Transcript Statistics in HRM - School of Business Administration

Statistics in HRM
Kenneth M. York
School of Business Administration
Oakland University
Applied Research in HRM
• Statistics are used to answer applied
research questions in HRM, such as:
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ORG434
Does this selection test have adverse impact?
Is this selection test valid?
Is this selection test reliable?
What is the reliability of this selection test?
How much should this job be paid?
2
Determining whether a selection
test has adverse impact
• Civil Rights Act of 1964, SEC. 2000e-2.
[Section 703
– It shall be an unlawful employment practice
for an employer –
• to fail or refuse to hire or to discharge any
individual, or otherwise to discriminate against any
individual with respect to his compensation, terms,
conditions, or privileges of employment, because
of such individual's race, color, religion, sex, or
national origin;
ORG434
3
Determining whether a selection
test has adverse impact
• The Uniform Guidelines on Employee Selection ,
Section 41CFR60-3.4(d), Adverse impact and the
“four-fifths rule.''
– A selection rate for any race, sex, or ethnic group
which is less than four-fifths (4/5) (or eighty percent)
of the rate for the group with the highest rate will
generally be regarded by the Federal enforcement
agencies as evidence of adverse impact, while a
greater than four-fifths rate will generally not be
regarded by Federal enforcement agencies as evidence
of adverse impact.
ORG434
4
Determining whether a selection
test has adverse impact
• Calculating Adverse Impact by the 4/5ths
Rule
– Selection Ratio Minority = # minority hired / #
minority applicants
– Selection Ratio Majority = # majority hired / #
majority applicants
– Adverse Impact Ratio = SRminority /
SRmajority
ORG434
5
Determining whether a selection
test has adverse impact
Applicant Flow Data...
Minority
Majority
Hired
40
99
Not Hired
15
14
Total
55
113
SR
0.73
0.88
Adverse Impact Calculations...
Adverse Impact Ratio (AIR)
ORG434
139
29
168
0.83
6
Determining whether a selection
test has adverse impact
• The Chi Square is the appropriate
statistical test, when the sample size is
large enough:
Applicant Flow Data...
Minority
Majority
Hired
40
99
Not Hired
15
14
Total
55
113
SR
0.73
0.88
Adverse Impact Calculations...
Adverse Impact Ratio (AIR)
Chi Square Test (df=1)
ORG434
139
29
168
0.83
5.74
0.0166
7
Determining whether a selection
test is valid
• Uniform Guidelines on Employee Selection
Proceedures, Section 41CFR60-3.3(a),
Discrimination defined: Relationship between
use of selection procedures and discrimination
– Procedure having adverse impact constitutes discrimination
unless justified. The use of any selection procedure which has an
adverse impact on the hiring, promotion, or other employment or
membership opportunities of members of any race, sex, or ethnic
group will be considered to be discriminatory and inconsistent
with these guidelines, unless the procedure has been validated in
accordance with these guidelines, or the provisions of section 6
of this part are satisfied.
ORG434
8
Determining whether a selection
test is valid
• Must show a statistically significant
correlation between test scores and job
performance
– Pearson Correlation Coefficient:
ORG434
9
Determining whether a selection
test is valid
Employee
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
Sum:
Squared:
X
650
625
480
440
600
220
640
725
520
480
370
320
425
475
490
620
340
420
480
530
680
420
490
500
520
Y
3.8
3.6
2.8
2.6
3.7
1.2
2.2
3.0
3.1
3.0
2.8
2.7
2.6
2.6
3.1
3.8
2.4
2.9
2.8
3.2
3.2
2.4
2.8
1.9
3.0
XY
2470
2250
1344
1144
2220
264
1408
2175
1612
1440
1036
864
1105
1235
1519
2356
816
1218
1344
1696
2176
1008
1372
950
1560
X2
422500
390625
230400
193600
360000
48400
409600
525625
270400
230400
136900
102400
180625
225625
240100
384400
115600
176400
230400
280900
462400
176400
240100
250000
270400
Y2
14.44
12.96
7.84
6.76
13.69
1.44
4.84
9.00
9.61
9.00
7.84
7.29
6.76
6.76
9.61
14.44
5.76
8.41
7.84
10.24
10.24
5.76
7.84
3.61
9.00
12460
71.2
36582
6554200
210.98
155251600
5069.44
Pearson Correlation:
ORG434
27398
---------------------42002.53807
0.65
10
Determining whether a selection
test is valid
• Checking the correlation coefficient for
statistical significance:
– df = (# pairs –2); Alpha = .05
– If the correlation is equal to or greater than the
tabled value, the correlation is statistically
Level of significance
significant
ORG434
df
20
21
22
23
24
25
0.05
0.423
0.413
0.404
0.396
0.388
0.381
11
Determining whether a selection
test is valid
• Calculate the multiple correlation between
test scores and job performance:
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.652294
R Square 0.425487
Adjusted R Square
0.400509
Standard Error
0.452644
Observations
25
ANOVA
df
Regression
Residual
Total
ORG434
SS
MS
F
Significance F
1 3.490017 3.490017 17.03393
0.00041
23 4.712383 0.204886
24
8.2024
12
Determining the reliability of a
selection test
• Reliability is the upper limit of validity
– For a test to be valid, it must be reliable
• To measure the reliability of a test over
time (stability), calculate Test-Retest
Reliability Coefficient
– Correlate a set of test scores at Time1 and
Time2
ORG434
13
Determining the reliability of a
selection test
• To measure the reliability of a test with
only one test administration, calculate the
Internal Consistency using the SpearmanBrown prophecy formula:
ORG434
14
Determining the reliability of a
selection test
• Step1: Divide whatever test into two halves and score
them separately (usually the odd numbered items are
scored separately from the even-numbered items)
• Step2: Calculate a Pearson correlation coefficient
between the scores on the even-numbered items and the
scores on the odd-numbered items.
• Step3: Apply the Spearman-Brown prophecy formula to
adjust the half-test reliability to full-test reliability. A
longer test will generally be more reliable than a shorter
test. The Spearman-Brown prophecy formula was
developed to estimate the change in reliability for
different numbers of items.
ORG434
15
Determining the reliability of a
selection test
Applicant
1
2
3
4
5
6
7
8
9
10
ORG434
Half1
82
85
87
90
83
78
90
80
70
60
Half2
88
90
82
88
75
82
87
84
77
65
Correlation
0.824818
Spearman-Brown
0.904001
16
Determining the reliability of a
selection test
• To determine the reliability of a panel of
interviewers, use the Intraclass Correlation
Coefficient
Performance Appraisal Panel
Employee Rater1
Rater2
Rater3
Hanks
5
6
5
Iverson
9
8
7
Jackson
3
4
3
Kennedy
7
5
5
Lewis
9
2
9
Mayer
3
4
3
Nystrom
7
3
7
ORG434
17
Determining the reliability of a
selection test
• Agreement between each pair of
interviewers an be calculated, and the ICC
gives the level of agreement among all the
interviewers
Rater1
Rater1
Rater2
Rater3
1
0.112946
1
0.924925 -0.161449
Intraclass Correlation Coefficient =
ORG434
Rater2
Rater3
1
Mean Squares Rows (Employees) - Mean Squares Remainder
Mean Squares Rows + (raters-1)*Mean Squares Remainder
0.328278
18
Determining how much a job
should be paid
• People should be paid fairly based on two
factors:
– The work that they do (difficulty, hazard,
responsibility, education, etc.)
• Internal Equity
– What the market is paying
• External Competitiveness
ORG434
19
Determining how much a job
should be paid
• Job Evaluation
– Evaluate the job, how much of each of the compensable factors
does the job require?
• Hazards: Occasional, intermittent or constant exposure to
mechanical, electrical, chemical, biological, or physical factors
which involve risks of accident, personal injury, health impairment
or death
– 1. Safe/minimal: General office or equivalent conditions result in little
or no exposure to injury or accident
– 2. Marginal/moderate: Occasional exposure to hazards or risk of injury
which are generally protected against or predictable
– 3. Dangerous/considerable:Regular exposure to conditions which are
unpredictable/uncertain and which result in risk of personal injury
– 4. Hazardous/Extreme:Continuous exposure to life threatening
conditions or accidents which are difficult to identify or protect against
ORG434
20
Determining how much a job
should be paid
• Job Evaluation
– Collect salary survey data on benchmark jobs,
how much do other organizations pay?
Michigan University
Rank
Michigan State University
Full
$77,500
Assoc
$58,000
Asst
$47,500
Full
$76,100
Assoc
$55,600
Asst
$48,500
Full
$96,700
Assoc
$68,200
Asst
$54,500
Full
$82,100
Assoc
$62,600
Asst
$48,900
Michigan Tech University
University of Michigan
Wayne State University
Western Michigan UniversityFull
ORG434
Salary
$69,700
Assoc
$55,500
Asst
$45,300
21
Determining how much a job
should be paid
• Job Evaluation
– Do a regression analysis, to determine the
midpoint salary for the benchmark jobs
– Interpolate/Extrapolate to determine the salary
for non-benchmark jobs, using the equation:
Salary = JETotal*Coeff+Intercept
Intercept
Job Evaluation Total
ORG434
Coefficients
34794.54887
332.387218
22
Statistics Pretest
• What statistic do you use?
– To determine the validity of a selection test
– To determine the adverse impact of a selection test
– To determine whether women get significantly lower
scores on a test than men
– To determine whether alternate (parallel) forms of a
test are statistically equivalent
– To determine how well a panel of interviewers agrees
with each other about candidates they’ve interviewed
ORG434
23
Statistics Pretest
• Are the people who went through the
training sessions (variable 1) more
productive than the other employees?
t-Test: Two-Sample Assuming Equal Variances
Mean
Variance
Observations
Pooled Variance
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
ORG434
Variable 1
Variable 2
86.32
73.76
66.89333333 111.7733333
25
25
89.33333333
0
48
4.698268973
1.11711E-05
1.677224191
2.23422E-05
2.01063358
24
Statistics Pretest
• Applicants completed a set of three
selection tests…interpret the results:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.576980571
R Square
0.33290658
Adjusted R Square
0.270366572
Standard Error
96.57244442
Observations
36
ANOVA
df
Regression
Residual
Total
ORG434
3
32
35
SS
MS
F
Significance F
148933.4153 49644.47178 5.323097801
0.004328422
298439.5847 9326.237021
447373
25
Statistics Pretest
• Does this selection test have adverse
impact?
Minority Majority
Hired
25
35
Not Hired
25
15
Total
SR
50
50
0.50
0.70
Chi square =
df =
Chi square critical value =
Chi square probability =
ORG434
Total
60
40
100
4.17
1
3.84
0.0412
26