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Total Survey Error: Past, Present, and Future

Robert M. Groves

University of Michigan and

Joint Program in Survey Methodology

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Outline

• Evolution of “total survey error” (TSE)

• Weaknesses of the TSE framework

• Strengths of the TSE framework

• Future of surveys and research agenda ideas

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Deming (1944) “On Errors in Surveys”

• American Sociological Review!

• First listing of sources of problems, beyond sampling, facing surveys

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Comments on Deming (1944)

• Does include nonresponse, sampling, interviewer effects, mode effects, various other measurement errors, and processing errors

• Omits coverage errors• Includes nonstatistical notions (auspices)• Includes estimation step errors (wrong

weighting)• “total survey error” not used as a term

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Sampling Text Treatments of Total Survey Error

• Deming, Some Theory of Sampling, 1950– repeats set of comments in 1944 article

• Hansen, Hurwitz, Madow, Sample Survey Methods and Theory, 1953– 9 of 638 pages on response and other

nonsampling errors– “errors due to faulty planning,” “coverage

errors,” “classification errors,” “publication errors”

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Sampling Text Treatment of Total Survey Error

• Kish, Survey Sampling, 1965– 65 of 643 pages on various errors, with

specified relationship among errors– Graphic on biases

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Sampling Biases

Frame biases

“Consistent” Sampling Bias

Constant Statistical Bias

Nonsampling

Biases

Noncoverage

NonresponseNonobservation

Field: data collection

Office: processingObservation

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Sampling Text Treatment of Total Survey Error

• Särndal, Swensson, Wretman, Model Assisted Survey Sampling, 1992– Part IV, 124 pp. of 694, coverage,

nonresponse, measurement error; omits processing error

• Lohr, Sampling Design and Analysis, 1999– 34 of 500 pages, nonresponse, randomized

response

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Health Survey Methods Conferences

• Mid 1970’s, “data error archive” idea of Horvitz

• 1977 key paper, “Total Survey Design: Effect of Nonresponse Bias and Procedures for Controlling Measurement Errors,” Kalsbeek and Lessler

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Total Survey Error (1979)Anderson, Kasper, Frankel, and Associates

• Empirical studies on nonresponse, measurement, and processing errors for health survey data

• Initial total survey error framework in more elaborated nested structure

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Total Error

VariableError

Sampling

Nonsampling

Field

Processing

Bias

Nonsampling

Observation

Field

Processing

Sampling

Frame

Consistent

Nonobservation

Noncoverage

Nonresponse

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Survey Errors and Survey Costs (1989), Groves

• Attempts conceptual linkages between total survey error framework and– psychometric true score theories– econometric measurement error and selection bias

notions

• Ignores processing error• Highest conceptual break on variance vs. bias• Second conceptual break on errors of

nonobservation vs. errors of observation

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Coverage Nonresponse Sampling Interviewer Respondent Instrument Mode

Coverage Nonresponse Sampling Interviewer Respondent Instrument Mode

Errors ofNonobservation

ObservationalErrors

Bias

Errors ofNonobservation

ObservationalErrors

Variance

Mean Square Error

construct validitytheoretical validityempirical validityreliability

criterion validity - predictive validity - concurrent validity

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Nonsampling Error in Surveys (1992), Lessler and Kalsbeek

• Evokes “total survey design” more than total survey error

• Omits processing error

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Components of Error Topics

Frame errorsMissing elements

Nonpopulation elements

Unrecognized multiplicities

Improper use of clustered frames

Sampling errors

Nonresponse errorsDeterministic vs. stochastic view of nonresponse

Unit nonresponse

Item nonresponse

Measurement errorsError models of numeric and categorical data

Studies with and without special data collections

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Introduction to Survey Quality, (2003), Biemer and Lyberg

• Major division of sampling and nonsampling error

• Adds “specification error” (a la “construct validity”)

• Formally discusses process quality

• Discusses “fitness for use” as quality definition

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Sources of Error Types of Error

Specification error Concepts

Objectives

Data element

Frame error Omissions

Erroneous inclusions

Duplications

Nonresponse error Whole unit

Within unit

Item

Incomplete Information

Measurement error Information system

Setting

Mode of data collection

Respondent

Interview

Instrument

Processing error Editing

Data entry

Coding

Weighting

Tabulation

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Survey Methodology, (2004) Groves, Fowler, Couper, Lepkowski, Singer,

Tourangeau• Notes twin inferential processes in surveys

– from a datum reported to the given construct of a sampled unit

– from estimate based on respondents to the target population parameter

• Links inferential steps to error sources

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Construct Inferential Population

Measurement

Response

Target Population

Sampling Frame

Sample

Validity

Measurement Error

Coverage

Error

Sampling

Error

Measurement Representation

Respondents

Nonresponse

ErrorEdited Data

ProcessingError

Survey Statistic

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Key Statistical Developments in Total Survey Error 1

• Criteria for true values (1951)1. uniquely defined2. defined in a manner that purposes of survey are

met3. when possible, defined in terms of operations that

can be carried through

• Essential survey conditions, correlated response variance (1959)

– conditioning factors for variance estimate– factors that affect value of variance– often ignore by users of ])([

11

2

mmr

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• Correlated response variance (1959)– assume no covariance between true values and response deviations– assume no correlation of response deviations across interviewers– correlated response variance independent of workload– use of interpenetration

• Simple response variance via reinterviews (1964)– assumes no covariance between trials

• Relaxed assumptions of zero covariance of true values and response deviations (1964)– combine use of interpenetration and reinterview

• “Error Profile” of Current Population Survey (1978)• Multi-method multi-trait models on survey measures (1984)

– within-construct, among item covariance as tool for “simple response variance

– imported from psychometrics

Key Statistical Developments in Total Survey Error 2

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• Measurement of imputation error variance through multiple imputation (1987)

• Total error model for PES (1991)• Measurement Errors in Surveys (1992)

– attempt to juxtapose psychometric notions with survey statistical notions of measurement error

• Latent class model applications to survey errors (late 1990’s)

Key Statistical Developments in Total Survey Error 3

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• Understudied components– coverage error variance– nonresponse error variance– all processing errors– biases

Key Statistical Developments in Total Survey Error 4

25Variance

Bias

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Summary of the Evolution of “Total Survey Error”

• Roots in cautioning against sole attention to sampling error

• Framework contains statistical and nonstatistical notions

• Most statistical attention on variance components, most on measurement error variance

• Late 1970’s attention to “total survey design”• 1980’s-1990’s attempt to import psychometric

notions• Key omissions in research

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Weaknesses of the Common Usage of “Total Survey Error” 1

1. Exclusions of key quality concepts– notably a user perspective is missing

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Key National Indicator Initiative Quality Workshop

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Credibility

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Relevance

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Estimator Quality

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Data Quality

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Weaknesses of the Total Survey Error Paradigm 2

2. Lack of routine measurements- error/quality profiles are useful but rare

3. Ineffective influence on professional standards - little expansion beyond sampling error in practice

- press releases on Federal statistics rarely contain even sampling errors

4. Large burden on design of some estimators- interpenetration, reinterviews for variance estimation not routine

5. Patently wrong assumptions- correlation of true values with errors (drug use reports)- intraclass correlation independent of workload (interviewer experience effects)

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Strengths of the Total Survey Error Framework

1. Taxonomic decomposition of errors• nomenclature for different components

2. Separation of phenomena affecting statistics in different ways

• variance vs. bias; observation vs. nonobservation; respondent/interviewer/measurement task; processing

3. Conceptual foundation of the field of survey methodology

• subfields defined by errors

4. Tool to identifying lacunae in the research literature• e.g., where are the error evaluation papers on processing?

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A Vision of the Future

Why “total survey errorists” have permanent employment opportunities:

1. new areas of study using surveys

2. populations being studied change their behavior

3. external world offers new measurement tools

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Needed Steps in a Research Agenda for Total Survey Error 1

1. Integrating causal models of survey errors• cognitive psychological mechanisms (anchoring, recall decay)

2. Research on interplay of two or more error sources jointly

• e.g., nonresponse and measurement error

3. Research on the interplay of biases and variances• e.g., does simple response variance increase accompany

some response bias reductions (self-administration effects)

4. Development of diagnostic tools to study model-error• progress is slowed with just-identified models without

sensitivity analysis

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5. Guidance on tradeoffs between quality measurement and quality maximization- how much should we spend on quality enhancement vs. measurement of quality (Spencer, 1985)?

6. Integrating other notions of quality into the total survey error paradigm- if “fitness for use” predominates as a conceptual base, how can we launch research that incorporates error variation associated with different uses?

7. Exploiting a multiple-mode, multiple frame, multiple phase survey world- how can we build models that exploit non-randomized design variations to give insight into various survey errors?

Needed Steps in a Research Agenda for Total Survey Error 2

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A Summary Pitch for the Union of Design and Estimation

“To err is human, to forgive divine – but

to include errors in your design is statistical.

Kish, 1977