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One--Way ANOVA Demonstration
One--Way ANOVA Demonstration
Program Transcript
MATT JONES: This week we're going to be introducing you to
one--way ANOVA.
This is a comparisons--of--means test. Let's go to SPSS to
see how we'll perform
this specific test. To perform the one--way ANOVA in SPSS,
we start up at the
Analyze tab. If we click that, we get a dropdown menu.
Since one--way ANOVA over is a comparisons--of--means
test, we can move our
cursor down to Compare Means, scroll across, and we see that
one--way ANOVA
is down at the bottom. If we click on that, a dialog box is
opened up, where we
have a Dependent List and a Factor. For one--way ANOVA,
our dependent
variable needs to be a metric level variable. That is it's an
interval or ratio level of
measurement. This is important because one one--way
ANOVA compares means
across a factor.
The factor is our grouping variable. This needs to be a
categorical variable.
Typically, one--way ANOVA is used with grouping variables
that have three or
more levels or attributes to them. In this case, let's go ahead
and test whether the
means of the socioeconomic status index differ across a
respondent's highest
degree.
To begin with, well, we'll go ahead, and we'll put
socioeconomic status index into
our Dependent List box. So you can see off to the left are
choice of variables.
Socioeconomic Status is down towards the bottom of our
Variable list. If I place
my cursor over it, we'll see it highlighted. You'll also note,
again, a little scale
ruler off to the left, which indicates that this is an interval-
-ratio--level variable.
Once I click on that variable, it's highlighted. I can just simply
click on the arrow
box, which moves that variable over into the Dependent List.
Now I need to make
sure and enter my factor as well. I'll scroll up till I find
Respondents Highest
Degree. I can see that it's right here. I can hover over this
variable and then
highlight it.
Again, click on my arrow that places it into the Factor box.
For basic omnibus
ANOVA test, we are finished. We can go ahead and click OK
and examine our
output. This is the SPSS one--way ANOVA omnibus output.
You can see here
Respondent Socioeconomic Index is our dependent variable.
SPSS provides us with information about between--groups and
within--groups
variance. The between--groups variance is a squared
deviations between the
groups. The within--groups variance, also known as
unexplained variance, is the
variance within the sample. A ratio of the mean square of
between groups to
within groups is how we obtain the F--value. The F statistic is
a critical value that
determines the significance of our test.
©2016 Laureate Education, Inc. 1
One--Way ANOVA Demonstration
Here we can see that the significance level is 0.000. This
significance level is
well below the conventional threshold of 0.5. Therefore we can
reject the null
hypothesis that there are no differences in socioeconomic
status index across
respondents highest degree. To find out where possible
differences lie, we have
to perform a post--hoc test.
To perform a post--hoc test, we once again go back up to our
Analyze, Compare
Means, One--Way ANOVA. We can click on Post--Hocs, in
here you'll see that
there are a variety of options provided for you. We have equal
variances
assumed and equal variances not assumed. At this point, we
don't know that
whether we have equality of variances, and this is something
that we specifically
have to test for.
But as you're performing the one--way ANOVA test, you can
choose an equal
variances assumed test, an equal variances not assumed test,
and then on your
output, go to the appropriate test after examining the variances.
So we can click
on a Bonferroni Test for equal variances and also Games-
-Howell for equal
variances not assumed. Click Continue.
If we click our Options box, this is how we determine
whether we have
homogeneity of variances, or said another way, equality of
variances. As you
know from your reading, this is an assumption of the one-
-way ANOVA test. If we
click on that and activate this test, going to hit Continue and
then click OK. Right
away you'll see that we get quite a bit more output than we had
before.
Our first piece of output is the test of homogeneity of
variances, also known as a
Levene's test. This tests the null hypothesis of homogeneity
of variances. Here, if
you look at the significance level, you'll see that we are at
0.000, which is well
below the threshold of 0.05. This means we reject our null
hypothesis that
variances are equal. Therefore, we have to assume that the
variances are not
equal in the one--way ANOVA.
As we noted before, the overall test, also sometimes referred to
as the omnibus
test, is significant. Since the omnibus test is significant, we
know that at least one
of the means differs from another. Therefore we need to
examine our post--hoc
tests to determine which means differ. Again, moving with the
assumption of
inequality of variances, we have to move down to our Games-
-Howell all Post--
Hoc test.
If you remember, we chose Bonferroni as a test for equality of
variances, but
tested for the equality of variances and found they were not
equal. The Games--
Howell test performs a pairwise comparison for all levels of
our variable. Here
you'll see less than high schools compared to high school, less
than high school
to junior college, less than high school to bachelor, less than
high school to
graduate, and so forth, until all possible combinations are
achieved.
©2016 Laureate Education, Inc. 2
One--Way ANOVA Demonstration
The next column shows us our mean difference. We can see
that on the
socioeconomic status index, our dependent variable, those
with less than high
school have a mean score of 10.08 units lower than high
school. If we move over
to our significance level, we see that, indeed, this pairwise
comparison is
statistically significant a at the 0.05. Therefore there is a
statistically significant
difference between those with less than high school and those
with a high school
degree.
As we move down our output, we can examine all of these
pairwise comparisons.
Again, less than high school to junior college, there is a
difference of 17.38, and it
is statistically significant. If we move to a less than high
school to bachelor's, we
can see that the difference increases. Again, it is statistically
significant, and the
same is true for less than high school to graduate.
Moving through our output, we can go ahead and examine all
of these pairwise
comparisons, move over to our significance column, and see
that they are indeed
all statistically significant. You'll notice on the main difference
that SPSS also
puts an asterisk next to each mean difference to highlight or
flag those
differences that are statistically significant. We can conclude
from our output and
our post--hoc tests that there is indeed a difference in
socioeconomic status index
across respondents highest degree and that all pairwise
comparisons are
statistically significant, concluding that the higher a
respondent's degree, the
higher their socioeconomic status index on average.
And that concludes our SPSS demonstration on one--way
ANOVA. As a couple of
parting thoughts, be sure and remember that your dependent
variable in one--way
ANOVA needs to be a metric variable, that is an interval
ratio level of
measurement. Your independent variable, or your factor, needs
to be a
categorical variable. This is because one--way ANOVA of is
a comparison--of--
means test.
Also, it's very important to test the assumption for
homogeneity of variances, so
be sure and look at that Levene's test. If you have any further
questions, be sure
and use your textbook. And also, your instructor is a very
valuable resource.
©2016 Laureate Education, Inc. 3
Student Name: Date: Research Design
Alignment Table | Using an alignment table can assist with
ensuring the alignment of your research design.
Research Problem, Purpose, and Framework
Provide one sentence for each. These must align with all rows.
Research Question(s), Method, & Design
List one or more RQs, as needed; select method; identify
design. Use a separate form for additional RQs.
Data Collection Tools & Data Sources
List the instrument(s) and people, artifacts, or records that will
provide the data for each RQ.
Data Points
List the variables, specific interview questions, scales, etc. that
will be used for each RQ.
Data Analysis
Briefly describe the statistical or qualitative analysis that will
address each RQ.
Problem:
Purpose:
Framework:
RQ1:
Design:
RQ2:
Design:
RQ3:
Design:
Note. The information in the first column must align with all
rows, and each individual RQ row must show alignment across
the columns for that row. Once your Research Design
Alignment Table is completed, reflect on your design alignment.
Ask yourself:
1. Is there a logical progression from the research problem to
the purpose of the study?
2. Does the identified framework ground the investigation into
the stated problem?
3. Do the problem, purpose, and framework in the left-hand
column align with the RQ(s) (all rows)?
4. Does each RQ address the problem and align with the purpose
of the study?
5. Does the information across each individual row match/align
with the RQ listed for that row?
· By row, will the variables listed address the RQ?
· By row, will the analysis address the RQ?
· By row, can the analysis be completed with the data points
that will be collected?
Journal of Applied Psychology
1977, Vol. 62, No. 3, 335-343
An Investigation of the Influence of Job Level and Functional
Specialty on Job Attitudes and Perceptions
Edward F. Adams, Dennis R. Laker, and Charles L. Hulin
University of Illinois at Urbana-Champaign
One hundred and fifty-two jobs in a large (N = 1,313)
midwestern printing com-
pany were classified into vertical (job level) and horizontal ( f u
n c t i o n a l specialty)
distributions to investigate differences in employee attitudes.
Descriptions of
leader behavior (the Leader Behavior Description
Questionnaire's Initiating
Structure scale) and four aspects of satisfaction (the Job
Descriptive Index
Scales: Satisfaction with Work, Pay, Supervision, and Co-
Workers) were as-
sessed. A 3 (job level) X 5 (functional specialty) multivariate
analysis of vari-
ance demonstrated significant differences in job attitudes for
both job level and
functional specialty. A discriminant analysis separated the f u n
c t i o n a l specialty
and job-level groupings along two dimensions in terms of
satisfaction with work
itself and pay, and initiating structure. The results suggest that
these two
organizational structure characteristics summarize influences of
managerial style,
local norms, goals, and job requirements that a f f e c t
individual attitudes and
perceptions of work situation.
Organizational structure has been used to
describe norms and values, relationships
among groups, and patterns of behavior. In
this article, the term structure is restricted to
two features of organizations: horizontal and
vertical distributions of organizational mem-
bers and their duties. Horizontal distribution
is the extent to which jobs in organizations
can be subdivided into homogeneous func-
tional clusters such as departments, divisions,
or functional specialties. Vertical distribution
is the extent to which organizational jobs can
be divided into layers or levels with different
amounts of authority, responsibility, and
task complexity. Conceptually, distinctions be-
tween these two distributions are independent.
In practice, the distinctions are more complex
The a u t h o r s wish to acknowledge and thank James
Terborg, Peter Horn, and Ralph Katerberg, Jr., for
their h e l p f u l comments and suggestions.
The research reported in this study was supported
in part by National Science Foundation Grant GS-
32096 and in part by the U.S. Office of Naval Re-
search Contract No. N 0014-75-C-0904, Charles L.
H u l i n , principal investigator.
Requests for reprints and other correspondence con-
cerning this research should be sent to Charles L.
Hulin, Department of Psychology, University of Il-
linois, Champaign, Illinois 61820.
and interrelated (Katz & Kahn, 1966; Per-
row, 1970).
Both structural characteristics of organiza-
tions and individual employee characteristics
have been found to influence job attitudes
(e.g., Herman, Dunham, & Hulin, 197S; Her-
man & Hulin, 1 9 7 2 ; Porter & Lawler, 196S;
Stone & Porter, 1975).
Herman and Hulin ( 1 9 7 2 ) found that struc-
ture variables reflecting departmental assign-
ment and functional specialty accounted for a
substantial portion of variance in individual
attitudes toward work. Stone and Porter
( 1 9 7 5 ) have taken issue with Herman and
Hulin. They concluded from their findings
that "the discrimination achieved by Herman
and Hulin may have been more a function of
jobs held by individuals in their sample than
of differences in either 'function, hierarchical
level or primary task orientation' " (p. 6 3 ) .
All 16 jobs sampled by Stone and Porter
were reported at the same hierarchical level.
Therefore, they concluded that job level did
not account for their discrimination among
job titles, and by implication that Herman
and Hulin's results could be explained by job
level. Job level could not have influenced
Stone and Porter's findings, but we believe the
possible implications of their conclusions con-
335
336 E. F. ADAMS, D. R. LAKER, AND C. I. HULIN
earning job level and function influences re-
main unclear and should be addressed. Also,
Stone and Porter's conclusions suggest that
one can separate a job from its level, function,
or department and q u a n t i f y the influences of
these components.
To test the impact of functional specialty,
one would collect data from workers having
the same job duties in d i f f e r e n t functional
subdivisions of the organization. Differences
should be found if function has an influence
on attitudes and perceptions. One cannot, ex-
cept in the crudest sense of the term, find em-
ployees in various subdivisions of an organiza-
tion who all have the same job duties. It is
the job duties that have led us to differentiate
among tasks and among employees who are
assigned to these tasks, and to categorize them
into different units. It is possible, however, to
find employees in different subunits who share
relevant job characteristics ( j o b complexity,
authority, autonomy, etc.). It would be pos-
sible to generate aggregations of organiza-
tional members who work in different f u n c -
tional subunits but would be classified as hav-
ing highly similar jobs in terms of complexity,
authority, etc.
As Stone and Porter argue, when one com-
pares different job clusters (departments or
functional areas), there is the potential prob-
lem of unintentionally confounding variables
of interest with other characteristics such as
job level. Job level has been shown to in-
fluence job attitudes (e.g., Cummings & El-
Salmi, 1970). Most studies using functional
specialty as an explanation for job attitude
differences have not specifically controlled for
differences in job level (Herman & Hulin,
1972; Herman, Dunham, & Hulin, 197S).
However, one can examine simultaneously the
effects of job level and functional area with
appropriate statistical techniques.
In the two studies mentioned above (Her-
man & Hulin, 1 9 7 2 ; Herman et al., 1 9 7 5 ) ,
there were no job-level differences across de-
partments or functions. The f a i l u r e of the
writers to discuss this is a serious oversight.
The appearance of the Stone and Porter ar-
ticle casts reasonable doubt on these findings
and may result in functional specialty and de-
partmental membership explanations of job
attitude differences being neglected in f u t u r e
research.
It is hypothesized that both functional
specialty and job level are related to meaning-
ful differences in job attitudes even when the
other factor is controlled. We do not hypoth-
esize that functional specialty or job level
cause differences in employee attitudes in a
direct cause-effect link. We do not hypothe-
size that job level or functional specialty clas-
sifications account for more or less variance in
work attitudes than job title. W7e hypothesize
that functional specialty and job level in-
fluence employee attitudes differently and
should be examined as potential variables
shaping job attitudes.
Method
The data were collected f r o m one plant of a mid-
western printing company. Questionnaires were ad-
ministered in small groups and required 30 minutes
to complete. All participants were assured anonymity
of their responses. The response rate was 88%. The
12%: nonresponse rate is an upper bound estimate of
nonresponse rates hased on inadequate records of
vacations, sick leaves, and unexcused absences from
work. Included among the 12%, however, are those
who simply did not show up at the survey room with
the rest of their department or office. Eight different
individuals administered the questionnaires. No ad-
ministrator effects in terms of missing data or overall
s a t i s f a c t i o n were observed. The total sample size
was 1,313.
Independent Variables
Seventeen departments were clustered into the five
f u n c t i o n a l area groupings of (a) preliminary prepara-
tion, (b) pressrooms, (c) bindery, (d) maintenance,
and (e) staff. The a u t h o r s clustered the 17 depart-
ments according to their roles in transforming "raw
materials" into finished products. The preliminary
preparation grouping readied materials for produc-
tion units in a supportive service capacity. Press-
rooms and binderies were two large and different
production functions. Maintenance ensured the up-
keep and proper working order of machines and fa-
cilities. Staff provided the administrative and man-
agerial functions of the company, such as planning,
organizing, and coordinating the units of the or-
ganization. Six additional departments (cartoning,
pallet, ink room, by-products, shipping, and ware-
h o u s i n g ) were not included in the study because the
tasks in these six departments were too heterogeneous
to be grouped into one m e a n i n g f u l functional group-
ing. In fact, these departments could have been con-
sidered separate f u n c t i o n a l specialty areas, but the
department sizes were so small that analyses could
JOB LEVEL AND FUNCTIONAL SPECIALTY 337
Table 1
Intercorrelations of Dependent Measures
Measure
1.
2.
3.
4.
S.
J D I Satisfaction with Work
JDI Satisfaction with Supervision
JDI Satisfaction with Pay
JDI Satisfaction with Co-Workers
LBDQ Initiating Structure
1.00
.45*
.41*
.44*
-.03
1.00
.31*
.32*
.00
1.00
.31*
.01
1.00
.12* 1.00
Note. N = 1,313. JDI = Job Descriptive Index. LBDQ =
Leadership Behavior Description Questionnaire.
*p < .01.
not be done. Tatsuoka (1970, p. 38) recommends that
the total sample size should be at least two or (prefer-
ably) three times the number of variables used.
Job level was determined through a rating of the
jobs by the principal investigators. These ratings
were arrived at through a process of iteration. Origi-
nal ratings of job level based on training time or edu-
cation required, responsibility, and authority were
provided by members of the personnel department.
Ratings provided by the personnel department were
modified by the investigators in an attempt to re-
move p e r t u r b a t i o n s introduced by the unwanted in-
fluence of wage rates. For example, jobs that ap-
peared "objectively" similar in all relevant character-
istics were at times rated differently by members of
the organization because one was a "male" job pay-
ing more whereas the other was a "female" job with
a lower pay rate. Differences in ratings caused by
such biases were removed whenever possible. Wage
rates were not confounded across functional spe-
cialties.
The resultant rating of job levels was a 20-point
scale. Examples of the different job levels scaled from
low to high are as follows: janitor (1), bagger (3),
Clerk Typist II (S), chemical mixer ( 7 ) , folding-
machine operator ( 9 ) , hoist-truck mechanic (11),
linotype operator (13), Program Analyst II (15),
maintenance foreman ( 1 7 ) , line department superin-
tendent (19), and staff group manager ( 2 0 ) . Because
of the small numbers of workers within these sepa-
rate job levels, the actual job level hierarchy was
trichotomized. Job Levels 1-6 (unskilled), 7-11
(skilled), and 12-20 (professional/supervisory) were
aggregated into three job level clusters. Each func-
tional area included people at these three levels of
the hierarchy resulting in a 3 (levels) X 5 (functional
specialties) design.
Dependent Variables
Job satisfaction. The Job Descriptive Index (JDI)
developed by Smith, Kendall, and Hulin (1969) was
used to measure f o u r aspects of job satisfaction:
Satisfaction with Work itself, Satisfaction with Co-
Workers, Satisfaction with Pay, Satisfaction with
Supervision. Satisfaction with promotion was not in-
cluded in the analyses because of considerations dis-
cussed below.
Perception of leader behavior. The Initiating
Structure scale of the Leadership Behavior Descrip-
tion Questionnaire (LBDQ; Stogdill & Coons, 19S7)
was used to obtain perceptions and descriptions of
average supervisory behavior from subordinates.
An attempt was made to sample the relevant re-
sponse domain broadly while simultaneously retain-
ing necessary degrees of freedom. The four JDI scales
assess several specific aspects of satisfaction and
should be related to job level and f u n c t i o n . JDI pro-
motions should be less related to function and job-
level differences than the other affect measures, espe-
cially because there was a company-wide policy on
promotions. Initiating S t r u c t u r e of the LBDQ was
t h o u g h t to be a better complement to the f o u r JDI
scales than the Consideration scale, which overlaps
more with the JDI Supervision scale. By selecting
these five dependent variables, all sample size to de-
pendent variable ratios, except as noted in Table 4,
coincided with Tatsuoka's (1970) suggestions and
other considerations of job/task homogeneity.
Demographic Data
Each respondent supplied information on com-
pany tenure, age, sex, level of education, marital
status, number of wage earners in the family, and
family size. Analyses of these data are reported else-
where (Hulin, Horn, & Herman, Note 1).
Results
The sample consisted of predominantly
married males under 45 years of age. Most
had a high school degree and had been with
the company more than 4 years. Demographic
variables accounted for less than °/o of the
unique variance in affective responses (Her-
man, Hulin, & Dunham, Note 2 ) .
The intercorrelations of the dependent mea-
sures are presented in Table 1. Intercorrela-
tions among the four measures of satisfaction
(JDI Satisfaction with Work, Supervision,
Pay, and Co-Workers scales) were significant
338 E. F. ADAMS, D. R. LAKER, AND C. I. HULIN
Table 2
Raw Cell Means
Group
Unskilled preliminary
Skilled preliminary
Professional/supervisory
preliminary
Unskilled press
Skilled press
Professional/supervisory press
Unskilled bindery
Skilled bindery
Professional/supervisory
bindery
Unskilled maintenance
Skilled maintenance
Professional/supervisory
maintenance
Unskilled staff
Skilled staff
Professional/supervisory staff
JDI
Satisfaction
with Work
24,91
29.14
32.63
19.03
25.03
32.04
19.22
25.48
29.54
28.07
36.29
36.54
33.56
30.07
37.83
J D I
Satisfaction
with Supervision
32.89
33.36
33.00
32.95
36.30
37.49
32.66
33.99
35.28
35.73
33.00
37.90
39.81
38.93
42.61
J D I
Satisfaction
with Pay
12.16
15.92
16.95
12.46
16.53
18.86
12.57
14.97
18.29
11.40
12.86
19.94
14.51
15.58
19.96
JDI
Satisfaction
with
Co-Workers
33.75
39.91
39.25
36.95
38.12
40.90
33.74
39.30
41.26
38.33
40.87
44.06
38.88
38.73
44.84
LBDQ
Initiating
Structure
30.84
30.00
32.39
34.95
34.47
34.91
34.24
34.81
34.87
29.80
30.86
33.22
28.44
30.53
31.67
Note. JDI = Job Descriptive Index. LBDQ = Leader Behavior
Description Questionnaire.
O < . 0 1 ) . The LBDQ Initiating Structure
scale was significantly correlated only with
the JDI Satisfaction with Co-Workers scale.
Multivariate Analysis oj Variance
A multivariate analysis of variance was
used to determine the main effects of func-
tional specialty and job level and any possible
interactions on the five dependent measures.
Discriminant analysis was used mainly in the
interpretation and explanation of job level
and functional specialty relationships with
the dependent measures.
The raw cell means on the five dependent
measures for the IS groups, a 3 X S design
(Job Level X Functional Specialty), are pre-
sented in Table 2. The main effect of job level
was significant, multivariate F( 10, 2588) =
36.66, p < .01. Univariate F ratios were com-
puted to assess the individual significance of
the five dependent measures. Four of the five
univanate F ratios on the scale items were
significant at p < .01: For the Satisfaction
with Work, F(2, 1298) = 141.52; for Satis-
faction with Supervision, F ( 2 , 1298) = 6.49;
for Satisfaction with Pay, F(2, 1298) =
87.91; and for Satisfaction with Co-Workers,
P(2, 1298) = 32.08.
The main effect of functional specialty was
also significant: The overall effect was F(20,
4 2 9 2 ) = 13.64, p < .01. All five univanate F
ratios computed for each dependent measure
were significant at p < .01: For Satisfaction
with Work, F(4, 1298) = 26.31; for Satis-
faction with Supervision, F(4, 1298) = 13.98;
for Satisfaction with Pay, ^(4, 1298) = 3 . 4 9 ;
for Satisfaction with Co-Workers, F(4, 1298)
= 4.31; and for LBDQ Initiating Structure,
F(4, 1298) = 29.74.
The Job Level X Functional Specialty in-
teraction was significant. The multivariate
overall effect was F(40, 5643) = 1.5298, p <
.01. Only one univariate F ratio, for Satisfac-
tion with Work, F(&, 1298) = 2.67, was sig-
nificant at p < .01.
Multiple-Group Discriminant Function
A nalysis
In order to interpret the results of the
multivariate analysis of variance, a multiple-
group discriminant function analysis was
done. Calculation of the discriminant analysis
JOB LEVEL AND FUNCTIONAL SPECIALTY 339
Table 3
Significant Discriminant Functions and
Proportion of Discriminable Variance
Accounted for by Each Function in a
Multiple-Group Discriminant Function
Analysis
Function
Measure
JDI Satisfaction with Work
J D I Satisfaction with
Supervision
JDI Satisfaction with Pay
JDI Satisfaction with
Co-Workers
LBDQ Initiating Structure
P of discriminable
variance"
1
.72
-.18
.43
.04
-.50
.70
2
-.07
-.06
.55
.04
.83
.19
3
-.42
.85
.14
.16
-.22
.08
Note. JDI = Job Descriptive Index; LBDQ =
Leader Behavior Description Questionnaire.
a Explained by discriminant function,
resulted in five discriminant functions. The
total discriminatory power accounted for by
these five functions was 39%. The correction
for small sample size relative to the number
of dependent measures for this particular
study is not necessary because the present
sample is sufficiently large (Tatsuoka, Note
3). The first three discriminant functions
were significant (p < ,01) and jointly ac-
counted for 91% of the discriminable vari-
ance. The third function contributed only 8%
of the discriminable variance and was not
interpreted.
The significant discriminant functions as
well as the proportion of discriminable vari-
ance accounted for by each function are
presented in Table 3.
The first significant function accounts for
70% of the total discriminable variance, x~
(18) =438.36, p < .01. The discriminating
power of the predictor variables was examined
by Bartlett's test (Rao, 1952) with p(k - 1)
degrees of freedom, where p is the number of
variables and k is the number of groups. The
second significant function accounts for
of the total discriminable variance,
134,31, p < .01. Application of the discrimi-
nant coefficients for the first and second func-
tion to the original group means yielded IS
group means in discriminant space that are
presented in Table 4.
Table 5 presents the structure matrix from
the discriminant analysis. The structure ma-
trix consists of correlations of each dependent
measure with the linear combination of the
dependent measures that maximally separate
the groups along each discriminant function.
Using the structure matrix and discriminant
scaled weights for purposes of interpretation
Table 4
Group Means on Discriminant Functions in a Multiple-Group
Discriminant Function Analysis
Function
Group
Unskilled preliminary
Skilled preliminary
Professional/supervisory preliminary
Unskilled pressroom
Skilled pressroom
Professional /supervisory pressroom
Unskilled binderies
Skilled binderies
Professional/su pervisory binderies
Unskilled maintenance
Skilled maintenance*
Professional/supervisory maintenance
Unskilled staff
Skilled staff
Professional/supervisory staff
3.05
8.32
10.13
-3.02
2.75
8.50
-2.56
2.70
6.89
5.19
11.84
15.30
10.48
7.51
14.01
30.04
31.34
33.64
34.16
35.43
36.63
33.50
35.00
36.60
28.56
29.92
35.40
28.55
31.17
34.01
44
66
204
109
60
120
218
140
76
15
7
50
41
60
103
a Sample size to dependent variable ratio <2:1.
340 E. F. ADAMS, D. R. LAKER, AND C. I. HULIN
Table 5
Structure Matrix from a Multiple-Group
Discriminant Function Analysis
Function
Measure
JDI Satisfaction with Work
J D I Satisfaction with Supervision
JDI Satsifaction with Pay
JDI Satisfaction with Co-Workers
LBDQ Initiating Structure
.88
.24
.S3
.36
-.26
.08
.03
.57
.26
.81
Note. JDI = Job Descriptive Index. LBDQ =
Leader Behavior Description Questionnaire.
(Tatsuoka, 1970), one can describe and in-
terpret differences among the I S groups. On
the first discriminant function, the functional
specialty areas of preliminary, maintenance,
and staff are separated f r o m pressroom and
bindery by Satisfaction with Work, Satisfac-
tion with Pay, and perception of less Initiat-
ing Structure. Job level groups are also sepa-
rated along this dimension, with higher job
levels associated with higher means. Both of
these interpretations can be confirmed by a
comparison of the raw cell means presented
in Table 2. Interpretation of the second dis-
criminant function, again using the structure
matrix and standardized discriminant weights,
yields a similar separation. This function sep-
arates pressroom and bindery from prelimi-
nary, maintenance, and staff, but in this in-
stance pressroom and bindery yield higher
discriminant means than the other three func-
tional specialties. In order of decreasing mag-
nitude, the LBDQ Initiating Structure scale
and the JDI Satisfaction with Pay scale ac-
count for this separation. Again, hierarchical
job level is reflected in the same manner as
before, higher job levels (within each func-
tional specialty) having higher cell means in
discriminant space. Comparison of the origi-
nal group means presented in Table 2 f u r -
ther support these interpretations. Group loca-
tions in discriminant space are shown in Fig-
ure 1. The labels on the axes are tentative and
reflect the structure matrix in Table 5.
Discussion
In only a few other studies have there been
simultaneous investigations of both the verti-
cal and horizontal distribution of organiza-
tional units. Porter (1963) categorized f o u r
levels of the vertical managerial hierarchy
(vice president, upper middle, lower middle,
and lower) and two horizontal subdivisions
(line and s t a f f ) of organizations on the basis
of the respondent's self-classification of his ot-
her position. Line managers reported greater
need satisfactions f r o m their jobs than staff
managers, especially in the areas of esteem
and self-actualization of needs. By examining
mean differences, he concluded that vertical
level of position within management had a
greater effect on perceived need fulfillment
deficiencies than did horizontal categorization
of line versus staff.
The present study investigated both the
horizontal and vertical subdivisions in one
printing organization. We attempted to sep-
arate statistically the effects of the vertical
subdivision (job level) and the horizontal
subdivision (functional specialty) on the job
attitudes by using a multivariate analysis of
variance. The results showed that both main
effects due to job level and functional spe-
cialty were statistically significant.
The Job Level X Functional Specialty in-
teraction (a multivariate analysis of variance)
was also significant. The univariate F for Sat-
isfaction with Work is the only measure con-
tributing to this interaction. If Figure 1 is
examined, the lowest skilled staff group
(Group 13) appears to be the group that is
out of line. This group consists of primarily
female clerical workers who seem to be hap-
pier with their work than their job level
would predict. The group means in Figure 1
demonstrate the main effect of job level
within functional specialty on work satisfac-
tion and initiating structure. With the excep-
tion of Group 13, unskilled groups reported
lower satisfaction with work and initiating
structure than skilled or professional groups.
Evidence for the vertical distribution of job
level influencing job attitudes has been well
supported in the past (e.g., Cummings & El-
Salmi, 1970; Herman & Hulin, 1973; Porter,
1962). Porter and Lawler's (196S) compre-
hensive review has summarized these differ-
ences in job attitudes across different orga-
nizational levels. The present study replicated
JOB LEVEL AND FUNCTIONAL SPECIALTY 341
INITIATING
STRUCTURE
II
38
36
34
32
30
28
26
10
S A T I S F A C T I O N W I T H T H E W O R K I T S E L F
14
Figure 1. Fifteen job levels by f u n c t i o n a l specialty
groupings plotted in two-dimensional func-
tional discriminant space. (Lines connect the three levels within
each functional specialty grouping
on the dimensions of satisfaction with work and initiating s t r u
c t u r e . Group numbers are as follows:
1 = unskilled preliminary; 2 = skilled preliminary; 3 —
professional/supervisory preliminary; 4 =
unskilled pressroom; S = skilled pressroom; 6 —
professional/supervisory pressroom; 7 = unskilled
binderies; 8 = skilled binderies; 9 = professional/supervisory
binderies; 10 = unskilled mainte-
nance; 11 — skilled maintenance; 12 = professional/supervisory
maintenance; 13 — unskilled s t a f f ;
14 = skilled s t a f f ; IS = professional/supervisory s t a f f . )
these earlier findings while controlling for
differences in functional specialty.
The main effect for functional specialty
confirms the hypothesis that horizontal sub-
divisions can be a meaningful differentiation
of job attitudes even when job level is con-
trolled. This finding also lends support to
the Herman and Hulin ( 1 9 7 2 ) and Herman
et al. ( 1 9 7 S ) findings that functional specialty
is a viable and useful manner of explaining
differences in organizational attitudes.
Examination of the means of the five func-
tional groupings on the two discriminant func-
tions indicates two interesting patterns. The
two production groups, pressroom and bind-
ery, have lower means on the first function of
satisfaction with work and pay than the other
three areas of maintenance, preliminary, and
staff, This separation is clearly seen in Figure
1. The second function, defined by initiating
structure, separates the five functional spe-
cialties similarly, except that on this function,
bindery and pressroom have higher means
than the other three functional specialties. All
seem to have a production-nonproduction sep-
aration of groups. The bindery and pressroom
are production sectors of the organization,
whereas preliminary, maintenance, and staff
groups are less production oriented. Binderies
and pressrooms are also machine and line
paced and mechanically oriented. The tasks
in these departments are more well defined
and structured than are the tasks in the other
three areas.
Lawrence and Lorsch (1967) described
functional specialties as different subsystems
in the organization based on certain subtasks.
Lawrence and Lorsch ( 1 9 6 7 ) called these
horizontal subdivisions "basic functional de-
partments" (p. 30). Each of the subsystems
studied (production, sales, applied research,
and fundamental research) could be separated
on the dimensions of formality of structure,
interpersonal orientation, and time orienta-
tions. Each subsystem possessed certain char-
acteristics that were related to their primary
task. For example, the production subsystems
were highly structured but low on interper-
sonal relations and were oriented to short
terms. The research areas were low on struc-
342 E. F. ADAMS, D. R. LAKER, AND C. I. HULIN
ture but higher than production on interper-
sonal relations and were oriented to long-runs.
Herman and Hulin ( 1 9 7 2 ) used primary
functions of staff, productions, and produc-
tion service departments and found significant
differences between these functions on such
organizationally relevant attitudes as satis-
faction with line-staff relations, evaluation of
production management, effectiveness of sup-
portive services, satisfaction with plant, and
plant atmosphere. Porter's (1963) findings
separating line versus staff on need satisfac-
tion also seem to be consistent with the pres-
ent findings, although this dichotomy into line
and staff is less specific than the basic func-
tional departments, primary function, and
functional specialty horizontal categorizations
of other studies. The next logical question is
why these subsystems and structural dis-
tributions of organization units can differenti-
ate job attitudes.
Lawrence and Lorsch ( 1 9 6 7 ) have demon-
strated that there are actual internal charac-
teristics in various subsystems of an organiza-
tion that are determined by the tasks being
performed. In other words, employees in d i f -
ferent work situations (defined by depart-
ment, functional area, job level, etc.) will
experience different local norms, demands, re-
quirements, or managerial styles that are spe-
cific to that work situation. Newman (1975)
supports this view. He found that individuals
in different organizational positions perceived
their work environment differently. This
would be expected because the task and en-
vironment are different for different organiza-
tional positions.
It seems highly unlikely that attitudinal
predispositions caused the company to locate
individuals in different departments. Self-se-
lection into different functional specialties
may be part of the explanation. However,
what we have assessed are attitudes and de-
scriptions determined in large part by what
workers find on their jobs and not only by
what they bring with them to their jobs (Her-
man et al, 197S; Herman & Hulin, 1 9 7 2 ;
O'Reilly & Roberts, 1 9 7 S ) . Thus, although
self-selection probably does occur, it seems
tenuous to argue that it alone causes differ-
ences in job responses assessed at a later time.
Individuals in similar organizational posi-
tions should perceive their environments more
similarly than individuals in different posi-
tions or functions. Organizational structure
variables may simpl}' summarize a number
of important influences (managerial style,
specific goals, time orientations, local norms,
and structural differences) that affect an in-
dividual in his or her work situation. Future
research should identify which variables de-
fine work situations as well as influence in-
dividual's perceptions of the work situation
and how this knowledge can be used to under-
stand and predict relevant employee behav-
iors.
Reference Notes
1. Hulin, C. L., Horn, P. W., & Herman, J. B. In-
dividual differences, structural characteristics of
organizational positions and plant effects on re-
sponses (Tech. Rep. 76-3). Champaign: University
of Illinois, D e p a r t m e n t of Psychology, 1976.
2. Herman, J. B., Hulin, C. L., & D u n h a m , R. B. De-
veloping a response relevant typology of organiza-
tions (Tech. Rep. 7 6 - 2 ) . Champaign: University of
Illinois, Department of Psychology, 1976.
3. Tatsuoka, M. M. An examination of the statistical
properties of a multivariate measure of strength
of relationship (USDHEW Final Report, Project
No. 2-E-020, Grant No. OEG-5-72-0027, 509).
Urbana-Champaign: University of Illinois, De-
cember 1973.
References
Cummings, L. L., & ElSalmi, A. M. The impact of
role diversity, job level, and organizational size on
managerial satisfaction. Administrative Science
Quarterly, 1970, 75, 1-10.
Herman, J. B., D u n h a m , R. B., & Hulin, C. L. Or-
ganizational structure, demographic characteristics,
and employee responses. Organizational Behavior
and Human Performance, 1975, 13, 206-232.
Herman, J. B., & Hulin, C. L. Studying organiza-
tional attitudes from individual and organizational
frames of reference. Organizational Behavior and
Human Performance, 1972, 8, 84-108.
Herman, J. B., & Hulin, C. L. Managerial satisfac-
tions and organizational roles: An investigation of
Porter's need deficiency scales. Journal of Applied
Psychology, 1973, 57, 118-124.
Katz, D., & Kahn, R. The social psychology of or-
ganizations. New York: Wiley, 1966.
Lawrence, P. R., & Lorsch, J. W. Organization and
environment. Boston: Harvard University, Grad-
uate School of Business Administration, Division
of Research, 1967.
JOB LEVEL AND FUNCTIONAL SPECIALTY 343
Newman, J. E. Understanding the organization struc-
t u r e : Job attitude relationship through perceptions
of the work environment. Organisational Behavior
and Human Performance, 1975, 14, 371-397.
O'Reilly, C. A., & Roberts, K. H. Individual differ-
ences in personality, position in the organization,
and job satisfaction. Organizational Behavior and
Unman Performance, 197S, 14, 144-150.
Perrow, C. B. Organizational analysis: A sociological
view. Belmont, Calif.: Brooks/Cole, 1970.
Porter, L. W. A study of perceived job satisfactions
in bottom and middle management jobs. Journal
of Applied Psychology, 1961, 45, 1-10.
Porter, L. W. Job attitudes in management: I. Per-
ceived deficiencies in need fulfillment as a func-
tion of job level. Journal of Applied Psychology,
1962, 46, 375-384,
Porter, L. W. Job attitudes in management: III. Per-
ceived deficiencies in need f u l f i l l m e n t as a f u n c -
tion of line versus staff type of job. Journal of
Applied Psychology, 1963, 47, 267-275.
Porter, L. W., & Lawlcr, E. E. Properties of organiza-
tion s t r u c t u r e in relation to job attitudes and job
behavior. Psychological Bulletin, 1965, 64, 23-51.
Rao, C. R. The u t i l i z a t i o n of multiple measurements
in problems of biological classification. Journal of
the Royal Statistical Society, Series B, 1948, 10,
159-193.
Smith, P. C., Kendall, L. M., & Hulin, C. L. Mea-
surement of satisfaction in work and retirement,
Chicago: Rand McNally, 1969.
Stogdill, R. M., & Coons, A. E. Leader behavior: Its
description and measurement. Ohio State Univer-
sity Bureau of Business Research Monograph, 1957,
No. 88.
Stone, E. F., & Porter, L. W. Job characteristics and
job attitudes: A multivariate study. Journal of
Applied Psychology, 1975, 60, 57-64.
Tatsuoka, M. M. Discriminant analysis: The sttidy
of group differences. Champaign, 111.: Institute for
Personality and Ability Testing, 1970.
Received May 14, 1976 »

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One-­Way ANOVA Demonstra.docx

  • 1. One--Way ANOVA Demonstration One--Way ANOVA Demonstration Program Transcript MATT JONES: This week we're going to be introducing you to one--way ANOVA. This is a comparisons--of--means test. Let's go to SPSS to see how we'll perform this specific test. To perform the one--way ANOVA in SPSS, we start up at the Analyze tab. If we click that, we get a dropdown menu.
  • 2. Since one--way ANOVA over is a comparisons--of--means test, we can move our cursor down to Compare Means, scroll across, and we see that one--way ANOVA is down at the bottom. If we click on that, a dialog box is opened up, where we have a Dependent List and a Factor. For one--way ANOVA, our dependent variable needs to be a metric level variable. That is it's an interval or ratio level of measurement. This is important because one one--way ANOVA compares means across a factor. The factor is our grouping variable. This needs to be a categorical variable. Typically, one--way ANOVA is used with grouping variables that have three or more levels or attributes to them. In this case, let's go ahead and test whether the means of the socioeconomic status index differ across a respondent's highest degree. To begin with, well, we'll go ahead, and we'll put socioeconomic status index into our Dependent List box. So you can see off to the left are choice of variables. Socioeconomic Status is down towards the bottom of our Variable list. If I place my cursor over it, we'll see it highlighted. You'll also note, again, a little scale ruler off to the left, which indicates that this is an interval- -ratio--level variable. Once I click on that variable, it's highlighted. I can just simply
  • 3. click on the arrow box, which moves that variable over into the Dependent List. Now I need to make sure and enter my factor as well. I'll scroll up till I find Respondents Highest Degree. I can see that it's right here. I can hover over this variable and then highlight it. Again, click on my arrow that places it into the Factor box. For basic omnibus ANOVA test, we are finished. We can go ahead and click OK and examine our output. This is the SPSS one--way ANOVA omnibus output. You can see here Respondent Socioeconomic Index is our dependent variable. SPSS provides us with information about between--groups and within--groups variance. The between--groups variance is a squared deviations between the groups. The within--groups variance, also known as unexplained variance, is the variance within the sample. A ratio of the mean square of between groups to within groups is how we obtain the F--value. The F statistic is a critical value that determines the significance of our test. ©2016 Laureate Education, Inc. 1
  • 4. One--Way ANOVA Demonstration Here we can see that the significance level is 0.000. This significance level is well below the conventional threshold of 0.5. Therefore we can reject the null hypothesis that there are no differences in socioeconomic status index across respondents highest degree. To find out where possible differences lie, we have to perform a post--hoc test. To perform a post--hoc test, we once again go back up to our Analyze, Compare Means, One--Way ANOVA. We can click on Post--Hocs, in here you'll see that
  • 5. there are a variety of options provided for you. We have equal variances assumed and equal variances not assumed. At this point, we don't know that whether we have equality of variances, and this is something that we specifically have to test for. But as you're performing the one--way ANOVA test, you can choose an equal variances assumed test, an equal variances not assumed test, and then on your output, go to the appropriate test after examining the variances. So we can click on a Bonferroni Test for equal variances and also Games- -Howell for equal variances not assumed. Click Continue. If we click our Options box, this is how we determine whether we have homogeneity of variances, or said another way, equality of variances. As you know from your reading, this is an assumption of the one- -way ANOVA test. If we click on that and activate this test, going to hit Continue and then click OK. Right away you'll see that we get quite a bit more output than we had before. Our first piece of output is the test of homogeneity of variances, also known as a Levene's test. This tests the null hypothesis of homogeneity of variances. Here, if you look at the significance level, you'll see that we are at 0.000, which is well below the threshold of 0.05. This means we reject our null
  • 6. hypothesis that variances are equal. Therefore, we have to assume that the variances are not equal in the one--way ANOVA. As we noted before, the overall test, also sometimes referred to as the omnibus test, is significant. Since the omnibus test is significant, we know that at least one of the means differs from another. Therefore we need to examine our post--hoc tests to determine which means differ. Again, moving with the assumption of inequality of variances, we have to move down to our Games- -Howell all Post-- Hoc test. If you remember, we chose Bonferroni as a test for equality of variances, but tested for the equality of variances and found they were not equal. The Games-- Howell test performs a pairwise comparison for all levels of our variable. Here you'll see less than high schools compared to high school, less than high school to junior college, less than high school to bachelor, less than high school to graduate, and so forth, until all possible combinations are achieved. ©2016 Laureate Education, Inc. 2
  • 7. One--Way ANOVA Demonstration The next column shows us our mean difference. We can see that on the socioeconomic status index, our dependent variable, those with less than high school have a mean score of 10.08 units lower than high school. If we move over to our significance level, we see that, indeed, this pairwise comparison is statistically significant a at the 0.05. Therefore there is a statistically significant difference between those with less than high school and those with a high school degree. As we move down our output, we can examine all of these pairwise comparisons. Again, less than high school to junior college, there is a difference of 17.38, and it
  • 8. is statistically significant. If we move to a less than high school to bachelor's, we can see that the difference increases. Again, it is statistically significant, and the same is true for less than high school to graduate. Moving through our output, we can go ahead and examine all of these pairwise comparisons, move over to our significance column, and see that they are indeed all statistically significant. You'll notice on the main difference that SPSS also puts an asterisk next to each mean difference to highlight or flag those differences that are statistically significant. We can conclude from our output and our post--hoc tests that there is indeed a difference in socioeconomic status index across respondents highest degree and that all pairwise comparisons are statistically significant, concluding that the higher a respondent's degree, the higher their socioeconomic status index on average. And that concludes our SPSS demonstration on one--way ANOVA. As a couple of parting thoughts, be sure and remember that your dependent variable in one--way ANOVA needs to be a metric variable, that is an interval ratio level of measurement. Your independent variable, or your factor, needs to be a categorical variable. This is because one--way ANOVA of is a comparison--of-- means test.
  • 9. Also, it's very important to test the assumption for homogeneity of variances, so be sure and look at that Levene's test. If you have any further questions, be sure and use your textbook. And also, your instructor is a very valuable resource. ©2016 Laureate Education, Inc. 3 Student Name: Date: Research Design Alignment Table | Using an alignment table can assist with ensuring the alignment of your research design. Research Problem, Purpose, and Framework Provide one sentence for each. These must align with all rows. Research Question(s), Method, & Design List one or more RQs, as needed; select method; identify design. Use a separate form for additional RQs. Data Collection Tools & Data Sources List the instrument(s) and people, artifacts, or records that will provide the data for each RQ. Data Points List the variables, specific interview questions, scales, etc. that will be used for each RQ. Data Analysis Briefly describe the statistical or qualitative analysis that will address each RQ. Problem: Purpose: Framework: RQ1: Design:
  • 10. RQ2: Design: RQ3: Design: Note. The information in the first column must align with all rows, and each individual RQ row must show alignment across the columns for that row. Once your Research Design Alignment Table is completed, reflect on your design alignment. Ask yourself: 1. Is there a logical progression from the research problem to the purpose of the study? 2. Does the identified framework ground the investigation into the stated problem? 3. Do the problem, purpose, and framework in the left-hand column align with the RQ(s) (all rows)? 4. Does each RQ address the problem and align with the purpose of the study? 5. Does the information across each individual row match/align with the RQ listed for that row? · By row, will the variables listed address the RQ? · By row, will the analysis address the RQ? · By row, can the analysis be completed with the data points that will be collected?
  • 11. Journal of Applied Psychology 1977, Vol. 62, No. 3, 335-343 An Investigation of the Influence of Job Level and Functional Specialty on Job Attitudes and Perceptions Edward F. Adams, Dennis R. Laker, and Charles L. Hulin University of Illinois at Urbana-Champaign One hundred and fifty-two jobs in a large (N = 1,313) midwestern printing com- pany were classified into vertical (job level) and horizontal ( f u n c t i o n a l specialty) distributions to investigate differences in employee attitudes. Descriptions of leader behavior (the Leader Behavior Description Questionnaire's Initiating Structure scale) and four aspects of satisfaction (the Job Descriptive Index Scales: Satisfaction with Work, Pay, Supervision, and Co- Workers) were as- sessed. A 3 (job level) X 5 (functional specialty) multivariate analysis of vari- ance demonstrated significant differences in job attitudes for both job level and functional specialty. A discriminant analysis separated the f u n c t i o n a l specialty and job-level groupings along two dimensions in terms of satisfaction with work itself and pay, and initiating structure. The results suggest that these two organizational structure characteristics summarize influences of managerial style, local norms, goals, and job requirements that a f f e c t
  • 12. individual attitudes and perceptions of work situation. Organizational structure has been used to describe norms and values, relationships among groups, and patterns of behavior. In this article, the term structure is restricted to two features of organizations: horizontal and vertical distributions of organizational mem- bers and their duties. Horizontal distribution is the extent to which jobs in organizations can be subdivided into homogeneous func- tional clusters such as departments, divisions, or functional specialties. Vertical distribution is the extent to which organizational jobs can be divided into layers or levels with different amounts of authority, responsibility, and task complexity. Conceptually, distinctions be- tween these two distributions are independent. In practice, the distinctions are more complex The a u t h o r s wish to acknowledge and thank James Terborg, Peter Horn, and Ralph Katerberg, Jr., for their h e l p f u l comments and suggestions. The research reported in this study was supported in part by National Science Foundation Grant GS- 32096 and in part by the U.S. Office of Naval Re- search Contract No. N 0014-75-C-0904, Charles L. H u l i n , principal investigator. Requests for reprints and other correspondence con- cerning this research should be sent to Charles L. Hulin, Department of Psychology, University of Il- linois, Champaign, Illinois 61820.
  • 13. and interrelated (Katz & Kahn, 1966; Per- row, 1970). Both structural characteristics of organiza- tions and individual employee characteristics have been found to influence job attitudes (e.g., Herman, Dunham, & Hulin, 197S; Her- man & Hulin, 1 9 7 2 ; Porter & Lawler, 196S; Stone & Porter, 1975). Herman and Hulin ( 1 9 7 2 ) found that struc- ture variables reflecting departmental assign- ment and functional specialty accounted for a substantial portion of variance in individual attitudes toward work. Stone and Porter ( 1 9 7 5 ) have taken issue with Herman and Hulin. They concluded from their findings that "the discrimination achieved by Herman and Hulin may have been more a function of jobs held by individuals in their sample than of differences in either 'function, hierarchical level or primary task orientation' " (p. 6 3 ) . All 16 jobs sampled by Stone and Porter were reported at the same hierarchical level. Therefore, they concluded that job level did not account for their discrimination among job titles, and by implication that Herman and Hulin's results could be explained by job level. Job level could not have influenced Stone and Porter's findings, but we believe the possible implications of their conclusions con- 335
  • 14. 336 E. F. ADAMS, D. R. LAKER, AND C. I. HULIN earning job level and function influences re- main unclear and should be addressed. Also, Stone and Porter's conclusions suggest that one can separate a job from its level, function, or department and q u a n t i f y the influences of these components. To test the impact of functional specialty, one would collect data from workers having the same job duties in d i f f e r e n t functional subdivisions of the organization. Differences should be found if function has an influence on attitudes and perceptions. One cannot, ex- cept in the crudest sense of the term, find em- ployees in various subdivisions of an organiza- tion who all have the same job duties. It is the job duties that have led us to differentiate among tasks and among employees who are assigned to these tasks, and to categorize them into different units. It is possible, however, to find employees in different subunits who share relevant job characteristics ( j o b complexity, authority, autonomy, etc.). It would be pos- sible to generate aggregations of organiza- tional members who work in different f u n c - tional subunits but would be classified as hav- ing highly similar jobs in terms of complexity, authority, etc. As Stone and Porter argue, when one com- pares different job clusters (departments or functional areas), there is the potential prob- lem of unintentionally confounding variables
  • 15. of interest with other characteristics such as job level. Job level has been shown to in- fluence job attitudes (e.g., Cummings & El- Salmi, 1970). Most studies using functional specialty as an explanation for job attitude differences have not specifically controlled for differences in job level (Herman & Hulin, 1972; Herman, Dunham, & Hulin, 197S). However, one can examine simultaneously the effects of job level and functional area with appropriate statistical techniques. In the two studies mentioned above (Her- man & Hulin, 1 9 7 2 ; Herman et al., 1 9 7 5 ) , there were no job-level differences across de- partments or functions. The f a i l u r e of the writers to discuss this is a serious oversight. The appearance of the Stone and Porter ar- ticle casts reasonable doubt on these findings and may result in functional specialty and de- partmental membership explanations of job attitude differences being neglected in f u t u r e research. It is hypothesized that both functional specialty and job level are related to meaning- ful differences in job attitudes even when the other factor is controlled. We do not hypoth- esize that functional specialty or job level cause differences in employee attitudes in a direct cause-effect link. We do not hypothe- size that job level or functional specialty clas- sifications account for more or less variance in work attitudes than job title. W7e hypothesize that functional specialty and job level in-
  • 16. fluence employee attitudes differently and should be examined as potential variables shaping job attitudes. Method The data were collected f r o m one plant of a mid- western printing company. Questionnaires were ad- ministered in small groups and required 30 minutes to complete. All participants were assured anonymity of their responses. The response rate was 88%. The 12%: nonresponse rate is an upper bound estimate of nonresponse rates hased on inadequate records of vacations, sick leaves, and unexcused absences from work. Included among the 12%, however, are those who simply did not show up at the survey room with the rest of their department or office. Eight different individuals administered the questionnaires. No ad- ministrator effects in terms of missing data or overall s a t i s f a c t i o n were observed. The total sample size was 1,313. Independent Variables Seventeen departments were clustered into the five f u n c t i o n a l area groupings of (a) preliminary prepara- tion, (b) pressrooms, (c) bindery, (d) maintenance, and (e) staff. The a u t h o r s clustered the 17 depart- ments according to their roles in transforming "raw materials" into finished products. The preliminary preparation grouping readied materials for produc- tion units in a supportive service capacity. Press- rooms and binderies were two large and different production functions. Maintenance ensured the up- keep and proper working order of machines and fa- cilities. Staff provided the administrative and man-
  • 17. agerial functions of the company, such as planning, organizing, and coordinating the units of the or- ganization. Six additional departments (cartoning, pallet, ink room, by-products, shipping, and ware- h o u s i n g ) were not included in the study because the tasks in these six departments were too heterogeneous to be grouped into one m e a n i n g f u l functional group- ing. In fact, these departments could have been con- sidered separate f u n c t i o n a l specialty areas, but the department sizes were so small that analyses could JOB LEVEL AND FUNCTIONAL SPECIALTY 337 Table 1 Intercorrelations of Dependent Measures Measure 1. 2. 3. 4. S. J D I Satisfaction with Work JDI Satisfaction with Supervision JDI Satisfaction with Pay JDI Satisfaction with Co-Workers LBDQ Initiating Structure 1.00 .45* .41* .44*
  • 18. -.03 1.00 .31* .32* .00 1.00 .31* .01 1.00 .12* 1.00 Note. N = 1,313. JDI = Job Descriptive Index. LBDQ = Leadership Behavior Description Questionnaire. *p < .01. not be done. Tatsuoka (1970, p. 38) recommends that the total sample size should be at least two or (prefer- ably) three times the number of variables used. Job level was determined through a rating of the jobs by the principal investigators. These ratings were arrived at through a process of iteration. Origi- nal ratings of job level based on training time or edu- cation required, responsibility, and authority were provided by members of the personnel department. Ratings provided by the personnel department were modified by the investigators in an attempt to re- move p e r t u r b a t i o n s introduced by the unwanted in- fluence of wage rates. For example, jobs that ap- peared "objectively" similar in all relevant character- istics were at times rated differently by members of the organization because one was a "male" job pay-
  • 19. ing more whereas the other was a "female" job with a lower pay rate. Differences in ratings caused by such biases were removed whenever possible. Wage rates were not confounded across functional spe- cialties. The resultant rating of job levels was a 20-point scale. Examples of the different job levels scaled from low to high are as follows: janitor (1), bagger (3), Clerk Typist II (S), chemical mixer ( 7 ) , folding- machine operator ( 9 ) , hoist-truck mechanic (11), linotype operator (13), Program Analyst II (15), maintenance foreman ( 1 7 ) , line department superin- tendent (19), and staff group manager ( 2 0 ) . Because of the small numbers of workers within these sepa- rate job levels, the actual job level hierarchy was trichotomized. Job Levels 1-6 (unskilled), 7-11 (skilled), and 12-20 (professional/supervisory) were aggregated into three job level clusters. Each func- tional area included people at these three levels of the hierarchy resulting in a 3 (levels) X 5 (functional specialties) design. Dependent Variables Job satisfaction. The Job Descriptive Index (JDI) developed by Smith, Kendall, and Hulin (1969) was used to measure f o u r aspects of job satisfaction: Satisfaction with Work itself, Satisfaction with Co- Workers, Satisfaction with Pay, Satisfaction with Supervision. Satisfaction with promotion was not in- cluded in the analyses because of considerations dis- cussed below. Perception of leader behavior. The Initiating Structure scale of the Leadership Behavior Descrip-
  • 20. tion Questionnaire (LBDQ; Stogdill & Coons, 19S7) was used to obtain perceptions and descriptions of average supervisory behavior from subordinates. An attempt was made to sample the relevant re- sponse domain broadly while simultaneously retain- ing necessary degrees of freedom. The four JDI scales assess several specific aspects of satisfaction and should be related to job level and f u n c t i o n . JDI pro- motions should be less related to function and job- level differences than the other affect measures, espe- cially because there was a company-wide policy on promotions. Initiating S t r u c t u r e of the LBDQ was t h o u g h t to be a better complement to the f o u r JDI scales than the Consideration scale, which overlaps more with the JDI Supervision scale. By selecting these five dependent variables, all sample size to de- pendent variable ratios, except as noted in Table 4, coincided with Tatsuoka's (1970) suggestions and other considerations of job/task homogeneity. Demographic Data Each respondent supplied information on com- pany tenure, age, sex, level of education, marital status, number of wage earners in the family, and family size. Analyses of these data are reported else- where (Hulin, Horn, & Herman, Note 1). Results The sample consisted of predominantly married males under 45 years of age. Most had a high school degree and had been with the company more than 4 years. Demographic variables accounted for less than °/o of the
  • 21. unique variance in affective responses (Her- man, Hulin, & Dunham, Note 2 ) . The intercorrelations of the dependent mea- sures are presented in Table 1. Intercorrela- tions among the four measures of satisfaction (JDI Satisfaction with Work, Supervision, Pay, and Co-Workers scales) were significant 338 E. F. ADAMS, D. R. LAKER, AND C. I. HULIN Table 2 Raw Cell Means Group Unskilled preliminary Skilled preliminary Professional/supervisory preliminary Unskilled press Skilled press Professional/supervisory press Unskilled bindery Skilled bindery Professional/supervisory bindery Unskilled maintenance Skilled maintenance Professional/supervisory maintenance
  • 22. Unskilled staff Skilled staff Professional/supervisory staff JDI Satisfaction with Work 24,91 29.14 32.63 19.03 25.03 32.04 19.22 25.48 29.54 28.07 36.29 36.54 33.56 30.07 37.83 J D I Satisfaction with Supervision 32.89 33.36 33.00
  • 23. 32.95 36.30 37.49 32.66 33.99 35.28 35.73 33.00 37.90 39.81 38.93 42.61 J D I Satisfaction with Pay 12.16 15.92 16.95 12.46 16.53 18.86 12.57 14.97 18.29 11.40 12.86 19.94 14.51
  • 25. 34.95 34.47 34.91 34.24 34.81 34.87 29.80 30.86 33.22 28.44 30.53 31.67 Note. JDI = Job Descriptive Index. LBDQ = Leader Behavior Description Questionnaire. O < . 0 1 ) . The LBDQ Initiating Structure scale was significantly correlated only with the JDI Satisfaction with Co-Workers scale. Multivariate Analysis oj Variance A multivariate analysis of variance was used to determine the main effects of func- tional specialty and job level and any possible interactions on the five dependent measures. Discriminant analysis was used mainly in the interpretation and explanation of job level and functional specialty relationships with the dependent measures. The raw cell means on the five dependent measures for the IS groups, a 3 X S design (Job Level X Functional Specialty), are pre-
  • 26. sented in Table 2. The main effect of job level was significant, multivariate F( 10, 2588) = 36.66, p < .01. Univariate F ratios were com- puted to assess the individual significance of the five dependent measures. Four of the five univanate F ratios on the scale items were significant at p < .01: For the Satisfaction with Work, F(2, 1298) = 141.52; for Satis- faction with Supervision, F ( 2 , 1298) = 6.49; for Satisfaction with Pay, F(2, 1298) = 87.91; and for Satisfaction with Co-Workers, P(2, 1298) = 32.08. The main effect of functional specialty was also significant: The overall effect was F(20, 4 2 9 2 ) = 13.64, p < .01. All five univanate F ratios computed for each dependent measure were significant at p < .01: For Satisfaction with Work, F(4, 1298) = 26.31; for Satis- faction with Supervision, F(4, 1298) = 13.98; for Satisfaction with Pay, ^(4, 1298) = 3 . 4 9 ; for Satisfaction with Co-Workers, F(4, 1298) = 4.31; and for LBDQ Initiating Structure, F(4, 1298) = 29.74. The Job Level X Functional Specialty in- teraction was significant. The multivariate overall effect was F(40, 5643) = 1.5298, p < .01. Only one univariate F ratio, for Satisfac- tion with Work, F(&, 1298) = 2.67, was sig- nificant at p < .01. Multiple-Group Discriminant Function A nalysis
  • 27. In order to interpret the results of the multivariate analysis of variance, a multiple- group discriminant function analysis was done. Calculation of the discriminant analysis JOB LEVEL AND FUNCTIONAL SPECIALTY 339 Table 3 Significant Discriminant Functions and Proportion of Discriminable Variance Accounted for by Each Function in a Multiple-Group Discriminant Function Analysis Function Measure JDI Satisfaction with Work J D I Satisfaction with Supervision JDI Satisfaction with Pay JDI Satisfaction with Co-Workers LBDQ Initiating Structure P of discriminable variance" 1 .72
  • 29. Leader Behavior Description Questionnaire. a Explained by discriminant function, resulted in five discriminant functions. The total discriminatory power accounted for by these five functions was 39%. The correction for small sample size relative to the number of dependent measures for this particular study is not necessary because the present sample is sufficiently large (Tatsuoka, Note 3). The first three discriminant functions were significant (p < ,01) and jointly ac- counted for 91% of the discriminable vari- ance. The third function contributed only 8% of the discriminable variance and was not interpreted. The significant discriminant functions as well as the proportion of discriminable vari- ance accounted for by each function are presented in Table 3. The first significant function accounts for 70% of the total discriminable variance, x~ (18) =438.36, p < .01. The discriminating power of the predictor variables was examined by Bartlett's test (Rao, 1952) with p(k - 1) degrees of freedom, where p is the number of variables and k is the number of groups. The second significant function accounts for of the total discriminable variance, 134,31, p < .01. Application of the discrimi- nant coefficients for the first and second func- tion to the original group means yielded IS group means in discriminant space that are
  • 30. presented in Table 4. Table 5 presents the structure matrix from the discriminant analysis. The structure ma- trix consists of correlations of each dependent measure with the linear combination of the dependent measures that maximally separate the groups along each discriminant function. Using the structure matrix and discriminant scaled weights for purposes of interpretation Table 4 Group Means on Discriminant Functions in a Multiple-Group Discriminant Function Analysis Function Group Unskilled preliminary Skilled preliminary Professional/supervisory preliminary Unskilled pressroom Skilled pressroom Professional /supervisory pressroom Unskilled binderies Skilled binderies Professional/su pervisory binderies Unskilled maintenance Skilled maintenance* Professional/supervisory maintenance Unskilled staff Skilled staff Professional/supervisory staff 3.05
  • 32. 44 66 204 109 60 120 218 140 76 15 7 50 41 60 103 a Sample size to dependent variable ratio <2:1. 340 E. F. ADAMS, D. R. LAKER, AND C. I. HULIN Table 5 Structure Matrix from a Multiple-Group Discriminant Function Analysis Function Measure JDI Satisfaction with Work J D I Satisfaction with Supervision
  • 33. JDI Satsifaction with Pay JDI Satisfaction with Co-Workers LBDQ Initiating Structure .88 .24 .S3 .36 -.26 .08 .03 .57 .26 .81 Note. JDI = Job Descriptive Index. LBDQ = Leader Behavior Description Questionnaire. (Tatsuoka, 1970), one can describe and in- terpret differences among the I S groups. On the first discriminant function, the functional specialty areas of preliminary, maintenance, and staff are separated f r o m pressroom and bindery by Satisfaction with Work, Satisfac- tion with Pay, and perception of less Initiat- ing Structure. Job level groups are also sepa- rated along this dimension, with higher job levels associated with higher means. Both of
  • 34. these interpretations can be confirmed by a comparison of the raw cell means presented in Table 2. Interpretation of the second dis- criminant function, again using the structure matrix and standardized discriminant weights, yields a similar separation. This function sep- arates pressroom and bindery from prelimi- nary, maintenance, and staff, but in this in- stance pressroom and bindery yield higher discriminant means than the other three func- tional specialties. In order of decreasing mag- nitude, the LBDQ Initiating Structure scale and the JDI Satisfaction with Pay scale ac- count for this separation. Again, hierarchical job level is reflected in the same manner as before, higher job levels (within each func- tional specialty) having higher cell means in discriminant space. Comparison of the origi- nal group means presented in Table 2 f u r - ther support these interpretations. Group loca- tions in discriminant space are shown in Fig- ure 1. The labels on the axes are tentative and reflect the structure matrix in Table 5. Discussion In only a few other studies have there been simultaneous investigations of both the verti- cal and horizontal distribution of organiza- tional units. Porter (1963) categorized f o u r levels of the vertical managerial hierarchy (vice president, upper middle, lower middle, and lower) and two horizontal subdivisions (line and s t a f f ) of organizations on the basis of the respondent's self-classification of his ot-
  • 35. her position. Line managers reported greater need satisfactions f r o m their jobs than staff managers, especially in the areas of esteem and self-actualization of needs. By examining mean differences, he concluded that vertical level of position within management had a greater effect on perceived need fulfillment deficiencies than did horizontal categorization of line versus staff. The present study investigated both the horizontal and vertical subdivisions in one printing organization. We attempted to sep- arate statistically the effects of the vertical subdivision (job level) and the horizontal subdivision (functional specialty) on the job attitudes by using a multivariate analysis of variance. The results showed that both main effects due to job level and functional spe- cialty were statistically significant. The Job Level X Functional Specialty in- teraction (a multivariate analysis of variance) was also significant. The univariate F for Sat- isfaction with Work is the only measure con- tributing to this interaction. If Figure 1 is examined, the lowest skilled staff group (Group 13) appears to be the group that is out of line. This group consists of primarily female clerical workers who seem to be hap- pier with their work than their job level would predict. The group means in Figure 1 demonstrate the main effect of job level within functional specialty on work satisfac- tion and initiating structure. With the excep- tion of Group 13, unskilled groups reported
  • 36. lower satisfaction with work and initiating structure than skilled or professional groups. Evidence for the vertical distribution of job level influencing job attitudes has been well supported in the past (e.g., Cummings & El- Salmi, 1970; Herman & Hulin, 1973; Porter, 1962). Porter and Lawler's (196S) compre- hensive review has summarized these differ- ences in job attitudes across different orga- nizational levels. The present study replicated JOB LEVEL AND FUNCTIONAL SPECIALTY 341 INITIATING STRUCTURE II 38 36 34 32 30 28 26
  • 37. 10 S A T I S F A C T I O N W I T H T H E W O R K I T S E L F 14 Figure 1. Fifteen job levels by f u n c t i o n a l specialty groupings plotted in two-dimensional func- tional discriminant space. (Lines connect the three levels within each functional specialty grouping on the dimensions of satisfaction with work and initiating s t r u c t u r e . Group numbers are as follows: 1 = unskilled preliminary; 2 = skilled preliminary; 3 — professional/supervisory preliminary; 4 = unskilled pressroom; S = skilled pressroom; 6 — professional/supervisory pressroom; 7 = unskilled binderies; 8 = skilled binderies; 9 = professional/supervisory binderies; 10 = unskilled mainte- nance; 11 — skilled maintenance; 12 = professional/supervisory maintenance; 13 — unskilled s t a f f ; 14 = skilled s t a f f ; IS = professional/supervisory s t a f f . ) these earlier findings while controlling for differences in functional specialty. The main effect for functional specialty confirms the hypothesis that horizontal sub- divisions can be a meaningful differentiation of job attitudes even when job level is con- trolled. This finding also lends support to the Herman and Hulin ( 1 9 7 2 ) and Herman et al. ( 1 9 7 S ) findings that functional specialty is a viable and useful manner of explaining differences in organizational attitudes. Examination of the means of the five func-
  • 38. tional groupings on the two discriminant func- tions indicates two interesting patterns. The two production groups, pressroom and bind- ery, have lower means on the first function of satisfaction with work and pay than the other three areas of maintenance, preliminary, and staff, This separation is clearly seen in Figure 1. The second function, defined by initiating structure, separates the five functional spe- cialties similarly, except that on this function, bindery and pressroom have higher means than the other three functional specialties. All seem to have a production-nonproduction sep- aration of groups. The bindery and pressroom are production sectors of the organization, whereas preliminary, maintenance, and staff groups are less production oriented. Binderies and pressrooms are also machine and line paced and mechanically oriented. The tasks in these departments are more well defined and structured than are the tasks in the other three areas. Lawrence and Lorsch (1967) described functional specialties as different subsystems in the organization based on certain subtasks. Lawrence and Lorsch ( 1 9 6 7 ) called these horizontal subdivisions "basic functional de- partments" (p. 30). Each of the subsystems studied (production, sales, applied research, and fundamental research) could be separated on the dimensions of formality of structure, interpersonal orientation, and time orienta- tions. Each subsystem possessed certain char- acteristics that were related to their primary
  • 39. task. For example, the production subsystems were highly structured but low on interper- sonal relations and were oriented to short terms. The research areas were low on struc- 342 E. F. ADAMS, D. R. LAKER, AND C. I. HULIN ture but higher than production on interper- sonal relations and were oriented to long-runs. Herman and Hulin ( 1 9 7 2 ) used primary functions of staff, productions, and produc- tion service departments and found significant differences between these functions on such organizationally relevant attitudes as satis- faction with line-staff relations, evaluation of production management, effectiveness of sup- portive services, satisfaction with plant, and plant atmosphere. Porter's (1963) findings separating line versus staff on need satisfac- tion also seem to be consistent with the pres- ent findings, although this dichotomy into line and staff is less specific than the basic func- tional departments, primary function, and functional specialty horizontal categorizations of other studies. The next logical question is why these subsystems and structural dis- tributions of organization units can differenti- ate job attitudes. Lawrence and Lorsch ( 1 9 6 7 ) have demon- strated that there are actual internal charac- teristics in various subsystems of an organiza- tion that are determined by the tasks being
  • 40. performed. In other words, employees in d i f - ferent work situations (defined by depart- ment, functional area, job level, etc.) will experience different local norms, demands, re- quirements, or managerial styles that are spe- cific to that work situation. Newman (1975) supports this view. He found that individuals in different organizational positions perceived their work environment differently. This would be expected because the task and en- vironment are different for different organiza- tional positions. It seems highly unlikely that attitudinal predispositions caused the company to locate individuals in different departments. Self-se- lection into different functional specialties may be part of the explanation. However, what we have assessed are attitudes and de- scriptions determined in large part by what workers find on their jobs and not only by what they bring with them to their jobs (Her- man et al, 197S; Herman & Hulin, 1 9 7 2 ; O'Reilly & Roberts, 1 9 7 S ) . Thus, although self-selection probably does occur, it seems tenuous to argue that it alone causes differ- ences in job responses assessed at a later time. Individuals in similar organizational posi- tions should perceive their environments more similarly than individuals in different posi- tions or functions. Organizational structure variables may simpl}' summarize a number of important influences (managerial style, specific goals, time orientations, local norms, and structural differences) that affect an in-
  • 41. dividual in his or her work situation. Future research should identify which variables de- fine work situations as well as influence in- dividual's perceptions of the work situation and how this knowledge can be used to under- stand and predict relevant employee behav- iors. Reference Notes 1. Hulin, C. L., Horn, P. W., & Herman, J. B. In- dividual differences, structural characteristics of organizational positions and plant effects on re- sponses (Tech. Rep. 76-3). Champaign: University of Illinois, D e p a r t m e n t of Psychology, 1976. 2. Herman, J. B., Hulin, C. L., & D u n h a m , R. B. De- veloping a response relevant typology of organiza- tions (Tech. Rep. 7 6 - 2 ) . Champaign: University of Illinois, Department of Psychology, 1976. 3. Tatsuoka, M. M. An examination of the statistical properties of a multivariate measure of strength of relationship (USDHEW Final Report, Project No. 2-E-020, Grant No. OEG-5-72-0027, 509). Urbana-Champaign: University of Illinois, De- cember 1973. References Cummings, L. L., & ElSalmi, A. M. The impact of role diversity, job level, and organizational size on managerial satisfaction. Administrative Science Quarterly, 1970, 75, 1-10. Herman, J. B., D u n h a m , R. B., & Hulin, C. L. Or-
  • 42. ganizational structure, demographic characteristics, and employee responses. Organizational Behavior and Human Performance, 1975, 13, 206-232. Herman, J. B., & Hulin, C. L. Studying organiza- tional attitudes from individual and organizational frames of reference. Organizational Behavior and Human Performance, 1972, 8, 84-108. Herman, J. B., & Hulin, C. L. Managerial satisfac- tions and organizational roles: An investigation of Porter's need deficiency scales. Journal of Applied Psychology, 1973, 57, 118-124. Katz, D., & Kahn, R. The social psychology of or- ganizations. New York: Wiley, 1966. Lawrence, P. R., & Lorsch, J. W. Organization and environment. Boston: Harvard University, Grad- uate School of Business Administration, Division of Research, 1967. JOB LEVEL AND FUNCTIONAL SPECIALTY 343 Newman, J. E. Understanding the organization struc- t u r e : Job attitude relationship through perceptions of the work environment. Organisational Behavior and Human Performance, 1975, 14, 371-397. O'Reilly, C. A., & Roberts, K. H. Individual differ- ences in personality, position in the organization, and job satisfaction. Organizational Behavior and Unman Performance, 197S, 14, 144-150.
  • 43. Perrow, C. B. Organizational analysis: A sociological view. Belmont, Calif.: Brooks/Cole, 1970. Porter, L. W. A study of perceived job satisfactions in bottom and middle management jobs. Journal of Applied Psychology, 1961, 45, 1-10. Porter, L. W. Job attitudes in management: I. Per- ceived deficiencies in need fulfillment as a func- tion of job level. Journal of Applied Psychology, 1962, 46, 375-384, Porter, L. W. Job attitudes in management: III. Per- ceived deficiencies in need f u l f i l l m e n t as a f u n c - tion of line versus staff type of job. Journal of Applied Psychology, 1963, 47, 267-275. Porter, L. W., & Lawlcr, E. E. Properties of organiza- tion s t r u c t u r e in relation to job attitudes and job behavior. Psychological Bulletin, 1965, 64, 23-51. Rao, C. R. The u t i l i z a t i o n of multiple measurements in problems of biological classification. Journal of the Royal Statistical Society, Series B, 1948, 10, 159-193. Smith, P. C., Kendall, L. M., & Hulin, C. L. Mea- surement of satisfaction in work and retirement, Chicago: Rand McNally, 1969. Stogdill, R. M., & Coons, A. E. Leader behavior: Its description and measurement. Ohio State Univer- sity Bureau of Business Research Monograph, 1957, No. 88. Stone, E. F., & Porter, L. W. Job characteristics and
  • 44. job attitudes: A multivariate study. Journal of Applied Psychology, 1975, 60, 57-64. Tatsuoka, M. M. Discriminant analysis: The sttidy of group differences. Champaign, 111.: Institute for Personality and Ability Testing, 1970. Received May 14, 1976 »