Psychological Clinic
The
Copyright, 1927, by Lightner Witmer, Editor
Vol.
No. 7
XVI,
October,
1927
THE RELIABILITY AND VALIDITY OF THE WALLIN PEG BOARDS By Florence L. Goodenough Institute
of
Child
Welfare, University of
Minnesota
The Wallin series of
performance tests designed for use with of four boards, each measuring 3 by consists children very young 14 inches, % of an inch thick. Each board contains recesses for 6 pegs, similar in size but varying as to form. Board A includes only round pegs, Board B only square pegs, in Board C three round and three square pegs are arranged in alternating sequence, while in Board D there
are two round, two square, and two triangular pegs, arranged alternately. The round pegs are % of an inch in diameter; the square and the triangular pegs are % of an inch on a side. All pegs are 2y2 inches in length. The recesses correspond to the pegs in form, and are % of an inch deep. At least three previous investigators have published material dealing with the use of these pegs. The original report by Wallin1 is based upon results obtained from 101 subjects ranging in age from
also
9 months to
a
constitute
graded series,
Board D.
a
little
over
8 years.
Wallin shows that the four boards increasing in difficulty from Board A to
He finds that the
ability
measured
by the boards is one being able to place the
which increases with age: the older children pegs in the proper recesses in a shorter time and with fewer errors than the younger children. Tentative age norms are included in the report, but because of the small number of cases at each age, these can be regarded as suggestive only. No data as to the reli-
ability of the are given.
test or its correlation with other measures of
ability
Baldwin and Stecher2 gave the test to 59 children ranging in age from 2 to 6 years. Of these 22 were tested four times at two week intervals. Some improvement on the later occasions as com1
Wallin,
J. E. W.:
The
Peg
Form Boards.
Psychol.
Clinic, 1918, 12,
40-53. 2
Baldwin, Bird and Stecher, Child. D. Appleton and Co., 1925.
Lorle:
The
Psychology of
See pages 77-80.
the Pre-School
THE PSYCHOLOGICAL CLINIC
200
to the first is reported, but the correlations between the successive tests are not stated. No correlations with other tests are reported, but age norms in terms of average time required for a successful performance are given for each of the four boards separately. Since the method employed for administering the test dif-
pared
fers from that used by Wallin, the results obtained in the two studies cannot be compared directly. Boards A and B are included in the Stutsman series of performance tests for children of pre-school age.3 Percentile norms
performance of approximately 50 children in each of three groups?18 to 23.5 months, 24 to 29.5 months, and 30 to 35.5 months?are given. A steady decrease from age to age in time required for a successful performance is shown. No data on reliability or correlation with other tests are given. In the study about to be described, the test was given to 100 two-year-olds, 100 three-year-olds, and 100 four-year-olds?300 cases in all?selected to constitute a representative sampling of the population of Minneapolis, on the basis of a comparison of the distribution of paternal occupations within each of the three age groups with that reported for the city as a whole in the 1920 census.4 Exactly 50 boys and 50 girls were included within each age group. Ages were taken to the nearest birthday. Immediately following the peg board tests, all children were given the Kuhlman upon the age
Revision of the Binet tests. tests
man
are
reported
The results obtained from the Kuhl-
elsewhere.5
Since no alternative form of either test is available, reliability could be studied only by means of retests. The children were therefore re-examined after an average interval of six weeks.6 Both the peg boards and the Kuhlman were given on each occasion; the peg-
invariably being given first. Two examiners, the writer and Buffington, research assistant in the Institute, made all the tests. In order to gain some information as to the effect of a change of examiners upon the test score, the following plan was carried out: In each age group, 25 of the cases were examined by the
boards
Miss Mildred
Stutsman, Rachel: Performance Tests for Children of Pre-School Age. Psycliol. Mono., 1926, Vol. 1, No. 1. For a more detailed account of the method of selecting the cases, the reader is referred to The Kulilman-Binet Tests for Children of Pre-School Age, A Critical Study and Evaluation, by Florence L. Goodenough, University of Minnesota, Institute of Child Welfare, Monograph Series No. 2. 8
Genetic 4
6
Ibid.
6
The standard deviation of the interval between tests was 1.5 weeks.
201
TALLIN PEG BOARDS
both occasions, 25 by Miss Buffington on both occasions, by the writer, then by Miss Buffington, and the remaining 25 first by Miss Buffington, then by the writer. All examinations were made in a separate room where freedom writer 25
on
examined first
were
from
child seated at
a
desk at which the examiner sat.
pedestal was
could be insured. The tests were given with the low table which was placed at the left of a single
interruption
The
following procedure
used:
shyness had been overcome, and when the entirely at ease, the examiner asked, "Now wouldn't you like to see some of my blocks?" (The word blocks was used in preference to pegs since it is more familiar to little children.) Board A was then placed on the table before the child with the pegs in place, the long edge of the board parallel to the edge of the table. The examiner then continued, See these sticks ? After any initial
child seemed to be
''
Each
one
houses."
has its own little house. Let's take them out of their The examiner then removed the pegs, encouraging the
help. As the pegs were removed, they were placed at the of the board away from the child, the examiner taking care to side from rolling out of reach. When all the pegs had them prevent been removed, the examiner said, "Now I want to see how fast you child to
can
put them all back again.
you can."
wanted,
Hurry
If the child did not
up, put them back
seem to
the examiner illustrated with
comprehend
one or two pegs
as
fast
what
which
as
was were
then removed and the instructions
repeated. As soon as the child attempted to put the first peg into a hole, the stop watch was started and the time required for placing all the pegs correctly was recorded. Preliminary adjustment to the situation, fingering the pegs, holding them up for the examiner's approval, etc., was not Children under three cannot be depended signal, but once begun they will usually continue without intermission until the task is completed. For this reason, a time record taken from the beginning of the actual included in the time record. upon to start
on
attempt, i.e., from the time when the first
peg touches the
board,
is
likely to be a more stable measure than one taken from the pronouncing of a signal word or from the time when the first peg is touched, since the signal word is frequently ignored, or the peg merely taken up and played with. The children were not urged to greater speed during the placing
of the pegs, since this is
likely
to lead to mental confusion and
consequent increase in the number of
errors,
especially
with the
THE PSYCHOLOGICAL CLINIC
202 boards
containing
tion to this rule or
who
than one form of the pegs. The only excepmade in the case of children who stopped to talk their performance for other reasons. In such
more
was
interrupted
the examiner recalled his attention by a gesture toward the '' board, saying, Go ahead, hurry up, see how fast you can put them cases
Liberal praise was given as each board was completed, occasional word of encouragement or praise during the placof especially difficult pegs. Boards B, C, and D were given in the same manner as Board
all back." and
ing A.
an
If
a
child
at the
time, possible and recess
in,
placed a peg in the wrong hole, no comment was made but when the remaining holes had been filled as far as
the child found himself with a peg left into which it could be fitted, the examiner said,
will it?
Look at the rest of
over
with
no
''
It won't go hand along the
them"?passing a point out the error?"and see if you If the child then perceived his error can find what is the matter.'' he was permitted to correct it; if not, the board was counted as failed. Only a single suggestion of this sort was given. The boards were always presented in the same order, and one trial was allowed on each. In this study, a time limit of two minutes was allowed for each board, but when the data were worked up, it was found that nothing was added to the accuracy of the test by counting time over 100 seconds each for Boards A and B, and board but
taking
care not to
60 seconds each for C and D. Errors were also recorded, found to lower the taken of them in the
but, as penalizing for errors was the score, no account has been of reliability method scoring finally adopted. Both examin-
felt the error score to be an unreliable measure in itself, because the of many marginal cases when a child makes a tentative attempt to place a peg in the wrong recess but withdraws it almost instantly. Such cases are often overlooked if the child moves quickly, and at ers
all events, to assign equal weight to such a performance as to one in which the child persists for a long period in attempting to force a square peg into a round hole is a procedure which it is difficult
basis; while in the absence of an device it is difficult, if not impossible, to differentiate as to types of error. Since time is in part a function of error, and since the time score is affected not simply by the number of errors but also by their duration, it is perhaps not surprising to find that the time score alone is a more reliable and presumably to
justify
automatic
a more
on
any common-sense
recording
valid
measure
of
a
child's performance than
a
combined
Table I
Test 1 Board A Number of cases Median time (seconds) 90 percentile 10 percentile Board B Number of cases Median time (seconds).
Test 2
24-29.5
each of the four boards by half year age groups.
30-35.5
Test 1
Test 2
Test 1
Test 2
49.3 27.0 DNC2
40.6 24.5 77.0
51 31.0 25.8 47.8
51 30.8 19.7 43.3
51 26.5 17.6
49 94.2 39.2 DNC2
49 59.2 35.6 DNC
51 42.7 27.5 89.3
51 37.8 24.8 53.3
51 33.3 23.3 70.7
51 31.3
49 DNC 49.5 DNC
51 DNC 34.8 DNC
51 DNC 36.5 DNC
51 72.0 26.5 DNC
51 40.8
percentile percentile
49 DNC2 44.5 DNC2
Board D Number of cases Median time (seconds). 90 percentile 10 percentile
49 DNC2 DNC DNC
49 DNC DNC DNC
51 DNC 59.7 DNC
51 DNC
51 DNC 44.7 DNC
90
percentile
10 percentile Board C Number of cases Median time (seconds) 90 10
1 2
49
49
38.3
51 24.1
15.1 34.2
19.6
59.3
36-41.5 Test 1
42-47.5
Test 2
At the time of the first test. DNC?Did not complete.
49.7
Test 1
49
19.3
48 17.7
15.0
12.6
11.2
34.4
27.5
24.6
49 27.8 15.9 47.5
49 22.8
48 21.0 14.3 29.8
19.9 13.7 33.2
48
48
24.1
15.9 69.8
23.4 14.7 39.8
36.2
48 34.4 21.3 DNC
48 27.7 17.4 69.5
52 27.7 16.5 69.5
14.6
34.4 ?>
DNC
Test 2
49 21.4
48
52
17.4 10.6 23.7
15.4
48
10.2 23.9 52 16.6 10.9
23.8
r"
DNC
49 32.5 20.1 DNC
49 24.1 16.0 54.6
51 94.5 29.8 DNC
49 51.2 25.9 DNC
49 32.6 20.2 DNC
21.2
Test 1
48-53.5
52 19.5 12.6
Test 2
BOARDS PEG WALLIN
18-23.5
Age (months)1
success on
203
Medians and 10~00 percentile ranges of time required for
THE PSYCHOLOGICAL CLINIC
204 time-and-error than
in which all
score
errors are
given equal weight,
or
alone.
an error score
beginning of the study, three trials were given on each This is the method followed by Wallin and by Stutsman. After about 30 cases had been tested, the second and third trials were discontinued, since many of the children found the later trials quite irksome, and in a few instances an unfavorable emotional reAt the
board.
action ensued which persisted throughout the examination. StutsIt was man reports a similar difficulty with several of her cases. found, moreover, that the correlation between the time required for on the first trial, and time on the best trial was above .9 for this group of 30 cases. With only a single trial on each board, practically all the children enjoyed the test greatly.
the entire series
Table II
Reliability of the separate boards by Age
2
Age
age.
3
Age PE
PE
4
PE
Board A
.720
.032
.661
.038
.395
.057
B
.640
.040
.619
.042
.431
.055
.317
.061
.522
.049
.432
.055
.376
.058
D
time
Table I shows the median and the 10-90 percentile range of required to complete each of the four boards by half year age
groups.7 Table I shows a
a
steady
successful performance
on
decrease with age in time required for each of the boards. It also corroborates
findings as to the comparative difficulty of the four boards. slight effect of practice is seen when the median scores on the second test are compared with those earned six weeks previously, making allowance for the difference in age. This effect is, howWallin's A
7 Because of undistributed failures at the lower extreme, these measures have been used in preference to the mean and standard deviation. See Statistical Method by T. L. Kelley, Macmillan and Co., 1923, pages 75-77.
WALLIN PEG BOARDS
205
ever, less marked than was found for the Binet tests same
given
at the
sitting.8
Table II shows the
reliability of each of the four boards, calcuthe of correlation between the time scores on each of by the two tests. The Pearson product moment formula was used. lated
means
The data have been treated by age groupings of one year. Boards A and B are seen to be more reliable, on the average, than Boards C and D. This is in part a result of the fact that the test appears to be better suited to the study of two-year-olds than of older children, and, as was shown in Table I, only a small percentage of the two-year-olds succeed with Boards C and D. ?
Table III Correlations between Kuhlman-Binet mental age and the four peg boards *
Age
Age 3
2
PE
each of
score on
Age PE
4
PE
Board A
+ .457
+ .053
+ .289
?.062
+ .373
?.058
B
+ .473
?.052
+ .391
?.057
+ .277
?.062
+ .422
?.055
+ .402
?.058
+ .417
?.056
+.482
?.051
D *
Based upon the results of the first test.
Table III shows the correlation between Kuhlman-Binet mental age and time required for success on each of the four boards. The data are based upon the first of the two examinations given. In
deriving
weight
the time
a
combined score, a rough attempt was made to the separate boards both with reference and their correlation with the Binet mental age.
scores on
to their reliability It is obvious that the data do not warrant too great refinement of treatment, since the time scores are affected by many accidental factors which disturb the results in individual cases, and for which
clinical allowance must always be made. The method employed is based upon an inspection of the data in Tables I-III and weighting in round numbers ?
according
Previous reference.
to average
reliability,
correlation with
206
THE PSYCHOLOGICAL CLINIC
Binet,
and low
variability.
Four different
approximations,
one
of
combined time-and-error score were tried. The which involved method which was found to show the highest average reliability and correlation with Binet at the various ages is expressed by the fola
lowing
formula: Time
Score Board C
=
-J- J/3
letoitf
?
on
time
Z4to?95
Board A -f- time Board D.
on
Board B +
y2
time
on
on
JOtom
3bto415
42to 47.5
4dta%5
54t0m
Cfironological aye in months Fig. 1.
Maximum time Maximum time
allowance, Boards allowance, Boards
Maximum combined
score
=
A and B?100 seconds each. C and B? 60 seconds each.
250.
Figure 1 shows the median combined score on the four boards by age and sex on each of the two examinations. Allowance is made for the gain in age. The data of Figure 1 are given in Table IV. Figure 2 shows the median scores according to Kuhlman Binet mental age. Figure 3 shows the medians for each of the four boards separately.
207
WALLIN PEG BOARDS
negative acceleration is very apparent in of the the curves on each separate boards. This tendency is somewhat masked in the combined score, owing to the fact that, since A
tendency
toward
the boards constitute a graded series, the periods of most rapid gain do not coincide, so that slow improvement on the easier boards is
compensated
for
by rapid gain
on
the
difficult
more
ones.
?10
3b 4Z Mental Age in Months
Fig. 2. Fig. 2.
Table V shows the correlation between
first and second examinations by age and
corresponding figures
scores
for the Kuhlman-Binet
earned
on
separately. are given for
sexes
the The
com-
parison. At age two the test compares very favorably with the Kuhlman, as far as reliability is concerned. At ages three and four, it is less reliable, but even here the figures are sufficiently high to
THE PSYCHOLOGICAL CLINIC
208
warrant its use as a
supplementary measure, especially in the case handicap. Since the total time rerarely over five minutes, the test can the same sitting as a Binet without danger of
of children with a language quired for the four boards is
readily be given at overfatiguing the child.
Test! Test Z
Board C
Board D \
\
\ \ \ V? I
\ \
\
Test 1 Test 2 _l
18
50
4Z
5418
30
Age in
Age in months
42
54
months
Fig. 3.
on
Table VI shows the correlation between the total score earned the four boards and Kuhlman-Binet mental age for each of the
Table IV
Age (months)
Test 1 Median score... 90 percentile.... 10 percentile Test 2 Median score... 90 percentile 10
percentile
18-23.5
24-29.5
scores on
the four boards
age groups.
30-35.5
36-41.5
42-47.5
48-53.5
Boys
Girls
Boys
Girls
Boys
Girls
Boys
Girls
Boys
Girls
Boys
Girls
163.5 103.6 247.8
174.8 121.5 250.0
122.2
135.6 103.0 182.7
109.8 75.9 151.8
106.9
150.0
84.3 51.4 126.7
92.2 60.1 130.9
66.7 43.7 97.9
66.8 45.7 84.0
60.0 42.5 82.1
50.0 34.3 70.7
153.0 103.5 221.3
159.7 106.7 214.0
112.7 74.8
121.0 96.6 160.8
103.0 61.8 145.6
91.7 57.9 125.5
63.4 43.8 83.2
79.8 53.0 123.3
59.0 38.3
61.3 42.9 89.3
56.1 44.0
43.6 33.7
66.1
53.9
88.6 146.7
146.8
81.1
90.3
BOARDS PEG WALLIN
by half year
209
Medians and 10-90 percentile ranges of combined
THE PSYCHOLOGICAL CLINIC
210
It appears from these correlations that the mental functions measured by the two tests are not entirely identical, though they evidently have much in common. Even when correctwo examinations.
tion is made for the unreliability of measurement (correction for attenuation) the relationship is still far from perfect; averaging slightly above .7 for the various groups. It is doubtful whether Table V Correlation between Scores earned
Age
the First and Second Tests by Age and Sex.
on
Age 3
2
Age
4
Boys
Girls
Boys
Girls
Boys
r
.913
PE
.016
.675 .052
.751 .042
.625 .058
.457 .075
.709 .048
.706 .048
.817 .032
.902 .018
.832
.809 .033
Girls
Peg boards
Kuhlman-Binet r
.810
PE
.033
.029
tests of this sort, even though their reliability were to be greatly improved, should be looked upon as the equivalent of a Binet test. They supplement the Binet, but do not precisely duplicate it, either in form or significance. Table VI Correlation between Kuhlman-Binet Mental Age and Total Score on the four boards.
Age
2
Age 3 Girls
Boys
PE
PE Test 1 Test 2
.566 .488
.065 .073
.469 .432
Additional evidence
facts for
.074 .078
PE
Girls PE
Boys PE
Girls PE
,506 .071 .596 .061 ,428 .078 .496 .072 .539 .067 .587 .063 ,412 .079 .559 .065
the
significance of a test is afforded overlapping between successive chrono-
as to
of the amount of
by a study logical or mental
Boys
Age 4
age groups. Tables VII and VIII show these of 300 cases. The data are based upon the first
our group
of the two examinations
given.
WALLIN PEG BOARDS
211
Examination of Tables VII and VIII shows that the amount of overlapping between age groups is relatively small, and is somewhat less when the division is made upon the basis of mental age chronological age is used. Moreover, the amount of overlapping increases roughly in proportion to age.9 than when
of
Effect of a change testing was divided
in examiners upon the test score. The work between two examiners according to a defiTable VII
Percentage of each half year chronological age group equalling or exceeding the median of each successive chronological age group. 1-6 to 1-11.5
Mdn. = 171
2-0 2-5.5 Mdn. =
2-6 2-11.5 Mdn. = 124 102
3-0 3-5.5 Mdn. =
81
3-6 3-11.5 Mdn. = 65
4-0 4-5.5 Mdn. = 51
Cases
1-6 to 1-11.5
(Mdn.
=
171)
50.0
16.7
3.7
89.1
50.0
13.0
2.2
98.0
82.3
50.0
11.8
2.0
98.0
90.0
75.5
50.0
28.6
4.1
49
100.0
100.0
97.9
81.3
50.0
20.8
48
100.0
98.1
98.1
96.2
76.9
50.0
52
49
2-0 to 2-5.5
(Mdn.
=
124)
51
2-6 to 2-11.5
(Mdn.
=
102)
51
3-0 to 3-5.5
(Mdn. =81) 3-6 to 3-11.5
(Mdn. =65) 4-0 to 4-5.5
(Mdn.
=
51)
nitely laid out plan which was described in an earlier paragraph. A statistical study of the findings shows no consistent difference in the results obtained which can be attributed to a change in examiners, either for the peg boards or the Kuhlman Binet which was given at the same time. The results on the peg boards may be summarized briefly in the following statement: When both tests were
made
by
the
same
examiner,
the median
change
in total
? See Mental Tests by Frank N. Freeman, Houghton Mifflin page 280.
score
Co., 1926,
Table VIII
Percentage of each half
year mental age
Under 2-0 2-0 to 2-5.5 Mdn. Mdn. =
Under 2-0 Mdn. = 193)
193
=
122
group1 equalling
2-6 to 2-11.5 Mdn. =
3-0 to 3-5.5 Mdn.
108
or
exceeding the median of each successive mental 3-6 to
3-11.5 Mdn. = 68
4-0 to 4-5.5 Mdn. =
64
4-6 to 4-11.5 Mdn. = 53
5-0 to 5-5.5 Mdn. = 50
age group.
5-6 and over
Mdn. =
44
43
50.0
9.3
7.0
98.2
50.0
27.8
3.7
100.0
67.3
50.0
25.0
1.9
1.9
1.9
100.0
92.1
89.5
50.0
31.6
23.7
7.8
7.8
2.7
38
(Mdn. =68)
100.0
100.0
100.0
96.4
50.0
35.7
14.3
14.3
7.1
28
4-0 to 4-5.5 Mdn. = 64)
100.0
100.0
91.7
80.5
58.3
50.0
22.2
19.4
2.8
36
100.0
100.0
100.0
100.0
80.0
76.0
50.0
32.0
20.0
25
100.0
100.0
100.0
100.0
83.3
83.3
55.6
50.0
27.7
18
100.0
100.0
100.0
100.0
100.0
100.0
100.0
83.3
50.0
2-0 to 2-5.5
(Mdn.
=
122)
54
2-6 to 2-11.5
(Mdn.
=
108)
3-0 to 3-5.5 Mdn. =88)
52
-6 to 3-11.5
4-6 to 4-11.5
(Mdn. =53) 5-0 to 5-5.5
(Mdn. =50) 5-6 and
over
(Mdn. =44) 1
Tiy
given
on
t\ve
same
day.
WALLIN PEG BOARDS
213
amounted to a gain of 8.4 points; when there was a change of examiners, the corresponding change was 9.4 points. The difference of one point is well within the limits of chance, and its unreliability is further demonstrated by the fact that the direction of difference is not the same at all ages, and is always small in amount. Nevertheless, since only two examiners were involved, the findings obviously do not warrant wide generalization. They merely serve to show that under uniform testing conditions, reasonably competent examiners who follow a common procedure can secure essentially similar results. Sex differences. Figure 1 shows the gain in total score from age to age for sexes separately on each of the two examinations. The
curves
for the second examination have been moved forward
to allow for the difference in age.
that
differences
are very small, but that the boys accelerated than the girls. Figure are, on the average, slightly true when the groups are divided on the ba2 shows that this is also
It is
seen
sex
more
sis of mental age instead of chronological age. On the Binet tests given to the same children, the sex differences were also small, but the general tendency was in the opposite direction, i.e., toward a
slight superiority
of the
findings are in general agreereported for elementary school girls, as a rule, show some superiority over the Binet type, while boys are more likely to excel girls.
Both
ment with those which have been
children, where boys in tests of
the the
in form board tests. Socio-economic
differences.
that the children
It
was
stated in
selected to constitute
an
earlier para-
graph representative sampling of the population of Minneapolis. The basis of selection was paternal occupation. On the Kuhlman tests given to the same children on the same days, a very marked difference was found to exist between the average performance of children belonging to the different occupational classes. On the peg board tests, no such differences are apparent. When the average performance of the children belonging to the upper half of the occupational distribution is compared with that of the lower half, it is found that on the first test the children of the lower occupational groups do slightly were
a
better than those of the upper groups; on the second test the upper groups excel, but in neither case is the difference great enough to be reliable nor does it follow a consistent direction at the different age levels.
Even when the
performance
of the children of
day
la-
THE PSYCHOLOGICAL CLINIC
214
compared with that of the children whose fathers belong to the professional classes, no reliable differences were found. On the Kuhlman-Binet, the superiority of the professional group amounted to approximately one and one-fourth standard deviations borers is
of the total distribution of scores for the 300 cases. This difference in the social distribution of the abilities measured by the two methods must be regarded as highly significant. Since
exactly
the
same
children
were
used
as
subjects
for both
tests, and since the measurements were taken on the same day, the results cannot be explained on the basis of a difference in sampling. While the
permit
reliability
more
of the peg boards is not
than tentative classification of
quate for differentiation between
dren, same
groups.
sufficiently high to individuals, it is adeFor two-year-old chil-
it appears to be quite as reliable as the Kuhlman-Binet at the age level. This makes it possible to compare the standing of
contrasted social groups in respect to the two types of ability by of equally reliable measures applied to the same subjects. In average standing on the Kuhlman-Binet, the two-year-old chilmeans
belong to the professional classes exceed the by approximately one and one half standof the total distribution of ratings for the year peg boards, the children of day laborers exceed the professional classes, but the difference is less than
dren whose fathers children of
day
ard deviations
laborers
group. On the children of the one tenth of a standard deviation of the total distribution of at that age.
scores
These data tend to confirm the conclusion which was drawn from the table of correlations, that entirely apart from the question the two tests do not measure precisely It functions. would seem that the Kuhlman measures mental similar not measured certain functions by the peg boards, the distribution the of which among general population is skewed toward the upper of
comparative reliability,
while the peg boards appear to measure certain functions not measured by the Kuhlman which are more evenly distributed throughout the population. Our data do not permit us to judge the nature of these functions, though it might be noted in passing that the results of certain tests for mechanical ability re-
occupational levels;
cently
standardized at the University of Minnesota show a similar relationship to social status. It may be that the peg board
lack of
performance is in some degree related to potential scholastic achievement. ible, but it has not been verified.
Binet to
mechanical This
aptitude, the hypothesis is plaus-
WALLIN PEG BOARDS
215
Summary 1. The Wallin peg boards, Series A-D inclusive, were given to three groups of 100 children each, whose ages, taken to the nearest birthday, were two, three, and four years, respectively. These chila representative sampling of the Minneapolis on the basis of a comparison of the distribution of paternal occupations with that reported for the city as a whole in the 1920 census. Exactly 50 boys and 50 girls were in-
dren
were
population
selected to constitute of
cluded in each age group. 2. Since no alternative form of the test is available, all children were re-examined after an average interval of six weeks. The reliability of the test was determined by correlating the scores At age two the reliability was found to be .794; at age three, .688; at age four, .583. 3. The average correlation with the Kuhlman-Binet given on earned
on
the two occasions.
same day was .507 for single year age groups. There is little difference in the correlations obtained at the various ages. 4. The amount of overlapping of the scores increases approxi-
the
mately
in
5. A score, if form.
proportion to age. change in examiners the testing procedure
does not and
6. Sex differences in the test general tend to favor the boys. 7. Children
from
different
necessarily affect the test examining conditions are uni-
performance
are
small,
but in
socio-economic levels
equally well on this test, although they show their performance on the Kuhlman-Binet. for this discrepancy are discussed.
do about marked differences in
Possible
explanations