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Psychological Reports, 1967, 20, 50. © Southern Universities Press 1967
COURSES IN PSYCHOLOGY AND STUDENTST ATTITUDES
TOWARD MENTAL ILLNESS
CALVERT R. DIXON
East Carolina College, Greenville
In an earlier study of attitudes toward mental illness, Costin and Kerr (1962) dem-
onstrated that a course in abnormal psychology brought about more favorable attitudes of
students toward mental illness and mentally ill people, as measured on the Opinions About
Mental Illness Scale (OMI; Cohen & Struening, 1959). As their results differed from
those reported by Cohen and Struening for a sample of hospital employees (1959), they
suggested the futility of certain educational programs in mental hygiene. Doubting the
effect of short indoctrinational programs in producing attitude changes, these investigators
suggested that programs be subjected to origorous research scrutinyT before they are em-
ployed.
The purpose of the present study was to compare OMI scores of students with differ-
ent major areas of study while enrolled in psychology courses. The scale was administered
to students in six different classes in child development, adolescence, and mental hygiene.
The 167 underclassmen were classified then into five major groups (Nursing, N = 19;
Grammar Education, N = 37; Science, N = 24; Social Studies, N = 20; and Primary
Education, N = 67) and an analysis of covariance of the post-course scores with the pre-
course scores as a covariant was performed to discover changes in attitudes of members in
different psychology classes as well as changes in attitudes of students majoring in various
academic fields.
The mean differences (¢ tests) suggest that courses in psychology bring about some
favorable changes in studentsT attitudes toward mental illness. Nursing majorsT scores in-
dicated greater post-course authoritarianism (p .05); a high score for this attitude indi-
cates that mentally ill people are stigmatized, dangerous, and immoral. Grammar Educa-
tion (p .05), Science (p .05), and Social Studies majors demonstrated favorable
changes in Mental Hygiene Ideology (p .01), suggesting that the mentally ill be treated
with paternalism. Primary Education majorsT scores indicated favorable changes in Inter-
personal Etiology (p .01), suggesting that early love deprivation is the forerunner of
mental illness. Change scores of one class in adolescent psychology indicated greater post-
course authoritarianism (p .05). Two classes, child (p .05) and adolescent (p
.01) psychology, demonstrated favorable changes in Mental Hygiene Ideology, reflecting a
belief in the mental hygiene movement and the successful treatment of mental illness.
Two classes, child (pb .01) and mental hygiene (p .05), showed favorable changes
in Interpersonal Etiology.
Later interviews with instructors indicated that the changes in attitudes were more
closely related to the teacherTs position than to the material covered in the text. For instance,
students who began the course with a strong authoritarian attitude and were taught by an
authoritative instructor retained their authoritative attitude while, at the same time, chang-
ing their attitude in a desirable direction toward mental illness and the mentally ill. Fur--
ther indication of the teacher's effect on studentsT attitude change was demonstrated by the
classes in child psychology and mental hygiene where emphasis was placed upon the inter-
relationship of early deprivation and mental illness. It is conceivable then that the ob-
served changes are related to the activities of an instructor rather than to the content of
the text.
REFERENCES
COHEN, J., & STRUENING, E. L. Factors underlying opinions about mental illness in the
personnel of a large mental hospital. Amer. Psychologist, 1959, 14, 339. (Ab-
stract )
COSTIN, F., & KERR, W.D. The effects of an abnormal psychology course on studentsT at-
titudes toward mental illness. J. educ. Psychol., 1962, 53, 214-218.
Accepted December 20, 1966.
Psychological Reports, 1966, 19, 1239-1243. © Southern Universities Press 1966
DEPENDENCE OF RELIABILITY OF MULTIPLE-CHOICE TESTS UPON
NUMBER OF CHOICES PER ITEM: PREDICTION FROM THE
SPEARMAN-BROWN FORMULA!
DONALD W. ZIMMERMAN RICHARD H. WILLIAMS
East Carolina College Educational Testing Service
AND GRAHAM J. BURKHEIMER
East Carolina College
Summary"An equation is derived which expresses test reliability as a
function of number of item alternatives for the case in which only error due to
guessing is present. This result is compared with the modified Spearman-Brown
equation given by H. H. Remmers and his associates. Reliability coefficients
predicted by these equations are compared with coefficients generated by a com-
puter simulation method.
It has been known for some time that the reliability of multiple-choice tests
is influenced by the number of choices per item (Remmers, Karslake & Gage,
1940; Lord, 1944; Carroll, 1945; Plumlee, 1952). Since the probability of
chance success on an item is 1/a, where a is the number of choices per item, it
is to be expected that error variance introduced by chance success is a decreasing
function of number of choices and test reliability is an increasing function of
number of choices.
Remmers and his associates suggested the relationship could be described
by the Spearman-Brown formula, which is known to indicate increase in reliabil-
ity with increase in test length. The formula is
tnoo = Mfoo/|1 + (wm "1) fool , [1]
where 7, is the original reliability, 7,9. is the reliability of the test of increased
length, and 7 is the number of times the test is increased in length. Remmers
showed empirically that the reliability of various tests is approximated by this
function, when # refers to increase in number of choices instead of test length.
It has been pointed out, however, that there is no theoretical basis for predicting
this result (Lord, 1944; Guilford, 1950; Gulliksen, 1950).
COMPUTER SIMULATED RESULTS
In a previous paper (Zimmerman & Williams, 1965) a computer program
was used to simulate guessing error in multiple-choice tests. Distributions of as-
sumed true scores were prepared, and error scores were generated on the basis of
the probabilities to be expected from chance success due to guessing. The error
scores were added to true scores to obtain observed scores. Finally, product-
moment correlations between different sets of observed scores obtained by re-
peating the procedure several times gave an indication of test reliability.
TThis research was supported by a grant (OEC2-7-068209-0389) from the U. S. Office of
Education.
1240 D. W. ZIMMERMAN, ET AL.
The results of this procedure for tests differing in length and number of
choices are shown in Table 1. The data in this table can be used to examine the
effect of increased test length, as well as increased number of choices, upon reli-
ability. Apparently, there is an interaction between the effects of test length
TABLE 1
COMPUTER SIMULATED RESULTS FOR RELIABILITY
: N= 10 N= 10 N = 100 N = 100
fy see! Gm 4222 Zo 5
roo* 44 74 89 97
root * 7 89 97
foge*? .76 AF
foot *** .66 95
*Reliability given by computer program.
**Reliability given by substituting .44 or .74 in Equation [1].
***Reliability given by substituting .44 or .89 in Equation [5].
****Reliability given by substituting .44 or .89 in Equation [1], where 7 = 2.5.
and number of choices. For short tests (N = 10) reliability increases greatly
with increase in number of choices (.44 to .74). For long tests (N = 100) re-
liability increases slightly with number of choices (.89 to .97). Also, for 2
choices, reliability increases greatly with test length (.44 to .89). And for 5
choices reliability increases to a lesser degree with test length (.74 to .97).
From the table it is seen that the Spearman-Brown formula describes the
increase in reliability with increase in test length for both the 2-choice test and
the 5-choice test (Zimmerman & Williams, in press). Consider, now, Rem-
metsT suggestion that the same formula describes increase in reliability with in-
crease in number of choices. The results in the table show that there is a greater
discrepancy, although the predicted value for the longer test is close to that indi-
cated by the program.
INCREASED RELIABILITY AS A FUNCTION OF INCREASED
NUMBER OF CHOICES
It is possible to derive a simple equation showing the effect of increasing
the number of choices upon reliability for the case in which only error due to
guessing is present. Reliability is given by
foo = [(@"1)5:]/[(2a"1)s2£+N"T], [2]
where a is the number of choices, s;7 is the variance of true scores, N is the num-
ber of items, and T is the mean of true scores. This equation gives the value
which is approximated by the computer simulation method described above
(Burkheimer, 1965; Burkheimer, Zimmerman, & Williams, in press). When the
number of choices is increased, we can write
RELIABILITY OF MULTIPLE-CHOICE TESTS
fee = [(e " L)sA/[ ~ 1)s2 4+ N "TI , [3]
whete 7, is the reliability for the test with increased number of choices, a is the
original number of choices, aT is the increased number of choices, and the other
symbols are as defined above. Solving [2] for 5,7 gives
sP®= [(N "T) rool/[(@a"1) (1 " Poo) ] -
Substituting this result in (3) and simplifying, we have
fooT = [(a@ " 1) rool/[(#@ "1) + (4@"2@) fool .
The data presented in Table 1 show that substitution in this equation yields re-
sults close to those indicated by the computer program. The accuracy is greater
than that obtained by using [1] and of the same order as that obtained by using
[1] for increased test length.
If the method employed by Remmers were valid, the ratio aT/a would be
comparable to ? in [1], which could be written in this form:
rooT = [(a'/a) roo] /{1 + [(a/a) " 1]roo} . [6]
Simplifying, we obtain the following result
fooT == BToo/ (a+ (a " 4) Tool ; [7]
which can be compared to [5]. It is seen, therefore, that equation [5] differs
from the modification of the Spearman-Brown formula suggested by Remmers
only by subtraction of 1 from the a@T factor in the numerator and the 4 term in
the denominator. If both aT and a were large [1| and |5| would give nearly the
same results. For multiple-choice tests, however, aT and a are relatively small,
and some discrepancy can be expected.
Dividing both numerator and denominator of [5] by a " 1 gives
tooT = [(aT " 1) /(a " 1) roo] /{[(a " 1)/(a "1)] + [(aT " a) /(a " 1) Jroof - [8]
If, now, we define A as the ratio (a " 1)/(a" 1) and simplify, we have
foo = Afoo/ [1 ot (A on 1) roo] T . [9]
which has the same form as the Spearman-Brown formula. In other words, Rem-
mersT suggestion is valid if we employ the ratio (aT " 1)/(a " 1) in the Spear-
man-Brown formula, but not if we employ the ratio aT/a. It should be noted
that the above equations apply only to the case in which differences in reliability
result from chance success due to guessing.
1242 D. W. ZIMMERMAN, ET AL.
DEPENDENCE OF CORRELATION BETWEEN ERROR SCORES ON
PARALLEL FORMS UPON NUMBER OF CHOICES
It is of interest that an equation showing the dependence of the correlation
between error scores on parallel forms of a test upon number of choices can also
be derived. This quantity has been assumed to be zero in the classical theory of
mental tests. However, when chance success due to guessing is present, as in the
case of most multiple-choice tests, it can be shown that it is positive in value, that
it decreases with number of choices, and that the relationship is indicated by an
equation similar to [5].
Correlation between error scores on parallel forms is in fact given by the fol-
lowing equation:
reo = 5P/[s° + (a2"1)(N"T)], [10]
where the symbols are as defined above (Burkheimer, 1965; Burheimer, Zimmer-
man, & Williams, in press). When number of choices is increased, we can write
tee = 52/[s2 + (@ "1)(N"T)]. [11]
Solving [10] for s,° gives
$8 [ree (@"-D(N=T)Y (1 "re). [12]
Substituting [12] in [11] and simplifying leads to this result:
fooT =z (4 " 1) Fee/[(@ " 1) " (2 " @) ree] - [13]
Dividing both numerator and denominator of [13] by a " 1 gives
TeeT =[(4"1) (a " 1)reel/{[ (a " 1)/(# " 1)] + [C2 "@)/(a " 1) ree} . [14]
If we define B = 1/A = (a " 1)/(a@ " 1) and simplify, we have
Veo = Bree/|1 + (B noe 1) ree] T [15]
which, again, has the same form as the Spearman-Brown formula. There exists
no analogue of this equation in the classical theory of mental tests. From [13]
and [15] it is clear that the degree of correlation between error scores on parallel
forms decreases with increase in the number of choices.
The results given by the computer program for 7¢, are shown in Table 2.
Equation [13] predicts accurately the effect of increasing number of choices
upon f¢. Another fact of interest shown in the table is that, if 7,. is treated as
a reliability coefficient, the Spearman-Brown formula indicates accurately the
change in its value with change in test length (Zimmerman & Williams, in
press). For longer tests the correlation between error scores on parallel forms
RELIABILITY OF MULTIPLE-CHOICE TESTS 1243
TABLE 2
COMPUTER SIMULATED RESULTS FOR CORRELATION
BETWEEN ERROR SCORES ON PARALLEL FORMS
N= 10 "ieee | N = 100 N= 100
a=2 ete 2"7 79
feo* A6 a7 .89 65
Vest ?"? 90 .67
foc*** 18 .66
*Value given by computer program.
** Value given by substituting .46 or .17 in Equation [1].
*** Value given by substituting .46 or .89 in Equation [13].
becomes higher in value, and the degree of change is indicated by the Spearman-
Brown formula.
When chance success due to guessing is the only source of error in a multi-
ple-choice test, the following can be concluded. (1) Increase in reliability with
increase in number of choices is indicated only approximately by the Spearman-
Brown formula. (2) Increase in reliability with increase in number of choices
is indicated to a higher degree of accuracy by Equations [5] and [9]. (3) In-
crease in reliability with increase in test length is indicated accurately by the
Spearman-Brown formula. (4) Increase in correlation between error scores on
parallel forms with increase in test length is indicated accurately by substituting
this quantity in place of the reliability coefficent in the Spearman-Brown formula.
(5) Increase in correlation between error scores on parallel forms with increase
in number of choices is given by Equations [13] and [15].
REFERENCES
BURKHEIMER, G. J. Some effects of non-independent error in multiple-choice tests: a
binomial model. Unpublished M.A. thesis, East Carolina College, Greenville, N. C.,
1965.
BURKHEIMER, G. J., ZIMMERMAN, D. W., & WILLIAMS, R. H. The maximum reliability
of a multiple-choice test as a function of number of items, number of choices, and
group heterogeneity. J. exp. Educ., in press.
CARROLL, J. B. The effect of difficulty and chance success on correlations between items
or between tests. Psychometrika, 1945, 10, 1-19.
GUILFORD, J. P. Psychometric methods. (2nd ed.) New York: McGraw-Hill, 1954.
GULLIKSEN, H. Theory of mental tests. New York: Wiley, 1950.
Lorb, F. M. Reliability of multiple-choice tests as a function of number of choices per
item. J. educ. Psychol., 1944, 35, 175-180.
PLUMLEE, L. B. The effect of difficulty and chance success on item-test correlation and
on test reliability. Psychometrika, 1952, 17, 69-86.
REMMERS, H. H., KARSLAKE, R., & GAGE, N. L. Reliability of multiple-choice measur-
ing instruments as a function of the Spearman-Brown prophecy formula: I. J.
educ. Psychol., 1940, 31, 583-590. :
ZIMMERMAN, D. W., & WILLIAMS, R. H. Chance success due to guessing and non-
independence of true scores and error scores in multiple-choice tests: computer
trials with prepared distributions. Psychol. Rep., 1965, 17, 159-165.
ZIMMERMAN, D. W., & WILLIAMS, R. H. Generalization of the Spearman-Brown
formula for test reliability: the case of non-independence of true scores and error
scores. Brit. J. math. statist. Psychol., in press.
Accepted November 7, 1966.