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Taylor-Russell utility dichotomises the criterion. Naylor and Shine (1965) keep the criterion continuous and compute the expected criterion gain in standard-deviation units. This is usually a better match when performance is itself a continuous construct, which is the modal case in industrial-organisational research on job-performance taxonomies (Borman & Motowidlo, 1993; Campbell, 1990; Rotundo & Sackett, 2002).
library(personnelSelectionUtility)
naylor_shine(validity = .35, selection_ratio = .20)
#> <psu_ns>
#> validity: 0.35
#> selection_ratio: 0.2
#> selected_mean_z: 1.39981
#> expected_criterion_z: 0.489933
#> sdy: 1
#> n_selected: 1
#> tenure: 1
#> cost: 0
#> gross_utility: 0.489933
#> net_utility: 0.489933The expected gain has two components. First,
selected_mean_z() returns the expected standardised
predictor score among selected applicants, which under the normal model
is the inverse Mills ratio. Second, this is multiplied by the validity
coefficient to obtain the expected standardised criterion gain:
\[ \bar{Z}_{x_s} \;=\; \frac{\varphi(z_c)}{1 - \Phi(z_c)} \;=\; \frac{\lambda(SR)}{SR}, \qquad \bar{Z}_{y_s} \;=\; r_{xy} \cdot \bar{Z}_{x_s}, \]
where \(z_c = \Phi^{-1}(1 - SR)\) is the cutoff in standardised units and \(\lambda(\cdot)\) denotes the standard normal density.
Naylor-Shine is the natural starting point when the analysis stops at expected criterion gain in standard-deviation units. The transition to monetary utility is governed by Brogden’s (1949) demonstration that, under linearity and normality, the expected criterion gain in dollars equals \(r_{xy} \cdot SD_y \cdot \bar{Z}_{x_s}\).
Brogden (1946, 1949) and Cronbach and Gleser (1965) convert standardised criterion gain into monetary utility by multiplying by \(SD_y\), the standard deviation of job performance value. The expected incremental utility for \(N_s\) applicants selected with validity \(r_{xy}\) at selection ratio \(SR\) over a tenure horizon \(T\), net of total cost \(C\), is
\[ \Delta U \;=\; N_s \cdot T \cdot r_{xy} \cdot SD_y \cdot \bar{Z}_{x_s} \;-\; C. \]
When the comparator is an operating procedure with validity \(r_{\text{baseline}}\) rather than random selection, the focal validity is replaced by the difference \(r_{xy} - r_{\text{baseline}}\) (Sturman, 2000, 2001). Schmidt, Hunter, McKenzie, and Muldrow (1979) popularised the organisational implications of this formulation in their analysis of the Programmer Aptitude Test (PAT). Their estimates of multi-million-dollar utility gains generated the modern utility-analysis literature, and a stripped-down version of their calculation is the canonical pedagogical example.
bcg_utility(
validity = .35,
selection_ratio = .20,
sdy = 50000,
n_selected = 100,
tenure = 3,
cost = 75000
)
#> <psu_bcg>
#> validity: 0.35
#> selection_ratio: 0.2
#> baseline_validity: 0
#> baseline_selection_ratio: 0.2
#> selected_mean_z: 1.39981
#> baseline_selected_mean_z: 1.39981
#> focal_expected_criterion_z: 0.489933
#> baseline_expected_criterion_z: 0
#> incremental_criterion_z: 0.489933
#> sdy: 50000
#> n_selected: 100
#> tenure: 3
#> cost: 75000
#> gross_utility: 7349000
#> net_utility: 7274000The Schmidt et al. (1979) PAT calculation uses different inputs (notably \(SD_y\) in 1979 dollars, a much larger cohort, and a longer tenure horizon) and is reproduced in detail in the Reproducing canonical examples vignette. The simplified call above illustrates the structure: the gross utility is the product of \(N\), \(T\), \(r_{xy}\), \(SD_y\), and the inverse-Mills selection-intensity term \(\bar{Z}_{x_s}\), minus total cost.
The classical Brogden-Cronbach-Gleser expression compares the focal
selection procedure against random selection. Sturman (2000, 2001)
argued forcefully that the realistic baseline is rarely random choice.
Almost every organisation already operates with some procedure:
reference checks (used by \(97\%\) of
organisations according to Gatewood and Feild, 2001), unstructured
interviews (\(81\%\)), or biodata. The
package implements this critique through the
baseline_validity and baseline_selection_ratio
arguments. Setting baseline_validity to the validity of the
operating procedure shifts the comparison from “test versus random” to
“test versus current system”, which is the operationally relevant
difference.
random_baseline <- bcg_utility(
validity = .35,
selection_ratio = .20,
sdy = 50000,
n_selected = 100,
tenure = 3,
cost = 75000
)
operating_baseline <- bcg_utility(
validity = .35,
baseline_validity = .20,
selection_ratio = .20,
sdy = 50000,
n_selected = 100,
tenure = 3,
cost = 75000
)
c(random = random_baseline$net_utility,
operating = operating_baseline$net_utility)
#> random operating
#> 7274000 3074572The shift from random to operating baseline reduces the estimated utility by approximately \(40\%\) in this example, consistent with the average reduction of \(59\%\) that Sturman (2000) documented across the published utility-analysis literature. The decision to adopt the new procedure may be unchanged, since the incremental utility remains positive, but the expected return communicated to organisational decision-makers is materially different.
Because \(SD_y\) enters the Brogden-Cronbach-Gleser expression linearly, any error in its magnitude propagates one-for-one into the final \(\Delta U\) figure: doubling \(SD_y\) exactly doubles the reported utility, all else equal. As Holling (1998) documents empirically, plausible alternative methods can yield \(SD_y\) estimates that differ by a factor of two or more (with the corresponding doubling of \(\Delta U\)), so the choice of estimation method is not a technicality but a substantive decision that should be justified and triangulated.
Holling (1998) classifies the methods for estimating \(SD_y\) into four families. The package implements representative members of each.
The cost-accounting approach assigns a monetary value to each unit of measurable production, originating in Roche (1961, cited in Cronbach & Gleser, 1965). It is conceptually the most defensible method when production is genuinely measurable, but is operationally restricted to jobs with quantifiable output.
# 5 employees, 2 output types (e.g., transactions completed and customer-service
# hours); unit_values gives the monetary value of one unit of each type.
sdy_cost_accounting(
units = matrix(c(2400, 18,
3100, 22,
1800, 14,
2700, 25,
2200, 20),
ncol = 2, byrow = TRUE),
unit_values = c(25, 80)
)
#> $y
#> [1] 61440 79260 46120 69500 56600
#>
#> $sdy
#> [1] 12590.67Schmidt et al. (1979) proposed the percentile-judgement method: experts estimate the dollar value of performance at the \(15\)th, \(50\)th, and \(85\)th percentiles, and \(SD_y\) is approximated as \((P_{85} - P_{15}) / 2\) under the normal-model assumption. This method has been the most widely applied historically but has been criticised for between-judge dispersion, anchoring effects, and cognitive difficulty (Bobko, Karren, & Parkington, 1983).
Schmidt, Hunter, and Pearlman (1982) proposed proportional rules
tying \(SD_y\) to mean salary:
approximately \(40\%\) of mean pay for
jobs of low to medium complexity, and approximately \(70\%\) for jobs of high complexity or when
output value is the relevant criterion. Raju, Burke, and Normand (1990)
reformulated the model in terms of the coefficient of variation of
performance ratings, which is implemented in sdy_rbn().
CREPID (Cascio & Ramos, 1986) decomposes the job into weighted activities and estimates the dollar value of each, summing across activities to obtain \(SD_y\). Variants appear in Janz and Dunnette (1977), Edwards, Frederick, and Burke (1988), and the superior-equivalents technique of Eaton, Wing, and Mitchell (1985) and Burke and Frederick (1984, 1986).
# CREPID weights activities by time/frequency and importance, distributes the
# average salary across activities, and computes individual-level monetary value.
activities <- data.frame(
activity = c("Strategic planning", "Team supervision", "Reporting"),
time_frequency = c(.40, .35, .25),
importance = c(3, 2, 2)
)
ratings <- matrix(c(
4, 3, 3,
5, 4, 4,
3, 4, 3,
4, 5, 4,
5, 5, 5
), nrow = 5, byrow = TRUE)
sdy_crepid(activities, ratings, salary = 80000)
#> $activity_weights
#> activity time_frequency importance raw_weight final_weight dollar_value
#> 1 activity_1 0.40 3 1.2 0.5000000 40000.00
#> 2 activity_2 0.35 2 0.7 0.2916667 23333.33
#> 3 activity_3 0.25 2 0.5 0.2083333 16666.67
#>
#> $y
#> [1] 280000.0 360000.0 263333.3 343333.3 400000.0
#>
#> $sdy
#> [1] 56833.09
# Superior-equivalents: SDy = (superior - typical) / z_difference, with z_difference
# the standardised distance the analyst assumes separates the two anchors.
sdy_superior_equivalents(superior_value = 140000, typical_value = 100000)
#> [1] 40000The empirical comparisons of Bobko, Karren, and Parkington (1983), Becker and Huselid (1992), and Hakstian, Wooley, Woolsey, and Kryger (1991) indicate that CREPID and the \(40\%\) rule converge to broadly similar values, while the global percentile method tends to produce values approximately \(1.8\) times larger. Triangulation across at least two methods is the practice supported by these comparisons, and the analyst should report a sensitivity range rather than a single value. Direct estimation from observed monetary criterion data, when available, is the most defensible anchor.
A common conceptual error is to apply Brogden-Cronbach-Gleser to evaluation problems for which it is not designed. Schmidt, Hunter, and Pearlman (1982) developed the parallel utility model for interventions such as training programmes, where the appropriate effect size is Cohen’s \(d\) between treated and control groups rather than a validity coefficient:
\[ \Delta U_{SHP} \;=\; N \cdot T \cdot d \cdot SD_y \;-\; C, \qquad d \;=\; \frac{\bar{Y}_{\text{treated}} - \bar{Y}_{\text{control}}}{SD_{\text{pooled}}}. \]
The function shp_utility() implements this
formulation.
shp_utility(
effect_size_d = .50,
sdy = 50000,
n_treated = 100,
tenure = 3,
cost = 25000
)
#> <psu_shp>
#> effect_size_d: 0.5
#> approximate_r: 0.242536
#> sdy: 50000
#> n_treated: 100
#> tenure: 3
#> cost: 25000
#> gross_utility: 7500000
#> net_utility: 7475000The conversion between \(r\) and
\(d\) under the equal-variance binormal
assumption is provided by cor_to_d() and
d_to_cor(). Mathieu and Leonard (1987) and Cascio (1989)
document representative applications to training programmes, while Burke
and Day (1986) and Morrow, Jarrett, and Rupinski (1997) provide
cumulative meta-analytic and longitudinal estimates respectively. The
substantive point is that selection utility (\(r\)-based) and intervention utility (\(d\)-based) require different inputs and
different study designs, even when the outcome metric (\(\Delta U\) in dollars) is identical.
Boudreau (1983, 1991) extended the basic monetary utility model along several economically relevant dimensions: discounting future benefits to net present value, separating fixed from variable costs, applying tax rates, incorporating contribution margins, and modelling employee flows over multiple periods. Per period, the discounted incremental utility is
\[ \Delta U_t \;=\; \frac{N_t \cdot \Delta\bar{Z}_y \cdot SD_y \cdot (1 + V)(1 - TAX)}{(1 + i)^t} \;-\; C_t, \]
with \(N_t\) the active headcount in
period \(t\), \(V\) the variable-value (or
contribution-margin) multiplier, \(TAX\) the tax rate, \(i\) the discount rate, and \(C_t\) the period cost. Total utility is the
sum of \(\Delta U_t\) over the horizon.
The function boudreau_utility() accepts these inputs
through the arguments n_by_period,
cost_by_period, contribution_margin,
tax_rate, and discount_rate.
boudreau_utility(
validity = .35,
baseline_validity = .20,
selection_ratio = .20,
sdy = 50000,
n_by_period = c(100, 90, 80, 70),
contribution_margin = .30,
tax_rate = .25,
discount_rate = .08,
cost_by_period = c(75000, 10000, 10000, 10000)
)
#> <psu_boudreau>
#> delta_z_y: 0.209971
#> sdy: 50000
#> variable_value: 0
#> contribution_margin: 0.3
#> effective_margin: 0.3
#> tax_rate: 0.25
#> discount_rate: 0.08
#> net_present_value: 579234If the expected incremental standardised gain comes from an external
model, it can be passed directly through delta_z_y,
bypassing the internal computation from validity,
baseline_validity, and selection_ratio.
boudreau_utility(
delta_z_y = .25,
sdy = 50000,
n_by_period = c(100, 90, 80),
discount_rate = .08,
cost_by_period = c(75000, 10000, 10000)
)
#> <psu_boudreau>
#> delta_z_y: 0.25
#> sdy: 50000
#> variable_value: 0
#> effective_margin: 1
#> tax_rate: 0
#> discount_rate: 0.08
#> net_present_value: 2829790When inflation is non-trivial, the discount rate should be adjusted
accordingly. Tziner, Meir, Dahan, and Birati (1994) show that the
inflation-adjusted rate is \(i_a = i + f + i
\cdot f\), where \(i\) is the
nominal discount rate and \(f\) is the
inflation rate. The package exposes this transformation as
inflation_adjusted_rate().
The combined boudreau_utility() framework is closer to
the standard capital-budgeting practice of corporate finance, but it
inherits the well-documented difficulties that Hunter, Schmidt, and
Coggin (1988) identified from inside the Schmidt-Hunter programme:
discount-rate selection, period definition, and the boundary between
fixed and variable costs are all decisions that materially affect the
estimate and that admit no purely statistical resolution.
When multiple predictors are combined into a single composite score,
the validity, reliability, and intercorrelation of the composite follow
from the well-known formulae in Lord and Novick (1968). The package
implements these as the fuse_* family.
weights <- c(.5, .3, .2)
item_validities <- c(.40, .30, .25)
item_reliabilities <- c(.85, .80, .75)
item_cor <- matrix(c(
1.00, .30, .20,
.30, 1.00, .25,
.20, .25, 1.00
), 3, 3, byrow = TRUE)
fuse_validity(weights, item_cor, item_validities)
#> [1] 0.4626814
fuse_reliability(weights, item_cor, item_reliabilities)
#> [1] 0.8787037
# fuse_composite_cor() returns the correlation matrix between several composites
# whose weights are stacked column-wise. The example below contrasts a unit-weighted
# composite with a validity-weighted composite of the same items.
W <- cbind(unit = c(1, 1, 1), validity_weighted = item_validities)
fuse_composite_cor(weights_matrix = W, item_cor = item_cor)
#> unit validity_weighted
#> unit 1.0000000 0.9900312
#> validity_weighted 0.9900312 1.0000000The composite validity is generally smaller than the largest
single-predictor validity unless the predictors carry independent
variance with respect to the criterion, which connects directly to the
incremental-validity reasoning developed below. Disattenuation of the
observed correlation for measurement error in the criterion is provided
by disattenuate_correlation().
disattenuate_correlation(r_observed = .35, reliability_x = .85, reliability_y = .70)
#> [1] 0.4537426Disattenuation moves the analysis from the observed-score metric to the true-score metric, which is the appropriate input for population-level utility statements but should be reported alongside the observed-score estimate (Schmidt & Hunter, 2015).
A second standard correction is for range restriction. Sackett, Laczo, and Arvey (2002) and Sackett, Lievens, Berry, and Landers (2007) distinguish direct range restriction, which operates on the predictor that was used as the selection variable, from incidental range restriction, which operates on variables correlated with the selected variable. The Thorndike Case II correction handles direct restriction; the Lawley (1943) multivariate correction handles incidental restriction in correlated predictors.
correct_r_direct_range_restriction(
r_restricted = .25,
range_restriction_ratio = 1.40
)
#> [1] 0.3399501The Lawley multivariate correction is more general and covers the case in which selection occurs on a composite or on a different variable than the one being corrected.
# Three-variable example: selection on X1 (cognitive ability, the predictor used as
# the selection variable); incidental restriction on X2 (interview) and Y (criterion).
sigma_star <- matrix(c(
1.00, .30, .25,
.30, 1.00, .20,
.25, .20, 1.00
), 3, 3)
# Unrestricted SD of X1 is 1/.6 times the restricted SD; variance increases by 1/.6^2.
sigma_ss_unrestricted <- matrix(1 / 0.6^2, 1, 1)
correct_r_lawley(
sigma_restricted = sigma_star,
selection_indices = 1,
sigma_ss_unrestricted = sigma_ss_unrestricted
)
#> $sigma_corrected
#> [,1] [,2] [,3]
#> [1,] 1.0000000 0.4642383 0.3952847
#> [2,] 0.4642383 1.0000000 0.2936101
#> [3,] 0.3952847 0.2936101 1.0000000
#>
#> $sigma_restricted
#> [,1] [,2] [,3]
#> [1,] 1.00 0.3 0.25
#> [2,] 0.30 1.0 0.20
#> [3,] 0.25 0.2 1.00
#>
#> $selection_indices
#> [1] 1
#>
#> $incidental_indices
#> [1] 2 3
#>
#> $u
#> [1] 0.6
#>
#> $sign_changes
#> [1] 0Ree, Carretta, Earles, and Albert (1994) document that multivariate range-restriction corrections can occasionally produce sign changes when the unrestricted covariance structure is poorly estimated, which is a strong argument for reporting both corrected and uncorrected values and for inspecting the implied unrestricted matrix for plausibility.
When a battery already exists and a candidate predictor is being considered for addition, the relevant quantity is not the marginal correlation of the new predictor with the criterion but the incremental validity of the augmented battery over the existing one. Sturman (2001) developed the matrix formulation of this problem as a restricted canonical correlation, in which the predictor-side weights are optimised given a fixed criterion-side composite weighting. With predictor correlation matrix \(\boldsymbol{\Sigma}_{11}\), predictor-criterion correlation matrix \(\boldsymbol{\Sigma}_{12}\), criterion correlation matrix \(\boldsymbol{\Sigma}_{22}\), fixed criterion weights \(\mathbf{b}\), and predictor weights \(\mathbf{a}\) to be determined,
\[ r_{uv} \;=\; \frac{\mathbf{a}^{\top} \boldsymbol{\Sigma}_{12} \mathbf{b}}{\sqrt{\mathbf{a}^{\top} \boldsymbol{\Sigma}_{11} \mathbf{a}} \cdot \sqrt{\mathbf{b}^{\top} \boldsymbol{\Sigma}_{22} \mathbf{b}}}, \]
with the optimal predictor-side weights given by \(\mathbf{a} \propto \boldsymbol{\Sigma}_{11}^{-1} \boldsymbol{\Sigma}_{12} \mathbf{b}\).
S11 <- matrix(c(1, .30, .30, 1), 2, 2)
S12 <- matrix(c(.30, .20, .25, .15), 2, 2)
S22 <- matrix(c(1, .40, .40, 1), 2, 2)
restricted_canonical_validity(S11, S12, S22, criterion_weights = c(.6, .4))
#> <psu_incremental_validity>
#> validity: 0.352614The function incremental_validity() evaluates the gain
from adding new predictors to an existing baseline.
Rxx <- matrix(c(1, .30, .20,
.30, 1, .25,
.20, .25, 1), 3, 3, byrow = TRUE)
Rxy <- matrix(c(.30, .20,
.25, .15,
.10, .35), 3, 2, byrow = TRUE)
Ryy <- matrix(c(1, .40, .40, 1), 2, 2)
incremental_validity(
predictor_cor = Rxx,
predictor_criterion_cor = Rxy,
criterion_cor = Ryy,
criterion_weights = c(.6, .4),
baseline_predictors = 1:2,
added_predictors = 3
)
#> <psu_incremental_validity>
#> baseline_validity: 0.34905
#> expanded_validity: 0.379438
#> incremental_validity: 0.0303873
#> added_predictors: 3Two contemporary methods for quantifying the relative importance of predictors complement this matrix formulation. Johnson’s (2000) relative-weights method decomposes the model \(R^2\) into approximately uncorrelated contributions, and Budescu’s (1993) dominance analysis evaluates each predictor across all subsets of the other predictors.
# For predictor-importance methods, the criterion side collapses to a single
# criterion (e.g., overall job performance):
rxy_single <- c(.30, .25, .35)
relative_weights(predictor_cor = Rxx, criterion_cor = rxy_single)
#> predictor raw_weight rescaled_weight percent_of_r2
#> 1 1 0.06156283 0.06156283 32.45758
#> 2 2 0.03381629 0.03381629 17.82886
#> 3 3 0.09429252 0.09429252 49.71356
dominance_analysis(predictor_cor = Rxx, predictor_criterion_cor = rxy_single)
#> <psu_dominance>
#> r_squared_full: 0.189672The substantive lesson, formalised by Sturman (2001), is that a predictor with high marginal correlation can have negligible or even negative incremental validity if it is highly redundant with predictors already in the battery, and conversely a predictor with low marginal correlation can have high incremental validity through suppression effects. Reporting both relative weights and dominance results, alongside the matrix-restricted canonical validity, provides a multi-method check on the importance of any candidate predictor.
Sturman (2001) integrates several of the corrections developed above
into a single comprehensive utility model: incremental validity over the
operating baseline, multidimensional criterion through restricted
canonical reweighting, multi-period employee flows, taxes and
discounting, probationary survival, and offer rejection. The function
sturman_comprehensive() composes these adjustments and
returns both the integrated estimate and the cumulative cascade.
S11 <- matrix(c(1, .30, .30, 1), 2, 2)
S12 <- matrix(c(.30, .10, .15, .25), 2, 2, byrow = TRUE)
S22 <- matrix(c(1, .40, .40, 1), 2, 2)
s <- sturman_comprehensive(
validity = .35,
baseline_validity = .20,
selection_ratio = .20,
sdy = 50000,
n_year_one = 100,
tenure = 5,
fixed_cost = 75000,
hires_per_period = c(100, 15, 15, 15, 15),
losses_per_period = c(0, 15, 15, 15, 15),
tax_rate = .25,
discount_rate = .08,
predictor_cor = S11,
predictor_criterion_cor = S12,
criterion_cor = S22,
criterion_weights = c(.7, .3),
probation_cutoff_z = -1,
acceptance_rate = .70,
quality_acceptance_correlation = -0.20
)
s
#> <psu_sturman: Sturman (2001) comprehensive utility>
#> Comprehensive net utility: 3759820
#> Effective validity: 0.3068 (baseline: 0.2 )
#>
#> Cascade:
#> step net_utility pct_of_naive
#> 1. Naive BCG (random baseline) 12173334 100.00000
#> 2. + operating baseline 5174286 42.50509
#> 3. + multidim. criterion (RCV) 3663342 30.09317
#> 4. + flows + tax + discount 2169473 17.82152
#> 5. + probation 5476999 44.99178
#> 6. + offer rejection 3759816 30.88567The cumulative cascade is available in s$cascade, the
effective validity actually used for the calculations after restricted
canonical reweighting in s$effective_validity, and the
active headcount per period after employee flows in
s$n_active_by_period. The applied reproduction of Sturman’s
(2001) cascade, including the published shrinkage to approximately \(8\%\) of the naive Brogden-Cronbach-Gleser
estimate, is developed in the Reproducing canonical examples
vignette.
naylor_shine() if the analysis stops at
expected criterion gain in standard-deviation units; do not introduce
\(SD_y\) unless the decision genuinely
requires monetary translation.bcg_utility() for transparent monetary utility, but
treat it as a starting point and not as an endpoint.boudreau_utility() when the analysis spans several
periods, when costs and returns occur at different times, or when taxes
and contribution margins are non-negligible.bcg_utility()) from
intervention utility (\(d\)-based,
shp_utility()); they are calibrated for different study
designs.disattenuate_correlation()
and correct for range restriction with correct_r_lawley()
or correct_r_direct_range_restriction() before
utility calculation; report both corrected and uncorrected values.restricted_canonical_validity() and
incremental_validity(), complemented by
relative_weights() and dominance_analysis()
for predictor-importance triangulation.sturman_comprehensive() as the integrated reporting
standard for continuous-monetary, compensatory-selection problems; the
cascade output makes the contribution of each adjustment auditable.Becker, B. E., & Huselid, M. A. (1992). Direct estimates of \(SD_y\) and the implications for utility analysis. Journal of Applied Psychology, 77, 227–233.
Bobko, P., Karren, R., & Parkington, J. J. (1983). Estimation of standard deviations in utility analyses: An empirical test. Journal of Applied Psychology, 68, 170–176.
Borman, W. C., & Motowidlo, S. J. (1993). Expanding the criterion domain to include elements of contextual performance. In N. Schmitt, W. C. Borman, & Associates (Eds.), Personnel selection in organizations (pp. 71–98). Jossey-Bass.
Boudreau, J. W. (1983). Economic considerations in estimating the utility of human resource productivity improvement programs. Personnel Psychology, 36, 551–576.
Boudreau, J. W. (1991). Utility analysis for decisions in human resource management. In M. D. Dunnette & L. M. Hough (Eds.), Handbook of industrial and organizational psychology (Vol. 2, pp. 621–745). Consulting Psychologists Press.
Brogden, H. E. (1946). On the interpretation of the correlation coefficient as a measure of predictive efficiency. Journal of Educational Psychology, 37, 65–76.
Brogden, H. E. (1949). When testing pays off. Personnel Psychology, 2, 171–183.
Budescu, D. V. (1993). Dominance analysis: A new approach to the problem of relative importance of predictors in multiple regression. Psychological Bulletin, 114, 542–551.
Burke, M. J., & Day, R. R. (1986). A cumulative study of the effectiveness of managerial training. Journal of Applied Psychology, 71, 232–245.
Burke, M. J., & Frederick, J. T. (1984). Two modified procedures for estimating standard deviations in utility analyses. Journal of Applied Psychology, 69, 482–489.
Burke, M. J., & Frederick, J. T. (1986). A comparison of economic utility estimates for alternative \(SD_y\) estimation procedures. Journal of Applied Psychology, 71, 334–339.
Campbell, J. P. (1990). Modeling the performance prediction problem in industrial and organizational psychology. In M. D. Dunnette & L. M. Hough (Eds.), Handbook of industrial and organizational psychology (Vol. 1, pp. 687–732). Consulting Psychologists Press.
Cascio, W. F. (1989). Using utility analysis to assess training outcomes. In I. L. Goldstein (Ed.), Training and development in organizations (pp. 63–88). Jossey-Bass.
Cascio, W. F., & Ramos, R. A. (1986). Development and application of a new method for assessing job performance in behavioral/economic terms. Journal of Applied Psychology, 71, 20–28.
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