Simple Regression Equation Multiple Regression

y = a + bx

Test Score

Slope

y-intercept

Predicted Score

y = a + b x + b x + b x …..

Predicted Score

y-intercept

1 1 2 2 3 3

Weights

Regression

Basic Process:

• All applicants take every test.

• Scores are weighted and combined to yield a predicted score for each applicant.

• Applicants scoring above a set cutoff score are considered for hire

Key Points:

• Regression is a compensatory approach. That is, a high score on one test can compensate for a low score on another.

• Best for tests to not relate to each other, but relate highly to the criterion.

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x

y

Test Scores

JobPerformanc

e

1 2 3 4 5 6 7 8 9 10 11 12

10

9

8

7

6

5

4

3

2

1

Y = 1 + .5X

X=12, what is y?

If satisfactory performance is a score of 5, what would the score on X need to be?

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How Four Job Applicants with Different Predictor Scores Can Have the Same Predicted Criterion Score Using Multiple Regression Analysis

Applicant Score on X Score on X Predicted Criterion Score 1 2

A 25 0 100

B 0 50 100

C 20 10 100

D 15 20 100

Note: Based on the equation Y = 4X + 2X. 1 2

Compensatory Example

Predictor 1 Criterion Predictor 2

R = r + r For example, if r = .60 and r = .50, then R = (.60) + (.50) = .36 + .25 = .61

2 2 2

2 2 2

c.12 1c 2c

1c 2c

c.12

r r1c 2c

Independent Predictors

R = 2

c.12

r r - 2r r r2 21c 2c 12 1c 2c

For example, if the two predictors intercorrelate .30, given the validity coefficients from the previous exampleAnd r = .30, we will have

12

R = = .472

c.12

1 - r212

(.60) + (.50) - 2(.30)(.60)(.50)2 2

1 – (.30)2

r r

r

1c 2c

12

Interrelated Predictors

Predictor 1 Predictor 2

Criterion

WAB

100

0

Pass

Fail

Cutoff score

Paper & Pencil Math Test

100

0

Pass

Fail

Cutoff score

Paper & Pencil Aptitude Test

100

0

Pass

Fail

Cutoff score

Basic Process:

• All applicants take every test.

• Applicant must achieve a passing score on every test to be considered for hire.

Key Point: A multiple cut-off approach can lead to different decisions regarding who to hire versus using a regression approach.

Multiple Cutoff Approach

X X

X

Interview

100

0

Pass

Fail

Cutoff score

Paper & Pencil Knowledge Test

100

0

Pass

Fail

Cutoff score

Work Sample Test

100

0

Pass

Fail

Cutoff score

Multiple Hurdle Approach

Basic Process:

• All applicants take the 1st test.

• Pass/fail decisions are made on the 1st and subsequent tests and only those who pass can continue on to the next test [a sequential process].

Key Point:

Useful when a lengthy, costly, and complex training process is required for the position.

Eliminated from the selection process

Eliminated from the selection process

Eliminated from the selection process

xxxx

xx

xxxxxxxxx

xxxxx

xx

xxx

x

“The basic premise behind banding is consistent with psychometric theory. Small differences in test scores might reasonably be due to measurement error, and a case can be made on the basis of classical measurement theory for a selection system that ignores such small differences, or at least does not allow small differences in test scores to trump all other consideration in ranking individuals in hiring.” (p. 82).

“There is legitimate scientific justification for the position that small differences in test scores might not imply meaningful differences in either the construct measured by the test or in future job performance.” (p. 85).

From the Scientific Affairs Committee of the Society for Industrial-Organizational Psychology (Report, 1994)

Banding

Banding Types

(e.g., bands determined based on trend analysis,

expert opinion)

100 - 90

89 - 80

79 - 70

(standard error of the difference)

Using tests of statistical significance to determine test bands considered equal

Consideration of the SEM of the test (standard deviation, test reliability, and level of confidence desired)

Traditional SED

Banding (cont.)

SED Banding Types

Fixed Sliding

.....

.....

Both use the top score to establish the top of the band

All those from the band are selected before those from the lower band

.

.....

.....

Bands slide down after each person is removed from the top (bands re-established)

SEM = 6.0

969290

888482

969492

888682

SEM = 6.0

90

Purposes of Banding ---

a) Fairness (e.g., test scores not significantly different are best treated as equivalent)

Some loss of predictive power (as compared to top-down selection)

b) Increase diversity

Greater diversity is obtained with the use of sliding bands and points for minority status

Banding (cont.)

Predicted Criterion Scores (in Z-score units) for Three ApplicantsTo Each of Three Job and Assignments Made under Three Alternative

Classification Strategies

Number of workersplaced according to their highest talent

Number of jobs adequately

heldWorker AWorker BWorker C

Minimum Qualification score (in Z-score units)Classification Strategies: Place each according to his best talent (vocational guidance)Fill each job with the most qualified person (pure selection)Place workers so that all jobs are filled by those with adequate talent (cut and fit)

Job 1 Job 2 Job 3

1.0 0.8 1.5 0.7 0.5 -0.2 -0.4 -0.3 -1.6

0.9 0.0 -2.0

Source: From Applied Psychology in Personnel Management (2nd ed) by Wayne Casco. 1982.

B C A 1 1

A A A 1 1

A B C 3 0