3. THE DISTRIBUTION OF FAILURES

That the failures are widely distributed by semesters, by ages, and for both boys and girls, is shown in [Table I].

TABLE I

THE DISTRIBUTION OF FAILURES ACCORDING TO THE AGE
AND THE SEMESTER OF THEIR OCCURRENCE[A]

SEMES-		AGES										UNDISTRIB-
TERS	12	13	14	15	16	17	18	19	20	21	22	UTED	TOTALS

1B.	0	20	321	650	575	167	34	16	2	. .	. .	10	1795
G.	1	19	356	813	611	236	67	3	0	. .	. .	13	2119
3914
2B.	. .	2	95	423	534	256	57	27	4	. .	. .	5	1403
G.	. .	6	99	483	589	280	91	5	0	. .	. .	7	1560
2963
3B.	. .	0	17	267	443	363	96	22	5	0	. .	2	1215
G.	. .	1	28	318	548	317	99	15	0	2	. .	1	1329
2544
4B.	. .	. .	5	101	437	403	169	32	7	2	. .	5	1161
G.	. .	. .	4	102	475	425	160	39	6	2	. .	6	1219
2380
5B.	. .	. .	1	19	195	377	214	61	13	3	. .	6	889
G.	. .	. .	0	15	277	438	212	60	15	0	. .	3	1020
1909
6B.	. .	. .	. .	4	70	322	326	99	33	3	. .	6	863
G.	. .	. .	. .	9	117	407	349	78	33	4	. .	3	1000
1863
7B.	. .	. .	1	0	17	155	227	106	16	4	1	4	531
G.	. .	. .	0	2	14	200	299	127	38	0	0	3	683
1214
8B.	. .	. .	. .	. .	0	42	173	109	49	2	. .	5	380
G.	. .	. .	. .	. .	2	58	244	140	49	10	. .	3	506
886
9B.	. .	. .	. .	. .	. .	0	31	32	18	1	. .	. .	82
G.	. .	. .	. .	. .	. .	4	39	67	31	5	. .	. .	146
														228
10B.	. .	. .	. .	. .	. .	. .	1	16	9	3	0	. .	29
G.	. .	. .	. .	. .	. .	. .	3	13	10	3	1	. .	30
59
Summary
B.	0	22	440	1464	2271	2085	1328	520	156	18	1	43	8348
G.	1	26	487	1742	2633	2365	1563	547	182	26	1	39	9612
17,960

[A] The expression of the above facts in terms of percentages for each age group was found to be difficult, since failures and not pupils are designated. But the total failures for each age group are expressed (on [p. 36]) as percentages of the entire number of subjects taken by these pupils for the semesters in which they failed. Such percentages increase as the ages rise. A similar statement of the percentages of failure by semesters will be found on [p. 41].

[Table I] reads: the boys had 20 failures and the girls had 19 failures in the first semester and at the age of thirteen; in the second semester, at the age of thirteen, the boys had 2 failures and the girls 6. For each semester, the first line represents boys, the second line girls. There is a total of 17,960 failures listed in this table. In addition to this number there are 1,947 uncompleted grades for the failing non-graduates. The semesters were frequently completed by such pupils but the records were left incomplete. Their previous records and their prospects of further partial or complete failure seem to justify an estimate of 55 per cent (1,070) of these uncompleted grades as either tentative or actual but unrecorded failures. Therefore we virtually have 1,070 other failures belonging to these pupils which are not included in [Table I]. Accordingly, since the number can only be estimated, the fact that they are not incorporated in that table suggests that the information which it discloses is something less than a full statement of the school failures for these pupils. In the distribution of the totals for ages, the mode appears plainly at 16, but with an evident skewness toward the upper ages. The failures for the years 16, 17, and 18, when added together, form 68.1 per cent of the total failures. If those for 15 years are also included, the result is 86 per cent of the total. Of the total failures, 65.7 per cent are found in the first two years (11,801 out of the total of 17,960). But the really striking fact is that 34.3 per cent of the failures occur after the end of the first two years, after 52.2 per cent of the pupils are gone, and with other hundreds leaving in each succeeding semester before even the end of the eighth. In [Table II] we have similar facts for the pupils who graduate.

TABLE II

THE DISTRIBUTION OF FAILURES ACCORDING TO THE AGES
AND THE SEMESTERS OF THEIR OCCURRENCE FOR THE GRADUATING PUPILS

SEMES- TERS	AGES
SEMES- TERS	13	14	15	16	17	18	19	20	21	22	TOTALS

1B.	0	66	84	60	5	2	3	. .	. .	. .	220
G.	4	68	123	68	23	4	0	. .	. .	. .	290
												510
2B.	0	30	95	96	41	3	2	. .	. .	. .	267
G.	1	25	119	121	30	11	2	. .	. .	. .	309
												576
3B.	0	6	108	98	71	22	1	3	. .	. .	309
G.	1	15	101	158	78	20	5	0	. .	. .	378
												687
4B.	. .	4	54	157	107	36	6	0	. .	. .	364
G.	. .	1	45	186	143	51	7	2	. .	. .	435
												799
5B.	. .	1	10	82	142	82	17	4	3	. .	341
G.	. .	0	9	145	187	88	22	9	0	. .	460
												801
6B.	. .	. .	4	34	158	139	32	9	2	. .	378
G.	. .	. .	2	70	235	178	40	13	1	. .	539
												917
7 B.	. .	1	0	10	115	140	65	4	4	1	340
G.	. .	0	2	7	130	187	69	19	0	0	414
												754
8 B.	. .	. .	. .	0	31	122	65	25	2	. .	245
G.	. .	. .	. .	2	45	150	95	37	2	. .	331
												576
9 B.	. .	. .	. .	. .	0	24	23	13	1	. .	61
G.	. .	. .	. .	. .	4	32	40	24	0	. .	100
												161
10 B.	. .	. .	. .	. .	. .	1	11	5	3	. .	20
G.	. .	. .	. .	. .	. .	3	12	6	1	. .	22
												42
Summary B.	. .	108	355	537	670	571	225	63	15	1	2545
G.	6	109	401	757	875	724	292	110	4	0	3278
												5823

In the facts which are involved and in the manner of reading them, this table is similar to [Table I]. The mode of the distribution of totals for the ages is at 17 in this table. Further reference will be made to both Tables [I] and [II] in later chapters of this study. (See pages [36], [37], [41], [42]).

A further analysis of the failures is here made in reference to the number of pupils and the number of failures each.

TABLE III

A DISTRIBUTION OF FAILING PUPILS ACCORDING TO THE NUMBER
OF FAILURES PER PUPIL, IN EACH SEMESTER

NO. OF FAILURES	SEMESTERS										TOTALS
NO. OF FAILURES	1	2	3	4	5	6	7	8	9	10	TOTALS

1 B.	459	430	375	352	271	221	157	113	22	11	2411
G.	561	535	428	421	328	261	167	123	35	9	2868

					32.5%							5279

2 B.	271	242	211	206	149	144	79	68	19	4	1393
G.	271	253	238	204	177	142	127	84	17	6	1519

					34.9%							2912

3 B.	144	106	81	73	59	60	45	27	6	2	603
G.	207	103	81	75	75	83	52	38	20	3	737

					35%							1340

4 B.	83	39	33	30	27	32	10	10	1	1	266
G.	95	50	38	35	27	39	19	19	3	0	325

					31.8%							591

5 B.	6	3	5	8	7	8	7	2	0	. .	46
G.	3	2	6	5	1	10	6	5	1	. .	39

					55.3%							85

6 B.	. .	. .	3	3	0	1	1	. .	. .	. .	8
G.	. .	. .	. .	. .	. .	. .	. .	. .	. .	. .	. .

					25%							8

Tot. B.	963	820	708	672	513	466	299	220	48	18	4727
G.	1137	943	791	740	608	535	371	269	76	18	5488
					10,215

[Table III] tells us that 459 boys and 561 girls have one failure each in the first semester of their high school work; 271 boys and the same number of girls have two failures in the first semester, and so on, for the ten semesters and for as many as six failures per pupil. The failures represented by these pupils give a total of 17,960. A distribution of the total failures per pupil, and the facts relative thereto, will be considered in [Chapter IV] of this study.

The above distribution of [Table III] is repeated here in [Table IV], so far as it relates to the failing graduates only.

TABLE IV

A DISTRIBUTION OF THE FAILING PUPILS WHO GRADUATE, ACCORDING TO
THE NUMBER OF FAILURES PER PUPIL IN EACH SEMESTER

NO. OF FAILURES	SEMESTERS										TOTALS
NO. OF FAILURES	1	2	3	4	5	6	7	8	9	10	TOTALS

1 B.	110	131	137	150	162	139	120	118	19	11	1097
G.	136	142	181	200	197	180	121	89	20	3	1269

					50%							2366

2 B.	34	49	61	69	61	75	47	28	15	3	442
G.	49	64	63	86	81	73	81	62	10	5	574

					53.2%							1016

3 B.	10	10	14	18	12	17	27	17	4	1	130
G.	16	9	14	13	27	43	30	20	16	3	191

					67.6%							321

4 B.	3	2	2	3	4	8	6	5	0	. .	33
G.	2	3	6	6	5	16	9	12	3	. .	62

					71.6%							95

5 B.	. .	. .	0	2	1	0	3	0	. .	. .	6
G.	. .	. .	1	0	0	4	1	2	. .	. .	8

					78.6%							14

6 B.	. .	. .	. .	. .	. .	1	1	. .	. .	. .	2
G.	. .	. .	. .	. .	0	0	. .	. .	. .	0

					100%							2

Tot. B.	157	192	214	237	240	240	204	163	48	15	1710
G.	203	218	265	305	310	316	242	185	49	11	2104
					3814

This table reads similarly to [Table III]. There is not the element of continuous dropping out to be considered, as in [Table III], until after the sixth semester is passed, for no pupils graduate in less than three years. The failures represented in this table number 5,823. This same distribution will be the subject of further comment later on. It discloses some facts that Table [III] tends to conceal, for instance, that the greater number of graduating pupils who have 2, 3, 4, 5, and 6 failures in a semester are found after the end of the second year.

4. DISTRIBUTION OF THE FAILURES IN REFERENCE
TO THE SUBJECTS IN WHICH THEY OCCUR

The following tabulation of failures will show how they were shared by both boys and girls in each of the school subjects which provided the failures here listed.

NUMBER OF FAILURES DISTRIBUTED BY SCHOOL SUBJECTS

Total	Math.	Eng.	Latin	Ger.	Fr.	Hist.	Sci.	Bus. Subj's.	Span. or Greek
B. 8348	2015	1555	1523	917	473	571	850	424	20
G. 9612	2300	1424	1833	812	588	1036	1013	593	13
Per Cent of Total	24.1	16.5	18.7	9.6	5.9	8.9	10.3	5.6	.2

The abbreviated headings above will be self-explanatory by reference to [section 3] of [Chapter I]. The first line of numbers gives the failures for the boys, the second line for the girls. Mathematics has 24.1 per cent of all the failures for all the pupils. Latin claims 18.7 per cent and English 16.5 per cent of all the failures. These three subjects make a total of nearly 60 per cent of the failures for the nine subject groups appearing here. But still this is only a partial statement of the facts as they are, since the total enrollment by subjects is an independent matter and far from being equally divided among all the subjects concerned. The subject enrollment may sometimes be relatively high and the percentage of failure for that subject correspondingly lower than for a subject with the same number of failures but a smaller enrollment. This fact becomes quite apparent from the following percentages taken in comparison with the ones just preceding:

PERCENTAGES ENROLLED IN EACH SUBJECT OF THE SUM TOTAL
OF THE SUBJECT ENROLLMENTS FOR ALL PUPILS AND ALL SEMESTERS

Math.	Eng.	Latin	Ger.	Fr.	Hist.	Sci.	Bus. Subj's.	Span. or Greek
17.3	24.0	11.9	8.5	6.8	10.2	12.5	8.3	.5

We note that the percentages for mathematics and English, which represent their portions of the grand total of subject enrollments, are virtually the reverse of the percentages which designate the amount of total failures produced by the same two subjects. That means that the percentage of the total failures produced by mathematics is really greater than was at first apparent, while the percentages of failures for English is not so great relatively as the statement of the total failures above would alone indicate. In a similar manner, we note that Latin has 18.7 per cent of all the failures, but its portion of the total enrollment for all subjects is only 11.9 per cent. If the failures in this subject were in proportion to the enrollment, its percentage of the failures would be reduced by 6.8 per cent. On the other hand, if the failures for English were in the same proportion to the total as is its subject enrollment, it would claim 7.5 per cent more of all the failures. In the same sense, French, history, science, and the business subjects have a smaller proportion of all the failures than of all the subject enrollments.

The comparison of failures by subjects may be continued still further by computing the percentage of failures in each subject as based on the number enrolled in that subject. Such percentages are here presented for each subject.

PERCENTAGE OF THE NUMBER TAKING THE SUBJECT
WHO FAIL IN THAT SUBJECT

Latin	Math.	Ger.	Fr.	Hist.	Sci.	Eng.	Bus. Subj's.	Span. or Greek
18.7	16.0	13.5	11.6	10.4	9.8	8.2	8.0	4.1

It becomes evident at once that the largest percentage of failures, based on the pupils taking the subject, is in Latin, although we have already found that mathematics has the greatest percentage of all the failures recorded ([p. 19]). But here mathematics follows Latin, with German coming next in order as ranked by its high percentage of failure for those enrolled in the subject. History has the median percentage for the failures as listed for the nine subjects above.

The failures as reported by subjects for other schools and other pupils will provide a comparison which may indicate something of the relative standing of this group of schools in reference to failures. The failures are presented below for thirteen high schools in New Jersey, involving 24,895 grades, as reported by D.C. Bliss[7] in 1917. As the schools were reported singly, the median percentage of failure for each subject is used here for our purpose. But Mr. Bliss' figures are computed from the promotion sheets for June, 1915, and include none of those who had dropped out. In this sense they are not comparable to the percentages of failure as presented in this study. Yet with the one exception of Latin these median percentages are higher. The percentages as presented below for St. Paul[8a] are in each case based on the total number taking the subject for a single semester, and include about 4,000 pupils, in all the classes, in the four high schools of the city.[B]

[B] It is a significant fact, and one worthy of note here, that the report for St. Paul is apparently the only one of the surveys which also states the number taking each subject, as well as the percentages of failure. Percentages alone do not tell the whole story, and they do not promote the further utilization of the facts to discover other relationships.

The facts presented for St. Louis[9] are for one school only, with 2,089 pupils, as recorded for the first half of the year 1915-16. All foreign languages as reported for this school are grouped together. History is the only subject that has a percentage of failure lower than that of the corresponding subjects for our eight schools. The figures for both St. Paul and St. Louis are based on the grades for all classes in school, but for only a single semester. One cannot avoid feeling that a statement of facts for so limited a period may or may not be dependable and representative for all periods. The percentages for Paterson[10] are reported for about 4,000 pupils, in all classes, for two successive semesters, and are based on the number examined. For Denver,[11] the records are reported for 4,120 pupils, and cover a two-year period. The percentages for Butte[12] are based on the records for 3,110 pupils, for one school semester. The figures reported by Rounds and Kingsbury[13] are for only two subjects, but for forty-six widely separated high schools, whose enrollment for these two subjects was 57,680.

PERCENTAGES OF FAILURE BY SUBJECTS—QUOTED FOR OTHER SCHOOLS

	Math.	Latin	Ger.	Fren.	Eng.	Hist.	Sci.	Bus. Subj's.
13 N.J. H.S.'s.	20.0	18.0	16.0	. .	14.0	11.0	. .	11.5
St. Paul	21.8	13.6	14.3	17.0	10.0	10.9	7.3	11.7
St. Louis	18.0	[——	16	——]	13.0	7.0	19.0	. .
Paterson	23.1	21.6	23.4	. .	12.2	13.9	18.3	8.5
Denver	24.0	21.0	12.0	. .	11.7	11.0	17.0	11.0
Butte	18.6	25.0	24.0	32.6	5.4	7.0	13.0	8.4
R and K	24.7	. .	. .	. .	18.5	. .	. .	. .
Our 8 H.S.'s	16.0	18.7	13.5	11.6	8.2	10.4	9.8	8.0

In some schools the reports were not available for all subjects. It is not at all probable, so far as information could be obtained, that the failures of the drop-out pupils for any of the schools were included in the percentages as reported above, or that the percentages are based on the total number in the given subjects, with the exception of one school. Moreover, it is certain for at least some of the schools that neither the failures of the drop-outs nor the pupils who were in the class for less than a whole semester were considered in the percentages above. So far, however, as these comparisons may be justified, the suggestion made in [Chapter I] that the schools included in this study are doubtless a superior group with respect to failures appears to be strengthened by the comparisons made above.

It becomes more apparent, as we attempt to offer a statement of failures as taken from the various reports, that they are not truly comparable. The bases of such percentages are not at all uniform. The basis used most frequently is the number enrolled at the end of the period rather than the total number enrolled for any class, for which the school has had to provide, and which should most reasonably form the basis of the percentage of failure. Furthermore, the failures for pupils who drop out are not usually counted. Yet, in most of the reports, the situation is not clearly indicated for either of the facts referred to. Still more difficult is the task of securing a general statement of failures by subjects, since the percentages are most frequently reported separately for each class, in each subject, and for different buildings, but with the number of pupils stated for neither the failures nor the enrollment. The St. Paul report[8b] is an exception in this regard.

To present the full situation it is indeed necessary to know the failures for particular teachers, subjects, and buildings, but it is also frequently necessary to be able to make a comparison of results for different systems. Consequently, in order to use the varied reports for the attempted comparison above, the plan was pursued of averaging the percentages as stated for the different classes, semesters, and years of a subject, in each school separately, and then selecting the median school thus determined as the one best representing the city or the system. This method was employed to modify the reports, and to secure the percentages as stated above for Denver, Paterson, and Butte. Any plan of averaging the percentages for the four years of English, or similarly for any other subject, may actually tend to misstate the facts, when the percentages or the numbers represented are not very nearly equal. But, in an incidental way, the difficulty serves to emphasize the inadequacy and the incomparability in the reporting of failures as found in the various studies, as well as to warn us of the hopelessness of reaching any conclusions apart from a knowledge of the procedure employed in securing the data.

The basis is also provided for some interesting comparisons by isolating from the general distribution of failures by school subjects ([p. 19]) the same facts for the failing graduates. That gives the following distribution.

THE FAILURES BY SCHOOL SUBJECTS FOR GRADUATES ONLY

Total	Math.	Eng.	Latin	Ger.	Fr.	Hist.	Sci.	Bus. Subj's.	Span. or Greek
5803 B.	660	403	521	241	191	180	251	91	7
6334 G.	782	347	673	257	240	410	394	162	12
Per Cent of Totals	24.8	12.9	20.5	8.5	7.4	10.1	11.	4.3	.3
SIMILAR PERCENTAGES FOR THE NON-GRADUATES

As above	23.6	18.3	17.7	10.1	5.3	8.4	10.	6.3	.1

It is a noteworthy fact that the percentages of failure (based on the total failures for the graduates) run higher in mathematics, Latin, history, French, and science for the graduates than for the whole composite number ([page 19]). The non-graduates have a correspondingly lower percentage of failure in these subjects, as is indicated above. The school influences in respect to the failures of the non-graduates differ from those of the graduates chiefly in the fact that the failures of the former tend to occur to a greater extent in the earlier years of these subjects, since so many of the non-graduates are in the school for only those earlier years; while the failures of the graduates range more widely and have a tendency to predominate in the upper years of the subject, as will be further emphasized in the later pages of this report (see also [Table IV]).