Definitions Correlation, Reliability, Validity, Measurement error Theories of Reliability

• Definitions– Correlation, Reliability, Validity, Measurement

error• Theories of Reliability• Types of Reliability

– Standard Error of Measurement• Types of Validity

• Article• Exercise

Quality of Measures

• Correlation– reflect direction (+/-) & strength (0 to 1) of the

relation between two variables

• Variance explained– Reflects the strength of relation of two variables

• Square of correlation

• Varies from 0 to 1

Definitions

90

130

170

210

250

150 160 170 180 190 200

Height (cm)

Wei

ght (

poun

ds)

Tom Cruise

Vince Carter

Calista Flockhart

Julia Roberts

90

130

170

210

250

150 160 170 180 190 200

Height (cm)

Wei

ght (

poun

ds)

Tom Cruise

Vince Carter

Calista Flockhart

Julia Roberts

r = .76

r2 = 58%

Effect of Measurement Error on Correlations

150

160

170

180

190

200

150 160 170 180 190 200

Height (cm)

Hei

ght (

cm)

r = 1.00

r2 = 100%

150

160

170

180

190

200

150 160 170 180 190 200

Objective Height (cm)

Self-

Rep

orte

d H

eigh

t (cm

) r = .98

r2 = 96%

100

125

150

175

200

225

250

100 125 150 175 200 225 250

Objective Weight (cm)

Self-

Rep

orte

d W

eigh

t (cm

)

r = .92; r2 = 85%

• Reliability• Consistency & stability of measurement• Reliability is necessary but not sufficient for

validity• E.g. A measuring tape to is not a valid way to measure

weight although the tape reliably measures height and height correlates w/weight

• Validity• Accuracy/meaning of measurement

• Example: unstructured vs. structured job interviews

Definitions

• Classical Test Theory explains random variation in a person’s scores on a measure• Effects of learning, mood, changes in

understanding etc.• Test score=true score + error

• Errors have zero mean• Errors are uncorrelated with each other• Errors are uncorrelated with true score• Constant error is part of true score

Theories of Reliability

• Test-retest • Consistency across time

• Parallel forms• Consistency across versions

• Internal • Consistency across items

• Scorer (inter-rater)• Consistency across raters/judges

Types of Reliability

Example: The Satisfaction with Life Scale (SWLS)

1. In most ways my life is close to ideal.2. The conditions of my life are excellent.3. I am satisfied with my life.4. So far I have gotten the important things I want in my life.5. If I could live my life over, I would change almost nothing.

1 2 3 4 5 6 7Strongly StronglyDisagree Agree

• Test-retest reliability• Correlation of scores on the same measure taken at

two different times• Time interval assumes no memory/learning effects

• Parallel-forms• Correlation of scores on similar versions of the

measure• Forms equivalent on mean, stan dev, inter-correlations• Can have time interval b/w admin of two forms


Test-retest Reliability Time 1 Time 2 I1 I2 I3 AvgT1 I1 I2 I3 AvgT2 P1 P2 P3 Correlate AvgT1 to AvgT2 to get reliability Parallel Forms Version 1 Version 2 I1 I2 I3 AvgV1 I1 I2 I3 AvgV2 P1 P2 P3 Correlate AvgV1 to AvgV2


I=item

P=participant

1

2

3

4

5

6

7

1 2 3 4 5 6 7

SWLS Time 1 (Beginning of Semester)

SWL

S T

ime

2 (E

nd o

f Sem

este

r)

r = .73; r2 = 50%

Test-retest reliability of SWLS

• Good test-retest reliability

•Participants have similar scores at Time 1 (beginning of semester) and at Time 2 (end of semester).

•Retest reliability is useful for constructs assumed to be stable

•Current mood (e.g., how you feel right now) shows low-retest correlations, but that does not mean that the mood measure is not reliable

• Internal Consistency• Correlation of scores on two halves of the measure• Length of measure increases reliability

• Inter-rater• Correlation of raters’ scores

• E.g., Scores on structured job interview• Can also include time interval

– e.g., ratings of the worth of jobs across time & across judges


Internal Reliability Half 1 Half 2 I1 I2 I3 AvgH1 I4 I5 I6 AvgH2 P1 P2 P3 Correlate AvgH1 to AvgH2 Inter-rater Reliability Rater 1 Rater 2 I1 I2 I3 AvgR1 I1 I2 I3 AvgR2 P1 P2 P3 Correlate AvgR1 to AvgR2


1

2

3

4

5

6

7

1 2 3 4 5 6 7

SWLS Items 1 & 2

SWL

S It

ems 3

, 4, &

5

r = .70; r2 = 49%

Internal consistency of SWLS

• Satisfactory internal consistency.

•Participants respond similarly to items that are supposed to measure the same variable.

•Should be .70 or higher

•Measurement error accounts for half of the variance in SWLS scores.

• Test-retest • Parallel forms• Internal • Scorer (inter-rater)


• SD of scores when a measure is completed several times by the same individual• Mostly used in selection contexts

• Decide which of two individuals are hired• Decide whether a test score is significantly higher/lower

than a cutoff score

Standard Error of Measurement

• Real correlation between two variables after removing unreliability of each measure• Divide observed correlation by product of the

square roots of individual reliabilities• Note: Selection research only controls for unreliability

in criterion bec. we are more interested in the value of the predictor given a perfectly reliable criterion

Correction for Attenuation

• Definitions– Correlation, Reliability, Validity, Measurement

error• Theories of Reliability• Types of Reliability• Standard Error of Measurement• Types of Validity

Quality of Measures

Validity

Evidence that a measure assesses the construct

Reasons for Invalid Measures

• Different understanding of items

• Different use of the scale (Response Styles)

• Intentionally presenting false information (socially desirable responding, other-deception)

• Unintentionally presenting false information (self-deception)

Types of Validity

Content Validity

Criterion Validity

Construct Validity

Predictive Validity

Concurrent Validity

Convergent Validity

Discriminant Validity

Adapted from Sekaran, 2004

• Content Validity• Extent to which items on the measure are a good

representation of the construct• e.g., Is your job interview based on what is required for

the job? • Content validity ratio based on judges’

assessments of a measure’s content• e.g., Expert (supervisors, incumbents) rating of job

relevance of interview questions

Types of Validity

• Criterion-related Validity• Extent to which a new measure relates to another

known measure• Validity coefficient= Size of relation between the new

measure (predictor) and the known measure (criterion) (a.k.a correlation)

• e.g., do scores on your job interview predict performance evaluation scores?

Types of Validity

• Concurrent• Scores on predictor and criterion are collected

simultaneously (e.g., police officer study)

• Distinguishes between participants in sample who are already known to be different from each other

• Weaknesses• Range restriction

– Does not include those who were not hired, fired & promoted

• Differences in test-taking motivation (employees vs. applicants)

• Experience with job can affect scores on criterion

Types of Criterion Validity

• Predictive• Scores on predictor (e.g., selection test) collected

some time before scores on criterion (e.g., job performance)

• Able to differentiate individuals on a criterion assessed in the future

• Weaknesses• Due to management pressures, applicants can be chosen

based on scores on predictor (can have range restriction, but this can be corrected)

• Often, special measures of job performance are developed for validation study

Types of Criterion Validity

• When full range of scores on predictor variable is available– Use unrestricted and restricted standard

deviations of predictor variable & the observed correlations b/w predictor & criterion

Correction for range restriction

• Construct Validity• Extent to which hypotheses about construct are

supported by data1. Define construct, generate hypotheses about

construct’s relation to other constructs2. Develop comprehensive measure of construct & assess

its reliability3. Examine relationship of measure of construct to other,

similar and dissimilar constructs

• Examples: height & weight; Learning Style Orientation measure; networking; career outcomes

Types of Validity (cont’d)

• Multi-trait multi-method matrix• Convergent validity coefficient

• Absolute size of correlation between different measures of the same construct

• should be large, significantly diff from zero,

• Discriminant validity coefficient• Relative size of correlations between the same construct

measured by different methods compared to• Different constructs measured by different methods• Different constructs measured by same method (method bias)

Establishing Construct Validity

O-H SR-H O-W SR-W

O-H 1.00

SR-H .98 1.00

O-W .55 .56 1.00

SR-W .68 .69 .92 1.00

Corr b/w Objective (O) & Self-Reports (SR) of Height & Weight

• Multi-trait multi-method matrix– Different measures of the same construct should be

more highly correlated than different measures of different constructs• e.g., Perceived career success & promotion vs.

networking vs. promotion/salary– Different measures of different constructs should

have lowest correlations• e.g., Networking vs. promotion/salary

Establishing Construct Validity

• Item Development Study (generate critical incidents)– N=67– Yes/no responses to statements– Recall of learning events

• Two types of learning: theoretical, practical• Two types of outcomes=success, failure• 2 x 2 events per participant• 112 items constructed in total

Learning Style Orientation Measure

• Item Development Study (questionnaire)– N=154– 112 items, 5 point likert scale (agree/disagree)

• 5 factor solution w/factor analyses• 54 items• Content validity sorting by 8 grad students

– Goldberg personality scale


• Item Development Study • Correlations b/w LSO & personality

• Only 1 sig correlation b/w 5 factors of LSOM!• High reliabilities of subscales of LSOM (.81-.91)• Construct (not really convergent) validity

– r b/w LSOM & personality subscales• .42 to -.26.


• Validation Study– N=350 -193– LSOM, Personality, old LSI, preferences for

instructional & assessment methods• Construct validity

– r b/w LSOM subscales & old LSI= .01 to .31– r b/w LSOM & personality subscales= .01 to .55– Confirmatory factor analysis

• 5-dimensions confirmed• High reliability


• Validation Study– Incremental validity

• Additional variance explained (LSOM vs LSI)


DV LSOM LSISubjective assessment .15 .01

Interactional instruction .21 .04

Informational instruction .06 .00

• Brainstorm constructs to develop measures• E.g. Dimensions of CIR professor effectiveness, CIR

student effectiveness

• Choose two constructs that can be measured similarly and be defined clearly

• Example measures– Self-report (rating scales)– Peer/informant reports – Observation– Archival measures– Trace measures etc etc.

In-class Exercise

• Form two-person groups to• Generate items of the 2 different measures for each of

the two constructs

• Appointed person collects all items for both measures for both constructs

• Compiles & distributes measures to class

• Class gathers data on both measures & both constructs

• Class enters data into SPSS format• Compute reliabilities,means, correlations

In-class Exercise

C1C2

M2M2

M1M1

Fill in the correlations

Types of Validity

Content Validity

Criterion Validity

Construct Validity

Predictive Validity

Concurrent Validity

Convergent Validity

Discriminant Validity

Adapted from Sekaran, 2004

Documents

Definitions Correlation, Reliability, Validity, Measurement error Theories of Reliability