupons or only clip from the newspaper and do not have dependents tend to spend more than you would otherwise expect. If any portion of an interaction parameter is redundant, the interaction parameter is redundant. The deviation in the values of the design effects from 1 indicate that some of the standard errors computed for these parameter estimates are larger than those you would obtain if you assumed that these observations came from a simple random sample, while others are smaller. It is vitally important to incorporate the sampling design information in your analysis because you might otherwise infer, for example, that the usecoup=3 coefficient is not different from 0! The parameter estimates are useful for quantifying the effect of each model term, but the estimated marginal means tables can make it easier to interpret the model results.

#### Estimated Marginal Means

Figure 17-9 Estimated marginal means by levels of gender

This table displays the model-estimated marginal means and standard errors of Amount spent at the factor levels of Who shopping for. This table is useful for exploring the differences between the levels of this factor. In this example, a customer who shops for themselves is expected to spend about $308.53, while a customer with a spouse is expected to spend $370.33, and a customer with dependents will spend $459.44. To see whether this represents a real difference or is due to chance variation, look at the test results.

176 Chapter 17 Figure 17-10 Individual test results for estimated marginal means of gender

The individual tests table displays two simple contrasts in spending. The contrast estimate is the difference in spending for the listed levels of Who shopping for. The hypothesized value of 0.00 represents the belief that there is no difference in spending. The Wald F statistic, with the displayed degrees of freedom, is used to test whether the difference between a contrast estimate and hypothesized value is due to chance variation. Since the significance values are less than 0.05, you can conclude that there are differences in spending. The values of the contrast estimates are different from the parameter estimates. This is because there is an interaction term containing the Who shopping for effect. As a result, the parameter estimate for shopfor=1 is a simple contrast between the levels Self and Self and Family at the level From both of the variable Use coupons. The contrast estimate in this table is averaged over the levels of Use coupons.

184 Chapter 18 Figure 18-3 Logistic Regression Reference Category dialog box

E Select Lowest value as the reference category.

This sets the did not default category as the reference category; thus, the odds ratios reported in the output will have the property that increasing odds ratios correspond to increasing probability of default.

E Click Continue. E Click Statistics in the Logistic Regression dialog box.

185 Complex Samples Logistic Regression Figure 18-4 Logistic Regression Statistics dialog box

E Select Classification table in the Model Fit group E Select Estimate, Exponentiated estimate, Standard error, Confidence interval, and Design effect in the Parameters group. E Click Continue. E Click Odds Ratios in the Logistic Regression dialog box.

186 Chapter 18 Figure 18-5 Logistic Regression Odds Ratios dialog box

E Choose to create odds ratios for the factor ed and the covariates employ and debtinc. E Click Continue. E Click OK in the Logistic Regression dialog box.

187 Complex Samples Logistic Regression

#### Pseudo R-Squares

Figure 18-6 Pseudo R-square statistics

There is no single statistic for logistic regression models that duplicates the properties of the R-square statistic for linear regression models, so these approximations are computed instead. Larger pseudo R-square statistics indicate that more of the variation is explained by the model, to a maximum of 1.

#### Classification

Figure 18-7 Classification table

The classification table shows the practical results of using the logistic regression model. For each case, the predicted response is Yes if that cases model-predicted logit is greater than 0. Cases are weighted by finalweight, so that the classification table reports the expected model performance in the population. Cells on the diagonal are correct predictions. Cells off the diagonal are incorrect predictions.

#### 188 Chapter 18

Based upon the cases used to create the model, you can expect to correctly classify 85.5% of the non-defaulters in the population using this model. Likewise, you can expect to correctly classify 60.9% of the defaulters. Overall, you can expect to classify 76.5% of the cases are classified correctly; however, because this table was constructed with the cases used to create the model, these estimates are likely to be overly optimistic.

Figure 18-8 Tests of between-subjects effects

Each term in the model, plus the model as a whole, is tested for whether its effect equals 0. Terms with significance values less than 0.05 have some discernable effect. Thus, age, employ, debtinc, and creddebt contribute to the model, while the other main effects do not. In a further analysis of the data, you would probably remove ed, address, income, and othdebt from model consideration.

189 Complex Samples Logistic Regression

Figure 18-9 Parameter estimates

The parameter estimates table summarizes the effect of each predictor. Note that parameter values affect the likelihood of the did default category relative to the did not default category. Thus, parameters with positive coefficients increase the likelihood of default, while parameters with negative coefficients decrease the likelihood of default. The meaning of a logistic regression coefficient is not as straightforward as that of a linear regression coefficient. While B is convenient for testing the model effects, Exp(B) is easier to interpret. Exp(B) represents the ratio change in the odds of the event of interest attributable to a one-unit increase in the predictor for predictors that are not part of interaction terms. For example, Exp(B) for employ is equal to 0.798, which means that the odds of default for people who have been with their current employer for two years are 0.798 times the odds of default for those who have been with their current employer for one year, all other things being equal. The design effects indicate that some of the standard errors computed for these parameter estimates are larger than those you would obtain if you assumed that these observations came from a simple random sample, while other are smaller. It is vitally

#### 190 Chapter 18

important to incorporate the sampling design information in your analysis because you might otherwise infer, for example, that the age coefficient is no different from 0!

#### Odds Ratios

Figure 18-10 Odds ratios for level of education

This table displays the odds ratios of Previously defaulted at the factor levels of Level of education. The reported values are the ratios of the odds of default for Did not complete high school through College degree, compared to the odds of default for Post-undergraduate degree. Thus, the odds ratio of 2.054 in the first row of the table means that the odds of default for a person who did not complete high school are 2.054 times the odds of default for a person who has a post-undergraduate degree.

191 Complex Samples Logistic Regression Figure 18-11 Odds ratios for years with current employer

This table displays the odds ratio of Previously defaulted for a unit change in the covariate Years with current employer. The reported value is the ratio of the odds of default for a person with 7.99 years at their current job compared to the odds of default for a person with 6.99 years (the mean).

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