Regression
Simple Regression Equation

Multiple Regression

y = a + b 1x1 + b2x2 + b3x3 …..
y = a + bx
Test Score
Predicted
Score
Slope
y-intercept
Predicted
Score
Weights
y-intercept
Basic Process:
Key Points:
• All applicants take every test.
• Regression is a compensatory approach. That
is, a high score on one test can compensate for
a low score on another.
• Scores are weighted and combined to yield a
predicted score for each applicant.
• Applicants scoring above a set cutoff score
are considered for hire
• Best for tests to not relate to each other, but
relate highly to the criterion.
y
Y = 1 + .5X
10
9
Job
Performance
X=12, what is y?
If satisfactory performance is a score of 5,
what would the score on X need to be?
8
7
6
*
*
*
*
5
*
*
*
*
*
*
*
4
*
*
3
*
*
*
*
2
*
*
*
1
*
1
2
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
* *
*
*
*
*
*
*
**
*
*
*
*
*
*
*
3
4
5
6
7
Test Scores
8
9
10 11 12
x
Compensatory Example
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
1
2
Predicted
Criterion Score
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
Independent Predictors
r
r
1c
Predictor 1
2c
Criterion
Predictor 2
R2 = r
2
1c
c.12
For example, if r = .60 and r
1c
+r
2
2c
= .50, then
2c
2
R c.12 =
2
2
(.60) + (.50)
= .36 + .25
= .61
Interrelated Predictors
Criterion
r
r
1c
2c
r
12
Predictor 1
2
Predictor 2
2
r 1c r 2c - 2r 12r 1cr 2c
2
R c.12 =
1 - r2
12
For example, if the two predictors intercorrelate .30, given the validity coefficients from the previous example
And r = .30, we will have
12
2
2
R c.12 =
2
(.60) + (.50) - 2(.30)(.60)(.50)
1 – (.30)2
= .47
Multiple Cutoff Approach
Pass
WAB
Paper & Pencil
Math Test
Paper & Pencil
Aptitude Test
100
X
100
X
100
Pass
Pass
Cutoff
score
Cutoff
score
Fail
X
Cutoff
score
Fail
Fail
0
0
0
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 Hurdle Approach
Paper & Pencil
Knowledge Test
100
Pass
xxx
xxx
xxx
xx
xx
Fail
Eliminated
from the
selection
process
xx
0
Pass
Interview
Work Sample
Test
100
100
xxx
xx
xxx
Pass
Cutoff
score
Cutoff
score
Cutoff
score
Fail
Eliminated
from the
selection
process
x
x
0
Fail
Eliminated
from the
selection
process
x
0
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.
Banding
“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 IndustrialOrganizational Psychology (Report, 1994)
Banding Types
Traditional
SED
(standard error of the difference)
(e.g., bands determined
based on trend analysis,
expert opinion)
100 - 90
89 - 80
79 - 70
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)
Banding (cont.)
SED Banding Types
Both use the top score to establish the top of the band
Fixed
96
92
90
88
84
82
..
.
..
..
.
..
Sliding
All those from the band
are selected before
those from the lower
band
96
94
92
90
88
86
82
SEM = 6.0
.
.
..
..
..
.
..
Bands slide down
after each person is
removed from the top
(bands re-established)
SEM = 6.0
Banding (cont.)
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
Predicted Criterion Scores (in Z-score units) for Three Applicants
To Each of Three Job and Assignments Made under Three Alternative
Classification Strategies
Worker A
Worker B
Worker 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)
Number of
jobs adequately
held
Number of workers
placed according to
their highest talent
Job 1
Job 2
Job 3
1.0
0.7
-0.4
0.8
0.5
-0.3
1.5
-0.2
-1.6
0.9
0.0
-2.0
B
C
A
1
1
A
A
A
1
1
A
B
C
3
0
Source: From Applied Psychology in Personnel Management (2nd ed) by Wayne Casco. 1982.