Calculating SDy and Utility (1)

7/18/2019 Calculating SDy and Utility (1)

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Assessing the Economic Impact of Individual Job Performance

Standard Deviation of Performance ( SDy)

The performance of all the employees in a particular function is not the same, like any

other individual difference variable such as age, height, weight, work experience, etc.,

performance of individuals also varies. If we plot this variation on a graph such that the X-

axis represents the different values that the variable can take and the Y-axis represents the

number of individuals who fit the particular value criteria, then we get a probability

distribution such that for every value of the variable x! we can find out the number of

individuals who posses that characteristic y!. "or all the variables mentioned above we find

that most individuals possess the characteristic closer to the sample mean while few persons

posses extremely high or low values of the characteristic. #uch a distribution where most of

the values are distributed about the mean is called a normal distribution. $ike most of the

variables mentioned above, we can assume that performance of all employees in a particular

role varies according to the normal distribution.%

&ne of the properties of the normal distribution is that if we know the standard

deviation of the normal curve, then we can predict the proportion of values which lie within acertain number of standard deviations away from the mean.' (ence, if we cover one standard

deviation on either side of the mean, we cover approximately ))* of the population

represented by the area of the normal curve and if we cover two standard deviations on either

% This assumption is more valid when we consider the entire population of eligible

candidates for a +ob as the population. Incumbents of a current +ob in an organiation may not

be distributed normally since the companys selection process would bias the population

towards relatively higher performing individuals.

'Incidentally, this is true for any regular figure which is measured in terms of its own

dimension. "or example, if you cover a certain distance say .'/ times the radius on either

side of the center along the diameter of a semi-circle the proportion of area of the semi-circle

covered would be the same irrespective of the sie of the semi-circle. #imilarly, for an

e0uilateral triangle, if you cover a certain distance say .11 times the base on either side of

the center of the base, the proportion of total area covered by you will be the same

irrespective of the sie of the triangle.

%



side of the mean, we cover approximately 2/* of the population represented by the area of

the normal curve. 3lmost the entire population of the normal curve is covered by moving a

distance of three standard deviations on either side of the mean.1

If we assume that employee performance in is normally distributed, then the

variability of employee +ob performance is measured as the standard deviation of the rupee

value of output and is represented by the term SDp. (owever, if performance is normally

distributed, then for a given organiation, the value added by employees in a particular role

will also be normally distributed. Thus, SDy expressed in 4upees per annum represents the

standard deviation of value added of all employees in a particular +ob. In order words, the

difference in value added between the best and the worst possible employee in a particular

+ob can be expressed as 56SDy 7 and 8 ' SDy on each side of the mean!.

Methods of calculating SDy

Calculating SDy using subjective assessments of supervisors or incumbents

The standard deviation in output for a particular +ob can be identified by asking a set

of supervisors to estimate the net value to the organiation in 4s.9annum! provided by an

employee at the :/th percentile a high performer!, at the / th percentile an average

performer! and an employee at the %)

th

percentile a low performer!.

5

;ractically, it may bedifficult for supervisors to independently assess net value of employees, in such cases< they

may assess both gross value and costs separately./

1 =ontinuing with the earlier analogy of the e0uilateral triangle, if we were to define a

new term, say S as e0ual to %9) of the length of the base, and then move 79-1S on either side

of the base, we would cover the entire area of the triangle.

5 >ven though during the derivation, we assumed SDy was based on a population ofeligible candidates, it is also possible to estimate SDy based on a population of incumbent

employees. The estimate thus obtained from existing employees will be a smaller and hence

more conservative estimate of SDy since one of the ob+ectives of a companys selection

process is to reduce variability in performance by selecting high performers only.

/ 3n example of this is shown in 4oth, ;., $., ;ritchard, 4. ?., #tout, @. ?., A Brown,

#. ( %225!. >stimating the impact of variable costs on #?y in complex situations. Journal of

Business and Psychology, 8!"C 51D-5/5.

'



3nother way of estimating #?y would be to think of your best and worst employees

in a particular grade and how much it would cost you to get a service e0uivalent to the best

and worst employee from the market. "rom this you can subtract the salaries of the best and

worst employees. This difference represents the difference in value added which is

approximately corresponding to 79- ' standard deviations along the distribution of value

added of employees.

"or example, the salary of an assistant professor is 4s. /,9- per month and an

assistant professor is expected to teach for approximately 1 hours9month. The director of the

institute estimates that if he were to replace his best teachers with visiting professors, he

would have to pay them at the rate of 4s. /9hour and if he were to replace his worst

teachers with visiting professors, he would have to pay them at the rate of 4s. %/9hour.

Thus the value added by the best professor is 4s. %/, 8 4s. /, or 4s. %, per

month and the value added by worst professor is 4s. 5/, 8 4s. /, E . The difference

between the value added by the best and worst professors is 4s. %, and this corresponds

to 5 times the standard deviation of output #?y!. (ence, #?y can be calculated as 4s.

'/,9- per month.

#he Cascio$%amos &stimate of Performance in Dollars C%&P'D"

The =4>;I? method assumes that the economic value of an individuals work is

reflected in his9her wages. The first step is to identify the main activities performed by +ob

incumbents rate each activity based on time9fre0uency and importance. The multiplication of

the time9fre0uency and importance ratings for each activity are added and normalied so that

the relative importance of each activity in the overall +ob can be calculated. By multiplying

the percentage weights of each activity with the average wages, we can arrive at the rupee

value of each activity on the +ob.)

The next stage is to rate each individual incumbent on a scale of -' ./ F % st

0uartile performer, % F median performer, %./ F 5th 0uartile performer! for each of the

activities. The point ratings assigned to each activity for an individual are then multiplied by

the rupee value of each activity, to get the net rupee value for that individual for a particular

activity. 3dding up all the rupee values for all the activities of one individual gives the total

)In case a detailed +ob evaluation is available, then an analysis of the @>

points9weights of compensable factors can be used.

1



rupee value of the output of that individual. Ghen this is done for all individuals in a

particular +ob, the mean and the standard deviation of economic output can be calculated.

"or example, 4amesh is a factory supervisor at #?I$ and his +ob involves four main

activities. The average salary for 4ameshs grade is 4s. 5,9annum. 3 summary of

4ameshs boss ratings of the activities and 4ameshs performance on each of them is given

belowC

=ommon for all factory supervisors "or 4amesh

;rincipal

3ctivity

Time

"re0.

Imp. &veral

l

Impact

4elativ

e

Geight

4upee Halue of

>ach 3ctivity

4s.

lacs9annum!

;erformanc

e 4ating

points!

et 4upee

Halue

4s.

lacs9annu

m!=oordinatio

n

5./ 1 %1./ ':.5* %.%5 %. %.%5

Juality

control

1. / %/ 1%./* %.') '. './1

#upervision ). ' %' '/.'* %.% ./ ./%

;roduction

planning

%. D D %5.D* ./2 %. ./2

Total 5D./ %* 5. 5.D)

If the last two rows are thus calculated for all employees, one can get the distribution

of value added across all employees and from that one can calculate the average value added

and the standard deviation of value added across employees in a particular category.

Calculating SDy using salary

(owever, practically, as a rule of thumb, SDy is taken as 5* of the average salary in

a particular +ob role. This value is based on empirical findings across a large number of +obs

in multiple industries.D This is a conservative estimate since many studies have shown that for

managerial +obs, SDy can be as high as :*.

D#chmidt, ". $., A (unter, @. >. %2:1!. Individual differences in productivityC 3n

empirical test of estimates derived from studies of selection procedure utility. Journal of

(pplied Psychology, )8, 5D-5%5.

5



Validit of Selection Process

The validity of a selection process is the extent to which a selection process is able to

predict performance on the +ob. It is measured as the correlation between scores achieved by

candidates in the selection process which form the basis of selection! and subse0uent

performance of candidates on the +ob. Halidity of a selection process can be measured in two

ways, vi., concurrent validity and predictive validity.

Concurrent validity

>xisting +ob incumbents are administered the selection test and the correlation

between their on-the-+ob performance scores and their test scores represents the concurrentvalidity.

Predictive validity

This is the extent to which a test score is able to predict a criterion measure in this

case on the +ob performance.

%ange restriction

4estriction of range is a common reason for validity being lower than actual. "or

example, if % persons apply for a particular +ob and of them, the ' top performers are

selected, while the prediction is done for all %, the accuracy of prediction is measurable

only for the top ' +ob incumbents. In order to correct for the restriction of range due to

unavailability of criterion data of unselected persons, a correction formula for range

restriction is applied as given belowC

r XY =S X r xy

√ S X

2

r xy2

+s x2

−s x2

r xy2

Ghere

i. Xs are the scores on the test and Ys are the performance ratings

ii. r xy is the observed correlation between X and Y in the restricted sample

iii. s x is the estimated standard deviation of X in the restricted sample

iv. S * is the estimated standard deviation of X in the unrestricted sample

v. r *+ is the estimated corrected correlation between X and Y in the unrestricted

sample when only the restricted sample has been used

/



!tilit Analsis for Selection Process

The utility of a selection device is the degree to which its use improves the 0uality of

the individuals selected beyond what would have occurred had that device not been used.

&ne of the most popular methods for assessing utility of a selection process is the Brogden-

=ronbach-Kleser utility e0uation.

"rogden#$ronbach#%leser ("$%) utilit e&uation

U =T N r xy SD y

h

p – N

c

p

GhereC

• # F expected tenure in years of the average selected candidate estimated based on

past records!

• - number of candidates selected in a given year

• r xyF validity of the process

• SDy - standard deviation of value added

• h = height of the normal curve at the predictor cut off

•

p = selection ratio• c F cost per applicant for new process

• c. F cost per applicant for old process

• U = gain in productivity in rupees by using the new selection procedure as

compared to random selection. These gains are received over time period #/ In

case the organiation already has a selection process in place, then 0 must be

calculated twice- first for the existing process as compared to random selection!

and then as per the new process as compared to random selection!. The difference

in the two values is the incremental utility of the new process.

&xample for BC1 utility e2uation

#?I$ selects approximately %' sales staff each year out of '5 applicants, using a

selection procedure having a validity of .%: and costing 4s. 2 per applicant. The average

tenure for sales staff is D.') years and their average salary is 4s. 1/,9- per annum.

=alculate the utility of using a test costing 4s. %D/ having a validity of .)%.

)



Ad'usting utilit analsis estimates to realistic values

The utility estimates in the above mentioned formula ignores a numbers of factors

such as variable costs which may be higher for high performers!, tax, the time value of

money, and effects of +ob-offer re+ections. These factors can either be accounted for by

including in an e0uation too complex to be included hereL! or we can apply a global Mfactor

of safetyN to our utility estimate and reduce the estimate by as much as :/* to get a more

realistic figure.2

In any case, if we plan to use the utility e0uation to compare across different

alternatives and not to actually predict the rupees that will be saved, the formula given above

is sufficient.

:"or a detailed analysis of this refer to =ascio, G., A Boudreau, @. ':!. 'nvesting

in people3 4inancial impact of human resource initiatives/ #(4O.

2#turman, O. =. '!. Implications of utility analysis ad+ustments for estimates of

human resource intervention value. Journal of 5anagement, 6)6"3 '2.

D



$alculating economic returns on a sill development program

The Brogden-=ronbach-Kleser model can be applied to training as followsC

Δ U =

T N d t SD y – C

GhereC

• ?elta P F Kain to the firm in rupees resulting from the program

• F number of employees trained

• # F expected duration of benefits in the trained group

• d t - is the Meffect sieN i.e., the difference between the mean of the trained and

untrained groups in standard deviation Q score! units

• SDy - standard deviation of value added in 4s9annum for the group of employees

trained.

d t =

´ X t − ´ X u

SD x

* t F average +ob performance score of the trained group

* u F average +ob performance score of the untrained group

SD x is the standard deviation of the +ob performance scores of the total group, trained and

untrained.

Practice problem

#?I$ has a maintenance staff of ' technicians who are paid an average salary of 4s.

1 lacs9annum. 4ecently you sent % of the technicians, for a week long training program

costing a total of 4s. ' lac. The training program is for Total ;roductive Oaintenance T;O!

and you expect that it will yield benefits for at least the next three years. 3fter the technicians

returned from the training program, the industrial engineering department who were not told

which of the technicians have gone for the program!, have been monitoring the performance

of all the technicians closely and on the basis of their observations, they have given each

technician a rating on a scale from -/. The data is shown in 3ppendix '.

3ssuming that there are totally % technicians in the company and the cost of

training them all is 4s. %/ lacs< is it worthwhile to go for the trainingR

:



Appendi* +

EmployeeNumber

Attended thetrainingprogram?

ObservedPerformance

(1=poor;=e!cellent"

1 #es

$ #es %

& #es &

% #es %

#es

' #es &

#es &

) #es

* #es $

1+ #es %

11 No &

1$ No $1& No 1

1% No $

1 No $

1' No $

1 No &

1) No

1* No $

$+ No %

2

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Calculating SDy and Utility (1)