Individual Differences in Productivity: An Empirical Test of Estimates Derived from Studies of Selection Procedure Utility

Abstract

A literature review indicates that the standard deviation of employee output averaged 20% of mean output under nonpiecework compensation systems and 15% under piecework systems. For both systems, variability around the mean was small. Implications for selection and workforce productivity are discussed. (25 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)

Full text

Journal of Applied Psychology
1983,
Vol 68, No 3, 407^114
In the public domain
Individual Differences in Productivity: An Empirical Test of
Estimates Derived From Studies of Selection Procedure Utihtv
Frank L. Schmidt
U.S Office of Personnel Management and
George Washington University
John E. Hunter
Michigan State University
Schmidt, Hunter, McKenzie, and Muldrow (1979) presented and applied a
method for estimating the standard deviation of employee output in dollars This
study cumulates empirical data from the research literature to estimate the stan-
dard deviation of employee output as a percentage of mean output
For jobs
with
nonpiecework compensation systems, the standard deviation was found to average
20%
of mean output This
figure
is not greatly different from the
24%
lower bound
predicted on the basis of previous studies in which the standard deviation was
in dollar form The figure for piecerate jobs was found to average about 15% of
mean output For both piecerate and nonpiecerate jobs, the variability around
the mean was small We conclude that the findings support the use of 40% of
salary as an estimate of
the
standard deviation of productivity in dollars Use of
20%
of mean output as the standard deviation value (or
15%
for piecework jobs)
in utility formulas allows evaluation of the impact of selection and nonselection
programs in terms of percentage increase in output For organizations that want
to hold output constant, this increase can be translated into payroll savings from
reduced hiring
A critical parameter in studies of the eco-
nomic utility of personnel selection and other
personnel programs (such as training) is the
standard deviation of employee contribu-
tions in dollars (SD
y
; Schmidt, Hunter,
McKenzie, & Muldrow, 1979; Schmidt,
Hunter, & Pearlman, 1982) Difficulties in
estimating this value have long discouraged
much needed utility analyses We have de-
vised a practical method for estimating SZ>
V
(Schmidt et al., 1979) and have examined the
resulting values as a percentage of salary for
the jobs
in question. The SD
y
as a percentage
of salary has ranged from 42% (Mack,
Schmidt, & Hunter, Note 1) to 60% (Hunter
&
Schmidt,
1982,
p
258).
As
a rule of thumb,
we have recommended (Hunter, Note 2;
Schmidt, Note
3)
that the round lower bound
The opinions expressed herein are those of the authors
and do not necessarily reflect official policy of
the
insti-
tutions with which they are affiliated
Requests for reprints should be sent to Frank L
Schmidt, Office of Personnel Research and Develop-
ment, Room 3G29, U S Office of Personnel Manage-
ment, 1900 E Street, N W, Washington, DC 20415
figure of
40%
of salary be used as a conser-
vative estimate of SD
V
when time and/or
resources do not permit the use of estimat-
ing SD
t
In addition to indices of employee vari-
ability in terms of dollars and in terms of a
percentage of salary or wages, it would also
be useful to express individual differences in
output in percentage terms. That is, it would
be useful to know the standard deviation of
output as a percentage of mean output (SD
P
)
for the job in question This figure would
allow gains from improved selection to be
expressed as percentage increases in output.
Aside from this practical value, knowledge
of the extent and magnitude of individual
differences in productivity is of general in-
formational and theoretical interest to the
field of applied differential psychology. We
would like to know how much employees in
the same job typically differ in productivity,
probably the most important dependant van-
able in industrial/organizational psychology.
Given the fact that in the United States
economy, wages and salaries make up ap-
proximately 57% of the total value of goods
407

408
FRANK L SCHMIDT AND JOHN E HUNTER
and services produced (Hunter & Schmidt,
1982,
p 268), we can derive lower and upper
bound predictions for the value of SD
P
:
Lower bound prediction = 42% (57%)
= 24%
Upper bound prediction = 60% (57%)
= 34%
The purpose of this study is to compare
these upper and lower bound predictions to
empirical figures for SD
P
that can be ex-
tracted from the cumulative research litera-
ture.
This literature consists of
(a)
studies that
report the mean and standard deviation of
actual employee production or output and
(b) studies that report the ratio of actual out-
put of highest producing employees to actual
output of lowest producing employees. In the
latter type of study, given the assumption of
normality of the full output distribution, the
standard deviation as a percentage of mean
output can be computed for all studies that
give
the sample size In either
case,
only stud-
ies based on actual physical counts of em-
ployee output can be used The mean of these
SD
P
values across studies can be compared
with the predicted lower and upper bound
values of
24%
and 34% The standard devia-
tion of
the
empirical SD
P
values provides in-
formation on the job to job variability in the
magnitude of individual differences Finally,
one can compute from each empirical SD
P
value the ratio of output at the 95th percen-
tile of production to the output at the 5th
percentile, again based on the assumption of
normality of
the
full distribution of output '
The mean of these ratios can then be com-
pared with the ratios predicted by our lower
and upper bound estimates 2.30 and 3.54,
respectively.
Method
A
review of the literature revealed
18
sources reporting
either distributions of actual employee output or ratios
of output of highest to lowest producing employees
These reports ranged in time from 1928 to 1978 Rothe
(1978) and Rothe and Nye (1959) have presented evi-
dence that variance of productivity distributions and
magnitude of productivity ratios vary as a function of
whether there is a piecerate incentive system We there-
fore analyzed the two kinds of data separately, however,
because of descriptive deficiencies in some of the studies.
it was not always possible to determine with certainty
whether an incentive system was present or not Such
uncertain cases were analyzed separately However, our
hypothesis was that in such cases compensation was not
on a piecerate basis It appeared that authors have de-
scribed a compensation system only when it was a
piecerate system
In the studies reviewed, employee output was
self-
paced, in none of the studies did employee rate of pro-
duction appear to be constrained
by the
production tech-
nology, as it would be in the case of an assembly line
A number of studies presented findings separately for
experienced employees and all employees, in such cases,
only the results for the experienced employees
were
used
Other studies specified that only data from experienced
employees were analyzed
For the incentive condition, there were 11 usable re-
ports,
for the nonmcentive condition, there were 14 For
the uncertain condition, there were 24 reports, but be-
cause of missing data.
SD
P
and the ratio of output of the
95th to 5th percentiles could be computed for only 15
of these reports
For studies that reported the mean and standard de-
viation of actual output, the ratio of the standard devia-
tion
to
the mean
was
computed directly For
those
studies
that reported only the ratio of output of the highest pro-
ducing to the lowest producing employee (R) and the
sample size, the following procedure was used The z
score in the normal distribution was determined for the
highest and lowest producing
employees,
and
the
distance
in standard deviation units (d) between these two points
was
computed For
example,
if the
two
:
scores are
+2 00
and -2 00, d = 4 00 The ratio of the 95th to 5th per-
centile (R
a
) is then
_(R + l)/2+ 1645(i?- \)/d
"~ (R +l)/2 -
1
645(/? - \)ld
The ratio of the SD to mean output is then
SD
" X '
Re- 1
1 645tR
o
+1)
Results and Discussion
Results for SD
P
Table 1 shows the results for the nonin-
centive condition. The last column shows the
standard deviation as a percentage of mean
output. The mean of this value across studies
is 185. The standard deviation of these val-
ues is quite small ( 052), even though it has
not been corrected for the effects of sampling
error and is therefore an overestimate of real
variability across jobs (Hunter, Schmidt, &
Jackson, 1982, chap. 3). (The formula for the
sampling error variance of this statistic is not
1
For example, if
SD
P
= 20, this ratio is (1 +
1
645
( 20))/1 -
1
645 ( 20)) or
1
98

INDIVIDUAL DIFFERENCES IN PRODUCTIVITY
409
known.)
The
value
of
18.5%
of
mean output
is
1.1
standard deviation units smaller than
our predicted lower bound value
of 24%.
Although this difference
is
statistically
sig-
nificant
(p <
.01),
the
observed mean value
is still
77% as
large
as the
predicted lower
bound value The mean ratio of output
at
the
95th
and 5th
percentiles
is
1
93,
which
is
again somewhat smaller than
the
predicted
lower bound value
of
2.30.
Although
the dif-
ference
is
again statistically significant,
the
observed value
is 84% as
large
as the pre-
dicted lower bound value.
The
difference
in
standard deviation units
is 93.
The results for piecerate systems are shown
in Table
2.
Consistent with Rothe's (1978)
hypothesis, both means
are
smaller than
the
corresponding values
in
Table
1,
although
those differences
are not
statistically signifi-
cant. Both Table
2
mean values
are
signifi-
cantly smaller than our predicted lower bound
values, which
is not
unexpected because
our
predictions were derived from,
and
intended
to apply
to,
jobs without incentive based
compensation systems.
As in
Table
1, the
variation around
the
mean values
is
quite
small
For the
mean
SD
n
, the
standard
de-
viation
is
only
.044; for the
mean ratio
of
95th
to 5th
percentiles,
it is
only
.29.
Both
figures are again overestimates because there
has been
no
correction
for
sampling error.
Table
3
shows
the
results
for
studies
in
which the compensation system could not
be
determined with certainty. This table
in-
cludes
one
extreme data point,
the
value
of
17
35 for
sales clerks from
the
study
by
Lawshe (1948) This value
is
24.84 standard
deviations above the mean of the distribution
of the values
and is
clearly
an
outlier Table
3 presents means
and
standard deviations
with
and
without this anomalous value
in-
cluded; however,
our
discussion
and
conclu-
sions are based on the data with suspect value
excluded
The
mean value
for SD
P
is .215,
which
is not
significantly different from
our
predicted lower bound value
of .24 The
mean output ratio
of
2.20
is
also
not signif-
icantly different from
the
predicted lower
bound value
of
2.30
The
observed values
in
Table
3 are 90% and 96% as
large
as
their
respective predicted lower bound values
Both observed values
are
larger than
the cor-
responding values
for the
nomncentive
con-
dition
in
Table
1
(although the differences are
Table
1
Productivity
Ratios
Under Nonpiecework Compensation
Systems
Study
Klemmer & Lockhead (1962)"
Study 1
Study 2
Rothe(1946)
Rothe (1947)
Time 1
Time 2
Time 3
Rothe & Nye (1958)
Rothe &Nye (1961)"
1958
1960
Rothe (1970)
Stead &Shartle (1940)
Lawshe (1948)
Tiffin (1947)
Barnes (1958)"
M
SD
Job
Card punch operators
Proof machine operators
Dairy workers
Machine operators
Machine operators
Machine operators
Industrial workers
Machine operators
Machine operators
Welders
Typists
Cashiers
Electrical workers
Assembly workers
N
Not reported
Not reported
8
130
130
130
27
37
61
25
616
29
33
294
Ratio of
95th to 5th
percentiles
1 47
1 57
2 23
190
2 69
2 80
1 94
1 77
1
41
1 91
1 89
1 95
1 83
160
193
40
Ratio ofSZ>
to average
116
135
232
189
.278
288
194
169
103
190
.187
196
178
140
185
052
a
Means and standard deviations for experienced workers given, ratios are based on these
b
Ns are averages across 11-12 weeks

410 FRANK L SCHMIDT AND JOHN E HUNTER
not statistically significant). Both values are
significantly larger (p < .05) than the corre-
sponding values for the incentive condition
(Table 2). These findings support our hy-
pothesis that studies in the uncertain cate-
gory are based predominantly or wholly on
data from jobs without piecerate compen-
sation systems and should be combined with
the studies in Table 1. When this is done, the
combined figures for Tables
1
and 3 are both
significantly larger (p < .05) than the corre-
sponding values in Table 2 These results in-
dicate that individual differences in produc-
tivity may be somewhat smaller under incen-
tive conditions than under nomncentive
compensation systems.
It may be that the effect of piecerate sys-
tems is to reduce individual differences in
work motivation, thereby reducing the con-
tribution of motivational differences to out-
put differences. Under incentive conditions,
output differences may be determined pri-
marily by job-related abilities, whereas under
nomncentive conditions, both ability and
motivation may make large contributions.
The combined nomncentive condition and
uncertain condition data yield a mean SD
P
value of
20.0%
of mean output (SD = .062)
The mean ratio of 95th to 5th percentiles is
2.06 (SD = .53). These values are 83% and
90%
as large, respectively, as our predicted
lower bound estimates, although the differ-
ence between each figure and the lower
bound estimate is statistically significant
0><.01).
The variability across studies of SD
P
is
smaller in all three tables and for the com-
bined data from Tables 1 and 3 than one
would have perhaps predicted. Further, some
of the observed variability is due to simple
sampling error (although the formulas needed
to estimate the size of the sampling error con-
tribution are not known). Thus real van-
ability across jobs is even less than indicated
by
the small standard deviations in the tables
This is somewhat surprising, in that one
would expect organizations to vary in the
extent to which they allow or encourage in-
dividual differences in productive capacity to
manifest themselves. Perhaps such interor-
gamzational differences, aside from the pres-
ence of piecerate compensation systems, pro-
duced only limited variability in the extent
of individual differences in output
(SD
P
).
Further research on this question would be
useful.
The low levels of variability for SD
P
across
jobs indirectly supports the assumption of
normality of the output distribution on which
the calculations for some studies were based.
(Notes
to the tables indicate studies for which
this assumption was not necessary.) Had this
Table 2
Productivity
Ratios
Under Piecerate Compensation
Systems
Study
Rothe(1951)
Rothe&Nye(1959)
Rothe (1978)"
Department A
Department B
Department C
Department D
Barnes (1958)"
Barnes (1937)"
Tiffin (1947)
Group 1
Group 2
Viteles(1932)
b
M
SD
Job
Candy manufacture
Machine operators
Foundry workers
Foundry workers
Foundry workers
Foundry workers
Assembly workers
Lathe operators
Electrical workers
Hosiery loopers
Weavers
N
18
42
26
19
17
21
314
121
39
99
239
Ratio of
95th to 5th
percentiles
150
2 35
1
66
1
43
1 52
1
45
142
1 63
2
08
1 91
1.58
169
29
Ratio of SD
to average
122
.245
.151
108
125
112
105
146
.213
.190
137
150
044
• Mean Ns, Ns varied slightly over weeks
b
Means and standard deviations given, ratios are based on these

INDIVIDUAL DIFFERENCES IN PRODUCTIVITY
411
assumption not been at least approximately
met and had the resulting values been off
appreciably as a consequence, the standard
deviation of the resulting values would prob-
ably have been larger. It would, of course,
nevertheless be desirable for future studies of
employee output to report the information
needed to compute SD
P
directly.
In light of the limited variability across
jobs,
the means and standard deviations in
Tables 1-3 could be computed weighting by
study sample sizes This change, however,
makes little difference. For Table 1, mean
SD
P
becomes .191 instead of .185, and the
standard deviation is .049 (vs. .052). The
sample size weighted values for Table 2 are
.140 (vs .150) and .040 (vs. .044). For Table
3,
the weighted values are .210
(vs.
.215) and
070 (vs .067). Combimng Tables 1 and 3,
mean SD
P
is virtually unchanged at.
199
(vs.
.200),
and its standard deviation is .058 (vs.
the unweighted .062).
The
findings
presented in Tables 1, 2, and
3 reflect primarily quantity of output, quality
of output is probably reflected only crudely
in these
figures
(e.g., by enforcement of min-
imum quality standards). If quality and
quantity are uncorrelated or positively cor-
Table 3
Productivity
Ratios in Studies with
Uncertain Compensation
Systems
Study
Hull (1928 p 35)
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
Evans (1940y
Stead & Shartle, (1940)
Group 1
Group 2
Group 3
Group 4
Group 5
Group 6
Lawshe(1948)
Group 1
Group 2
Group 3
Wechsler(1952)
b
Group 1
Group 2
Group 3
McCormick & Tiffin
(1974)
Group 1
Group 2
Group 3
M
c
srr
Job
Shoe factory workers
Hosiery factory workers
Textile industry workers
Shoe factory workers
Textile industry workers
Silverware manufacture
"A Number of handcraft jobs"
Sales clerks
Card punch operators
Day shift
Night shift
Lamp shade manufacture
Card punch operators
Sales clerks
Sales clerks
Drilling
Wool pullers
Sales clerks
Machine sewing
Electrical workers
Electrical workers
Cable workers
Electrical workers
Assemblers
N
NR
NR
NR
NR
NR
NR
NR
153
113
121
19
62
NR
NR
11
13
18
101
100
65
40
138
35
Ratio
95th to 5th
percentiles
NC
NC
NC
NC
NC
NC
2 22
3
46
162
1 80
147
2 84
NC
NC
3 37
200
17
35
196
1 54
178
2 29
191
2 54
2 20(3.21)
.62 (3 83)
Ratio of SD
to average
230
335
144
174
.116
291
330
.203
542
197
129
171
238
190
.264
215
(.237)
067
(.104)
Note NR = not reported, NC = not computable
a
Adjusted ratio computed based on information that for all of these jobs the standard deviation of output was
approximately
23%
of mean output
b
Means and standard deviations given, ratios are based on these
c
Values in parentheses include the Lawshe (1948) sales clerks, values not in parentheses do not.

412
FRANK L SCHMIDT AND JOHN E HUNTER
related, the SD of value of output as a per-
centage of
value
of mean output will be larger
than 20%. The corresponding high-low out-
put ratios will also be larger. Only one of the
studies reviewed investigated the relation be-
tween quality and quantity of
output.
Klem-
mer and Lockhead (1962) found a correla-
tion of .53 between amount of output and
freedom from errors for proof machine op-
erators (N = 459); for keypunch operators
(N =271), the correlation was 42. Thus the
high-producing employees also had higher
average quality of output. Therefore, if it had
been possible to include indices of quality of
output along with amount of output, the out-
put differences between good and poor em-
ployees might have been greater than Tables
1,2, and 3 indicate
2
This would mean that
the SD of output value would be greater (for
the combined nonpiecerate and uncertain
conditions) than 20% of value of mean out-
put. Our past studies of selection utility have
been based on a method of estimating
SD>
(Mack et al, Note 1, Schmidt et al., 1979,
Hunter & Schmidt, 1982) that takes into ac-
count both quality and quantity of output
This fact may explain why the estimates ob-
tained in this study for the nonpiecerate con-
dition (SD
P
- 20% of mean output) corre-
spond more closely to our lower bound es-
timate (SD
P
= 24% of mean output) than to
our upper bound estimate (SD
P
= 34% of
mean output). Further research on this ques-
tion might be profitable
The findings reported in this study are
based on blue collar skilled and semiskilled
jobs and lower level white collar jobs Our
predicted productivity ratio and standard
deviation of output, however, were based in
large part on middle level jobs (e.g., budget
analysts and computer programmers) Our
model predicts that the productivity ratio
and the standard deviation of output as a
percentage of mean output will be similar at
all job levels. This may not be the case
Higher level jobs may often allow for very
expensive errors, which increase the standard
deviation disproportionately relative to sal-
ary (Hunter & Schmidt, 1983). In this con-
nection, it would be desirable to obtain out-
put data on higher level jobs in the future
These findings and the associated consid-
erations discussed above indicate that when-
ever employee output is self-paced and there
is no piecerate or other incentive system, re-
searchers examining the utility of personnel
programs such as selection and training can
estimate the standard deviation of employee
output at 20% of mean output without fear
of overstatement. This figure is probably
somewhat conservative; exactly how much it
underestimates true variability remains to be
determined. The findings of this study pro-
vide support for the practice that we have
recommended
(e.g.,
Schmidt
&
Hunter, 1981)
of estimating SD
V
(the SD of output in dol-
lars) as 40% of mean salary when practical
considerations do not permit a direct esti-
mate of SD
V
. Given that wages and salaries
average 57% of the value of goods and ser-
vices in the United States economy (Hunter
& Schmidt, 1982, p. 268), 40% of salary cor-
responds to 40(.57) =
22.8%
of mean output.
This is close to the mean value of 20% ob-
tained in this study Allowing for the effects
of quality differences on SD
P
, a figure of
ap-
proximately
23%
of mean output may be rea-
sonably accurate.
Finally, we note that all of the
figures
above
were of necessity derived on incumbents
rather than applicants In most cases, the
standard deviation of output (whether in dol-
lars or as percentage of the mean) is probably
larger for applicants than incumbents, mak-
ing these figures conservative when used m
evaluating selection programs However, this
consideration does not apply when nonselec-
tion organizational interventions (e.g., train-
ing programs) are evaluated (Schmidt et al.,
1982).
In the latter case, it is the standard
deviation for incumbents that is appropriate
and needed
Practical
Implications
The findings of this study make it possible
to express the utility of selection methods in
2
Data to support this proposition were brought to the
attention of the first author after this study was com-
pleted In a study conducted recently in the U S Postal
Service in which quality as well as quantity was mea-
sured, SD
P
was 23 for mail earners, 26 for mail han-
dlers,
and 40 for mail distribution clerks (Mahoney,
Note 4) Quality was controlled by excluding all erro-
neous "production" from the counts of output

INDIVIDUAL DIFFERENCES IN PRODUCTIVITY
413
terms of percentage increases in workforce
output The formula for mean gain per per-
son selected per year in dollars (Schmidt et
al.,
1979) is
AU = r
xy
SDrf/p,
where r
xy
= the true (operational) validity of
the selection procedure in the applicant pop-
ulation; the observed validity corrected for
criterion unreliability and range restriction,
SD
y
= the yearly standard deviation of output
in dollars; p = the proportion selected;
<f>
=
the ordmate in the unit normal curve cor-
responding to p; and
4>/p
= the mean (ap-
plicant pool) z score of the selectees. If we
substitute 20 for SD
y
in this equation (i.e,
SD of output is 20% of mean output), utility
is expressed m terms of percentage increases
in output. For example if p = .30 and r
xy
=
.50,
then A
(7 =
11.4;
output among new hires
can be expected to be about 11% higher as
a result of employing the selection procedure
in question. If the selection ratio were 15,
the gam would be 15 2% Using the formulas
given in Schmidt et al (1982), one can make
similar evaluations of nonselection personnel
programs, such as incentive systems or train-
ing programs.
For employers who continue to hire the
same number of people as previously, the
result will be an increase in total output, even
though the newly hired, more productive em-
ployees are initially only a small portion of
the workforce. For employers who can mar-
ket more of their product than they are now
producing, this would be the appropriate op-
tion. However, for some organizations, in-
creased total output is not a goal. Such or-
ganizations see themselves as having an es-
sentially fixed amount of production to get
out per unit of
time,
that is, they see the de-
mand for their product as
fixed
and therefore
are concerned not with increasing output but
with increasing the efficiency (l e , reducing
the costs) of producing a fixed required
amount of output. Many service and public
organizations fall into this category Such
organizations may want to take the produc-
tivity gams from improved selection in the
form of reduced hiring, that is, in the form
of a reduced workforce and therefore m the
form of reduced payroll costs For example,
in the situation described above in which new
hires can be expected to have 11.4% higher
output, the number hired can be reduced by
approximately
10%
with no decline in output
(.114/(1 + .114) = .102). An employer hiring
200 new employees each year (to replace
losses due to turnover, retirement, etc.),
would now need to hire only 180. If
the
em-
ployees are paid an average of
$ 16,000
per
year, the payroll savings would be expected
to be 20 X $16,000 = $320,000 per year.
Additional savings would result if overhead
costs were also reduced. For example, the
employer may save the cost of providing the
employees with workplaces, offices, tools,
and so forth
For many organizations, a utility analysis
of this sort may be more useful than an anal-
ysis
that assumes a constant size for
the
work-
force and produces an estimate of increased
output, either in terms of a percentage in-
crease in annual output or in terms of the
dollar value of the yearly gam in output. This
procedure may therefore provide a useful tool
for personnel psychologists and their clients.
References Notes
1 Mack, M J . Schmidt, F L, & Hunter J E Esti-
mating the productivity costs in dollars of minimum
selection test cutoffs Unpublished manuscript. Per-
sonnel Research and Development Center, U S Office
of Personnel Management, Washington, D C , 1980
2 Hunter J E An analysis of the validity, differential
validity test fairness and utility oj the Philadelphia
Police Officers Selection Examination prepared by the
Educational Testing Service Unpublished manu-
script, Department of Psychology, Michigan State
University, East Lansing, Michigan, 1978
3 Schmidt, F L The impact of the clerical employees
selection test battery of the Philadelphia Electric Com-
pany on clerical productivity and payroll costs Un-
published manuscript, 1981
4 Mahoney J J Personal communication, March 10,
1983
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Revision received March 22, 1983 •