IB 935 
 18 H3 
 espy 1 
 
 IRST SERIES NO. 62 
 
 JUNE 1, 1922 
 
 UNIVERSITY OF IOWA 
 STUDIES 
 
 STUDIES IN CHILD WELFARE 
 
 VOLUME II 
 
 NUMBER 2 
 
 DIFFERENTIAL FECUNDITY IN IOWA 
 
 BY 
 
 HORNELL NORRIS HaRT 
 
 PUBLISHED BY THE UNIVERSITY, IOWA CITY 
 
 Issued semi-monthly throughout the year. Entered at the post office at Iowa City, 
 Iowa, as second class matter. Acceptance for mailing at special rates of postage 
 provided for in section 1103, Act of October 3, 1917, authorized on July 3, 1918 
 
 Monogrip* 
 
UNIVERSITY OF IOWA STUDIES 
 IN CHILD WELFARE 
 
 Professor Bird T. Baldwin, Ph. D., Editor 
 
 FROM THE IOWA CHILD WELFARE RESEARCH STATION 
 
 VOLUME II NUMBER 2 
 
 DIFFERENTIAL FECUNDITY IN IOWA 
 
 A STUDY IN PARTIAL CORRELATION 
 
 BY 
 
 HORNELL NORRIS HART, Ph. D. 
 
 PUBLISHED EY THE UNIVERSITY, IOWA CITY 
 
V 3 
 
CONTEXTS 
 
 Foreword 5 
 
 I. The Problem Stated 7 
 
 II. Technique 7 
 
 1. Derivation of Indices 7 
 
 Table 1. Indices of Fecundity and of Certain More or 
 Less Correlated Social Conditions in Iowa Counties in 
 1915 9 
 
 2. Calculation of Zero Order Correlations 13 
 
 3. Calculation of Partial Correlations 13 
 
 4. Fecundity Regressions 14 
 
 III. Interpretation of Fecundity Correlations and Regressions. .15 
 
 5. Rural-urban Distribution and Fecundity 15 
 
 Table 2. AD Correlations 15 
 
 6. Fecundity and the Age Index G 17 
 
 Table 3. Distribution of Iowa Counties According to 
 Fecundity (A) and Age Index (G) 17 
 
 Table 4. AG Correlations 17 
 
 Table 5. Distribution of States According to Average 
 Age of Women 21-44 (B) and Age Distribution Index 
 (G) 19 
 
 Chart 1. Age Distribution of Iowa Women in 1850 and 
 1910 20 
 
 7. Iowa's Declining Fecundity 23 
 
 8. Home Ownership and Fecundity (r 4M ) 23 
 
 Table 6. AM Correlations 24 
 
 9. Educational Status and Fecundity 25 
 
 Table 7. AJ Correlations 25 
 
 High School Attendance 26 
 
 Table 8. AQ Correlations 26 
 
 Past Education Reported by Adults 26 
 
 Table 9. AL Correlations 27 
 
 10. Religious Indices 28 
 
 Table 10. AN Correlations 28 
 
 Proportion Catholic 28 
 
 Proportion Protestant 28 
 
 Table 11. AO Correlations 29 
 
 Table 12. AP Correlations 29 
 
 11. Fecundity of the Foreign-Born 29 
 
 Table 13. Values of G for various nativity Groups ... .30 
 
 3 
 
4 CONTENTS 
 
 12. Fecundity and Proportion Married 31 
 
 Table 14. AI Correlations 31 
 
 13. General Interpretation of Fecundity Correlations 31 
 
 14. Curvilinear Regressions 33 
 
 IV. Conclusions 34 
 
 15. Summary 35 
 
 16. Recommendations 35 
 
 V. References Cited 37 
 
FOREWORD 
 
 The fundamental aim of the Child Welfare Research Station is 
 to help the State to conserve and to develop every child to the 
 maximum ability consistent with its native, endowment and special 
 aptitudes. In order to do this it is necessary that a series of search- 
 ing investigations be made from time to time into the various 
 aspects of child life in Iowa. 
 
 The problem of child welfare in Iowa is intimately bound up 
 with the number and quality of children born into our Iowa homes. 
 These two factors condition in a large measure the practical 
 methods of child rearing. 
 
 This second study by Dr. Hart throws definite light on the gen- 
 eral questions : What types of individuals in our State are be- 
 coming parents? Are more children born, proportionately, in the 
 city than in the country? Are the larger families found among 
 the native born, among the home owners, among those of average 
 or superior school training? The answers to these questions have 
 direct and significant bearings on the future citizenship of our 
 State. 
 
 Bird T. Baldwin. 
 
 Office of the Director, 
 
 Iowa Child Welfare Research Station, 
 
 University of Iowa. 
 
DIFFERENTIAL FECUNDITY IN IOWA 
 
 I. THE PROBLEM STATED 
 
 The problem of the declining birth rate is particularly acute in 
 Iowa. As is pointed out in the writer's study of Selective Migra- 
 tion (9, p. 122), the number of children per 1,000 women of child- 
 bearing age had decreased in 1915 to less than 40 per cent of 
 what it was in 1840. While this decline in fecundity* is more 
 spectacular than differential fecundity at the present date, the 
 latter is of far greater consequence from a sociological point of 
 view. 
 
 The rural districts in Iowa have been much more fecund than 
 the cities, and the foreign-born have had more children than the 
 native-born, but no searching study of differential fecundity in 
 Iowa has been made. (9, p. 123). The present inquiry seeks in- 
 formation primarily as to what types of persons in the Iowa 
 population are reproducing most rapidly, and as to the extent of 
 the differences in their fecundity. 
 
 II. TECHNIQUE 
 
 It is proposed to attack the problem by means of linear partial 
 regression equations predicting in terms of other correlated indices 
 fedundity rates in the 99 counties of Iowa. 
 
 1. Derivation of Indices. The latest, and by far the most com- 
 plete, statistics relating to the characteristics of the populations of 
 the counties of Iowa are contaiued in the 1915 State Census. (13). 
 On the basis of these data indices have been derived with a view to 
 testing, as far as possible, the current hypothesis relative to dif- 
 ferential fecundity, such as that rural populations are more fecund 
 than urban, foreign-born more fecund than native-born, the poor 
 and ignorant more fecund than the well-to-do and the well educated, 
 and Catholics more fecund than Protestants. The following indices 
 were derived, and were designated by the letters indicated. 
 
 A is the fecundity index, consisting in the number of children 
 under five years of age per 1,000 women 21 to 44 years of age 
 (13, pp. 418ff.). The age span employed differs from that used by 
 Wilcox (37) because of the method of age classification employed 
 by the state census. This fecundity index in more desirable for 
 
 ♦By the term "fecundity" as used in this study is meant not the physiological power of 
 procreation but the characteristic of actually producing offspring. 
 
 7 
 
8 IOWA STUDIES IN CHILD WELFARE 
 
 the study in hand than birth-rates would have been, even had ac- 
 curate birth-rates been available, because the number of children 
 under five years of age already has had deducted from it most of 
 the deaths of early infancy, and hence this index represents more 
 nearly net fecundity than would birth rates. Being based on the 
 number of women of child-bearing age, this index in far more 
 useful than any rate per 1,000 of population, for the variations in 
 the proportion of women of child-bearing age in the population 
 introduce serious errors into calculations where crude birth-rates 
 are employed. 
 
 D is the percentage of the population living in cities and towns 
 (State Census 13, pp. 606-7). This is not the percentage of urban 
 population as defined by the United States Census, for the Iowa 
 data include all incorporated places as urban, while the Federal 
 Census excludes places under 2,500. 
 
 6 is an index of the age distribution of women. It consists in 
 the number of women 19 to 20 years of age per 1,000 women 45 
 years of age and over. This index, as illustrated in Chart I on 
 page 20, is -15*^-1 (13, pp. 418-33). The reason for choosing these 
 age groups is that the age groupings reported by the State Census 
 are as follows : zero to four years, five to nine, 10 to 17, 18 to 20, 
 21 to 44, and 45 and over. The two groups selected are those 
 lying next above and below the age of child-bearing (21 to 44). 
 
 I is the number married per 1,000 females 21 to 44 (13, pp. 
 491ff.). 
 
 J is the number per 1,000 males 10 to 17 years of age attending 
 school nine months or over in 1914 (13, pp. 418ff., 512ff.). 
 
 L is the number, per 1,000 persons over school age, who were 
 reported as having attended school eight years or more (13, pp. 
 523ff.). 
 
 M is the number owning homes per 1,000 persons 21 to 44 years 
 of age (13, pp. 418ff., 618ff.). 
 
 N is the number of persons reported as members of Catholic 
 churches per 1,000 of population (13, pp. 418ff., 705ff.). 
 
 O is the number of non-Catholic church members reported per 
 1,000 of population (13, pp. 418ff., 705ff.). 
 
 P is the number of foreign-born persons per 1,000 of population 
 (13, p. xlix). 
 
 Q is the number of persons attending high school in 1914 per 
 1,000 persons 10 to 17 years of age in 1915 (13, pp. 418ff., 518ff.). 
 
 These indices, for the 99 counties of Iowa, are shown in Table 1. 
 
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12 
 
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 cd in in cd t- 
 
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 3 
 
 
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 ■31 
 
 Cm On 
 
 Pocahontas 
 
 Polk 
 
 Pottawattamie 
 
 Poweshiek 
 
 Ringgold 
 
 Sac 
 
 Scott 
 
 Shelby 
 
 Sioux 
 
 Story 
 
 Tama 
 Taylor 
 Union 
 Van Buren 
 Wapello 
 
 Warren 
 
 Washington 
 
 Wayne 
 
 Webster 
 
 Winnebago 
 
 Winneshiek 
 Woodbury 
 Worth 
 Wright 
 
DIFFERENTIAL FECUNDITY IN IOWA 13 
 
 2. Calculation of Zero Order Correlations. All of the linear 
 correlations in this study were calculated without grouping of items. 
 The method first used was to assume as the average for each 
 index, thus avoiding the use of negative deviations and products. 
 In practice, however, this method proved to require great labor 
 because of the large size of the squares and products involved. In 
 order to utilize the zero order correlations for the calculation of 
 partials of higher orders great accuracy is essential. This has been 
 insured by calculating all of the zero order correlations twice, 
 using two different assumed averages, and requiring that tb.3 results 
 check within .00005. All correlations were carried out to five 
 places. It was recognized, of course, that the probable errors of 
 the coefficients, due to random sampling, were so large as to make 
 five place r's ridiculous for the purposes of interpretation; this 
 degree of accuracy is required merely because of algebraic reasons. 
 Correlations are given in this text to only two places. 
 
 3. Calculation of Partial Correlations. To carry the calcula- 
 tion of seventh order partial correlations to the degree of accuracy 
 required would prove an immense task if all the values of \/l-v" 
 had to be calculated by ordinary methods. To obviate this diffi- 
 culty the author has devised a compact chart from which the 
 required values may be read off directly within an error of .00005. 
 Seventh order partials were derived by these methods with maxi- 
 mum errors of .0001. Most of the calculations were performed, 
 under the writer's direction, by Mr. James Sarkisian and Mr. 
 Arnold Wilbur. 
 
 Professor H. L. Rietz, who has been kind enough to read and 
 criticize this paper, raises the question whether the formula for 
 the probable errors of partial correlations is valid when used with 
 only 99 cases. It is obvious, of course, that if the number of items 
 considered were only as large as the number of variables involved 
 (e. g. two items for zero order correlations, three items for first 
 order, four for second order, and so on ) perfect positive or negative 
 correlations would always result, no matter what the true relation- 
 ship between the variables. In such a case, obviously, the usual 
 formula for probable error would be highly erroneous. This same 
 type of error will be present in diminished degree unless a con- 
 siderable number of items is involved. In defense of the use of 
 partials in this study it may be urged, first that the seventh order 
 partials show no signs of approaching ±1.0; that the partials 
 
14 IOWA STUDIES IN CHILD WELFARE 
 
 appear to act consistently when new variables are added, as will 
 be seen from a study of the tables which follow in the text; that 
 the final conclusions are based chiefly on correlations of less than 
 the fourth order ; and that the results as a whole are self-consistent, 
 and consistent with the results of other studies. 
 
 In passing it may be well to refer to the methods developed by 
 Truman Kelly for calculating partials (15, 16). His original tables 
 are, as he himself recognizes (15, pp. 5 and 6), not carried out for 
 enough places to be of use in calculating partials beyond the first 
 or second order. His more recent chart does not permit of suf- 
 ficient accuracy for the purposes of the present study. His method 
 of successixe approximation was not attempted. Where it is 
 important to be able to tudy the effect upon the original correlation 
 of assigning one factor after another it is a great advantage to 
 have the series worked out step by step. It is not necessary, of 
 course, to calculate the partial correlations of all of the possible 
 combinations of the indices. 
 
 The first series of partials calculated involved only the indices 
 A, D, I, J, L, M, N, 0, and P. When the results were analyzed, 
 certain conditions appeared to suggest the presence of an uncon- 
 trolled age variable, and index G was developed. The failure to 
 establish any important correlations between A and J when D 
 was constant seemed so surprising that index Q was developed. A 
 study of the data made it seem unnecessary to go farther than the 
 fourth order with partials involving G and Q. 
 
 ■i. Fecundity Regressions. For several purposes regression 
 coefficients are more useful than correlation coefficients. The 
 regressions recpiired have been calculated by the methods outlined 
 by Yule (41, p. 240). In calculating the probable errors of re- 
 gression coefficients the writer has expressed the formula given 
 by Yule (41, p. 253), in the more convenient form: 
 
 ,,„, .6745 b„ K Vl-r-, „ K 
 
 P.E.b 12 .K=— = -***- -^ 
 Vn r.„ t . 
 
 Where K represents any collection of secondary subscripts other 
 than 1 or 2. 
 
 The advantage of this formula over the one given by Yule is that 
 the latter involves the quantity <r 2 . K , which must ordinarily be 
 
DIFFERENTIAL FECUNDITY IN IOWA 
 
 15 
 
 specially calculated for this use, whereas the substitute formula 
 involves only quantities which have already been calculated. 
 
 In interpreting correlations in this study, interest centers about 
 differences, not between county and county, but between various 
 types of people. Counties are used simply as convenient units for 
 investigation. It happens that certain very significant factors, 
 such as home ownership, vary but little from county to county. 
 Correlations of fecundity with these indices, by counties, therefore 
 are low. At the well-recognized risk of misinterpreting trends 
 beyond the range of observation, the predictions of fecundity in 
 counties where these indices would reach their theoretical extremes 
 have been calculated, with a view to predicting for comparison the 
 fecundity of a population wholly of a given type with the fecundity 
 of a population wholly of the opposite type. 
 
 III. INTERPRETATION OF FECUNDITY CORRELATIONS 
 AND REGRESSIONS 
 
 5. Rural-Urban Distribution and Fecundity. The highest cor- 
 relations which occur in the entire series are those between fecundity 
 and percentage of urban population. The partial correlations 
 derived between A and D with various other factors assigned, are 
 shown in Table 2. 
 
 
 
 TABLE 2 
 
 
 
 
 
 AD Correlations 
 
 
 
 r AD 
 
 — .74±.03 
 
 r ADILNOP — .73±.03 
 
 r AD.LMNOP 
 
 — .77±.03 
 
 r ADG 
 
 — .84±.02 
 
 r AD.ILMNOP -72 — .03 
 
 r AD.LMNOP 
 
 — .77±.03 
 
 r AD GI 
 
 — .79±.03 
 
 r AD IMNOP — .71±.03 
 
 r AD.LMOP 
 
 — .77±.03 
 
 r AD.GIM 
 
 — .73±.03 
 
 Tad.ipq -.70±.03 
 
 r AD.LNOP 
 
 — .81±.02 
 
 r AD.GIP 
 
 — .79±.03 
 
 i-ad.j -.62±.04 
 
 r AD.MN 
 
 — .77±.03 
 
 r AD.GIQ 
 
 -~.77±.03 
 
 1-adjlmn- -67±.04 
 
 r AD.MNOP 
 
 — .77±.03 
 
 r AD GM 
 
 — .76±.03 
 
 r — Gl-*- 04 
 'ad.jlmno ■"- ■"* 
 
 r AD.MOP 
 
 — .77±.03 
 
 r AD 1 
 
 — .67±.04 
 
 'adjlmnop ■"'' — "^ 
 
 r AD.NOP 
 
 — .81±.02 
 
 r AD.IJLMNO 
 
 —.60 ±.04 
 
 r. U) , LMNP -.67+.04 
 
 r AD.O 
 
 — .76±.03 
 
 F AD IJLMNOP 
 
 — .62±.04 
 
 r AD.JLMOP — .69±.04 
 
 r AD.OP 
 
 — .80±.02 
 
 r AD IJLMNP 
 
 — .59±.04 
 
 r — fi9-*- 04 
 
 r AD JLNOP •°° u * 
 
 r AD.P 
 
 — .80±.02 
 
 r AD.IJLMOP 
 
 — .64±.04 
 
 Tad.jmnop --68±.04 
 
 r AD.PQ 
 
 — .77±.03 
 
 r AD IJLNOP 
 
 — .60±.04 
 
 Tad.lmn -.78±.03 
 
 r AD.Q 
 
 — .72±.03 
 
 r ADG = — .84±.02*; i. e. the correlation between fecundity and 
 
 ♦In interpreting this and other probable errors in this table and the following tables, 
 the fact that only 99 items are involved should be borne in mind. The probable errors 
 for the higher order partials are not very reliable. 
 
16 IOWA STUDIES IN CHILD WELFARE 
 
 percentage of urban population when the age index is assigned is 
 as likely as not to be between — -.82 and — .86, while the chances are 
 1,000 to 1 that the true correlation lies between — .76 and —.92. 
 
 This correlation is due in part to the negative correlation between 
 percentage of population living in cities and percentage of women 
 married : r D i= — -48 ± .05. 
 
 Certain of the other variables account to a small extent for t'x 
 correlation, but the lowest value reached is — .59 ±.05, so that a 
 clearly established negative correlation exists between fecundity 
 and the percentage of urban population, even when the other indies 
 listed are assigned. 
 
 In general, three types of explanation must be considered for a 
 correlation r X v. First, the presence or size of X may result from 
 the presence or size of Y; second, the presence or size of Y may 
 result from the presence or size of X; third, both X and Y may 
 result from some common cause or group of causes. In the ease of 
 r AD , it might theoretically be true that families move to the country, 
 or stay in the country, because they have babies, that families in the 
 country tend to have more babies than families in the city because 
 rural conditions are more favorable to fecundity than urban con- 
 ditions are, or that some common element, such as contentment with 
 a vegetative, domestic life, favors both remaining in the country 
 and rearing children. Of these three possibilities, the first seems 
 least likely, and the second most likely, though final de- 
 cision must wait upon further inquiry. 
 
 In any case it seems safe to conclude that women in cities have 
 fewer children than women in rural districts in Iowa, apart from 
 differences correlated with age distribution, nativity, religion, edu- 
 cation and home ownership. The amount of this difference in 
 fecundity is suggested by the regression equation for predicting A 
 from D, which is : 
 
 A' D =612±5— (4.4±.3)(L— 46±1)±37.* 
 
 If the percentage of urban population were zero, the fecundity 
 rate, according to this equation, would be 814±51 ; if the percentage 
 of urban population were 100, the fecundity would be 374±41. 
 The difference between these two rates, or — 440 ±65, represents 
 the maximum change in A which would correspond with a change 
 
 ♦In this and subsequent regression equations the probable errors of the averages and 
 regression coefficients are stated after the respective numbers, with a ± sign. The last 
 number in each regression equation is the probable error of estimate. 
 
DIFFERENTIAL FECUNDITY IN IOWA 
 
 17 
 
 of the whole possible range of D. As a check on this reasoning it 
 should be noted that the fecundity rates as estimated from data 
 dealt with in the writer's study of migration (9, p. 124) are 416 
 for purely rural territory, and 755 for urban territory. The dif- 
 ference between these two latter rates is — 339, instead of — 440 
 as estimated by regressions. The difference between the two esti- 
 mates (which is less than twice the probable error of the regression 
 prediction) is doubtless due, as will be shown later, to the existence 
 of a curvilinear instead of rectilinear relationship between fecundity 
 and rural-urban distribution. 
 
 6. Fecundity and the Age Index G. The relationship between 
 A and G is shown in Table 3. 
 
 TABLE 3 
 
 Distribution of Iowa Counties According to Fecundity (A) and 
 
 Age Index (G) 
 
 Derived from Table 1. 
 
 
 Fecundity 
 
 Age 
 Index 
 
 400- 
 449 
 
 450- 
 499 
 
 
 
 2 
 
 2 
 
 
 
 1 
 
 
 
 5 
 
 500- 
 549 
 
 
 
 4 
 
 3 
 
 2 
 
 
 
 
 
 9 
 
 550- 
 599 
 
 1 
 
 9 
 
 9 
 
 2 
 
 
 
 
 21 
 
 600- 
 649 
 
 
 
 4 
 13 
 
 8 
 
 3 
 
 
 28 
 
 650- 
 699 
 
 
 
 3 
 
 7 
 5 
 2 
 
 
 17 
 
 700- 
 749 
 
 
 
 
 
 2 
 
 7 
 
 2 
 
 1 
 12 
 
 750- 
 799 
 
 
 
 
 
 
 
 
 
 1 
 
 1 
 
 2 
 
 800- 
 845 
 
 
 
 
 
 
 
 
 
 
 
 1 
 1 
 
 Total 
 
 1 
 23 
 38 
 26 
 
 9 
 
 3 
 99 
 
 150-199 
 200-249 
 250-299 
 300-349 
 350-309 
 400-499 
 Total 
 
 
 1 
 2 
 1 
 
 
 4 
 
 Apart from the AD correlations the highest correlation with A 
 found in the study is r A a.Di=+.75±.03. The AG correlations are 
 shown in Table 4. 
 
 
 TABLE 4 
 
 
 
 AG Correlations 
 
 
 r AG 
 
 +53±.05 
 
 r A G.Dip +62±.04 
 
 r AG L 
 
 + 51±.05 
 
 r AG.D 
 
 +.73±.03 
 
 r A G.DiQ +-73±.03 
 
 r AC.M 
 
 +.69±.04 
 
 r AG.DI 
 
 +.75±.03 
 
 ,-,,.,,„, +68±.04 
 
 r AG.N 
 
 +.54±.05 
 
 r AG DIJ 
 
 +75±.06 
 
 +61±.04 
 
 1- AG.O 
 
 +.54±.05 
 
 r AG.DIL 
 
 -f.72±.03 
 
 i'ac ip +.51 ±.05 
 
 r AG P 
 
 +.55±.05 
 
 r AG.DIM 
 
 +.69 ±.04 
 
 r AGJ +66±.06 
 
 r \c; Q 
 
 +.47±.05 
 
 The lowest value in this series is r AG .Q=+.47±.05. It seems safe 
 to conclude, therefore, that the age distribution of the women, 
 when other factors noted are assigned, has a high, clearly estab- 
 
18 IOWA STUDIES IN CHILD WELFARE 
 
 lished, positive correlation with fecundity. The interpretation of 
 correlations involving G is not, however, as simple as it at first 
 seems. The correlation r A c=+-53±.05 might mean that the type 
 of age distribution where G is high results in a high net birth rate 
 per 1,000 women of child-bearing age, or it might mean that a high 
 fecundity tends to produce the type of age distribution where G 
 is large, or it might mean that certain factors favorable to the type 
 of age distribution where G is high are also favorable to high 
 fecundity. 
 
 With regard to the first of these possibilities, it has been recog- 
 nized by other investigators that fecundity varies sharply with 
 age. Whipple (36) quotes data from Budapest as indicating that 
 fecundity for females reaches its maximum between the 18th and 
 19th years, falling steadily to the age 50, when it practically ceases. 
 Perhaps the best American data on births in relation to the age 
 of the mothers are contained in the studies of Infant Mortality 
 made in certain cities by the United States Children's Bureau (32). 
 The United States Census gives the numbers of married women by 
 broad age groups in these cities in 1910 (29). From these data 
 rough estimates have been made as to the relative birth rates at 
 various ages, for Brockton, Mass., Johnstown, Pa., Manchester, 
 N. H., and Waterbury, Conn. Young (38) also presents data for 
 New Hampshire. Better data are available for other countries. 
 Webb's Dictionary of Statistics gives the mean annual number of 
 births or accouchements per 1,000 wives by five year age groups, 
 for Denmark, Sweden, Finland, Austria, France, New South Wales, 
 Victoria and Western Australia, for various dates from 1871 to 
 1903 (34). 
 
 All of the above data support the conclusions noted by Whipple, 
 that fecundity declines steadily from the teens until it disappears 
 at about the age of 50. The present study has been concerned with 
 the number of children, not per 1,000 married women, but per 
 1,000 women of child-bearing age. Careful computations indicate 
 that the above difference in birth rates would probably result in 
 a difference in the fecundity indices between the women 25-29 
 years of age and the group 40-44 of 350 to 500 points, depending 
 upon which birth rates are assumed. Hence it will be seen that 
 if the women 21 to 44 years of age were concentrated at the upper 
 end of this age period their fecundity would be expected, other 
 things being normal, to be approximately 240 points lower than 
 
DIFFERENTIAL FECUNDITY IN IOWA 
 
 19 
 
 the average, whereas if the women were concentrated at the ages of 
 25 to 29 the expected fecundity would be about 160 above the 
 average. 
 
 In order more accurately to judge the significance of differences 
 in average age as reflected in the G index, the value of G for each 
 state in the United States in 1910 was calculated from United States 
 Census data, (29, pp. 361ff., 548ff.) and for the 32 states in which 
 G fell within the range of that variable in Iowa counties in 1915 
 (which was 179 to 422) the weighted average age of the women 
 21 to 44 was calculated, by five year periods. This average will 
 hereafter be referred to as B. 
 
 The relationship between average age (B) and the age distribu- 
 tion index (G) is shown in Table 5. 
 
 TABLE 5 
 Distribution According to Average Age (B) and Age Distribu- 
 tion (G) of Women 21-44 of the 32 States in which 
 G lies between 179 AND 422 
 
 Age Index 
 (G) 
 
 Average Ag 
 
 e (B) 
 
 31.00- 
 31.24 
 
 31.25- 
 31.49 
 
 31.50- 
 31.74 
 
 31.75- 
 31.99 
 
 32.00- 
 32.24 
 
 32.25- | 
 32.49 | Total 
 
 179-199 
 200-249 
 250-299 
 300-349 
 350-399 
 400-422 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 3 
 3 
 
 
 
 
 2 
 1 
 
 3 " 
 
 
 
 
 3 
 6 
 1 
 
 10 
 
 
 
 7 
 2 
 
 
 9 
 
 3 
 
 
 
 
 
 
 3 
 
 3 
 
 
 
 10 
 
 10 
 
 5 
 
 4 
 
 32 
 
 Total 
 
 1 
 
 6 
 
 The correlation r B G = — .985±.009. The regression equation 
 of B on G is : 
 
 B = 31.80 ±.01— (.0046 ±.0004) (G— 325±3) ±.07* 
 
 With such an exceedingly close correlation it seems safe to assume 
 that the average ages of women 21 to 44 in Iowa counties may be 
 derived from G in terms of the above regression formula. The 
 range in average age of women 21-44 years of age in Iowa Counties, 
 as thus calculated from the actual range of G in Iowa counties is 
 only 1.12 ±.07 years, which would have a negligible effect upon 
 fecundity. Hence the correlations r A o do not indicate that the birth 
 rate is an effect of the age distribution. 
 
 The second possible interpretation of the AG correlations is that 
 
 •See footnote on page 16 
 
20 
 
 IOWA STUDIES IN CHILD WELFARE 
 
 a high birth rate tends to produce the type of age distribution 
 having a high value for G. It will be recalled that 
 
 Gx = 1,000 
 
 number of women 18-20 1,000 e 
 number of women 45-)- f 
 
 where x represents the year for which G is calculated. (See 
 Chart 1). In a community with no immigration or emigration, 
 the women 18 to 20 at date x would have been 1 to 3 years old at 
 a date 17 years previous to x, and the women 45 and over at date 
 
 130 
 
 CHART 1 
 
 Age Distribution of Iowa Women 
 
 per 1000 women 21 to 44 years of age 
 
 1850 and 1910 
 
 Distributions are based on United States Census 
 
 data (29) and (30). The age classification 
 
 shown by the vertical lines is, however, 
 
 that of the State Census (13). 
 
 O 5 10 18 81 45 90 
 
 x would have been 28 to 75, or thereabouts. If, in the x — 17, the 
 fecundity of women 21 to 44 yere high, G would tend to be high 
 in the year x, unless other factors, such as peculiarities in death 
 rates, interferred. In other words, G x tends to be correlated with 
 A ( . 17) , and if a correlation exists between A, X - 17 , and A x , 
 a correlation may be expected between Gx and A x . Extensive 
 migration might, however, tend to break up this correlation. 
 
 Other factors besides the birth rate in preceding years, however, 
 affect G. A high death rate among women over 20 years of age 
 would tend to produce a high value of G. Now a high death rate 
 of women over 20 might result from a high birth rate. It could 
 
DIFFERENTIAL FECUNDITY IN IOWA 21 
 
 scarcely be a cause of a high birth rate. Under the first alternative 
 deaths due to diseases caused by pregnancy and confinement come 
 to mind. The Children's Bureau has shown that such deaths of 
 mothers number approximately seven per 1,000 live births. A dif- 
 ference of several hundred in the fecundity rate, therefore, could 
 account for only a very small variation in G as a result of deaths 
 due directly to child birth. Bearing and caring for excessive 
 numbers of children might, however, lower the resistance of 
 mothers and hence promote high death rates from other causes. 
 Probably of greater importance is the well known correlation be- 
 tween poverty and high death rates from tuberculosis and other 
 causes. 
 
 On this last point data collected by Dublin for the Metropolitan 
 Life Insurance Company are significant (5). He compares death 
 rates among Metropolitan Industrial policy holders, and persons of 
 the same ages, sexes and races in the United States Registration 
 Area. As to differences between these policy holders and the 
 general population he indicates that the industrial policy holders 
 represent a group definitely below the average of the country in 
 economic status, but typical of the industrial population rather 
 than typical of the poverty-stricken. Women in this group 20 
 to 74 years of age show mortality rates, by five year age groups, 
 from six to 29 per cent higher than women in the registration area 
 of the United States. (5, p. 23). In a stationary population the 
 mortality rates shown would result in an age distribution, among 
 the women of industrial policy holding families, represented by 
 6=151. For the Registration Area the corresponding index is 
 G=142. This difference would, of course, be much more marked 
 if the comparison were made between wage earners and persons 
 of the professional and capitalistic classes than when made between 
 wage earners and the general population, and would be still higher 
 if a comparison of distinctly rich and poor classes were made. 
 
 For a more extreme comparison between the adult female age 
 distributions of poor and average well-to-do groups, the contrast 
 between the colored and white populations may be cited. Dublin 
 shows that colored females of the Metropolitan families had, in the 
 age group 20 to 24, a mortality 238.5 per cent as large as that of 
 white women of the same age, and that while this difference de- 
 creased steadily in each successive age group, its lowest point was 
 
22 IOWA STUDIES IN CHILD WELFARE 
 
 105.1 per cent of the white rate (5, p. 18). The effect of this 
 difference in adult female death rates upon the G index may be 
 determined directly from the United States Census. The following 
 values of G and A are derived from the 1910 census (29, pp. 307, 
 310, 356, 542). 
 
 G A 
 
 All white females in the United States, 1910 323 644 
 
 All negro females in the United States, 1910 533 718 
 
 All negro females in South Atlantic Division, 1910 549 815 
 
 All Indian females in the United States, 1910 373 1092 
 
 The total negro population of the United States is not affected 
 appreciably by immigration and emigration, as I have shown else- 
 where, (9, pp. 29-30), though the white population is. The high 
 value of the G index for negroes is not due to extremely high net 
 fecundity, judging by the 1910 and 1900 rates. The negro fecun- 
 dity rate in 1900 was 822, according to the United States Census 
 (29, p. 319). 
 
 Clearly, the difference between the values of G for white and 
 colored women must be the result chiefly of the difference in death 
 rates, and while some may urge that this is the effect of racial dif- 
 ferences, a more plausible hypothesis is that it results from the 
 notoriously unfavorable economic sanitary and social conditions 
 under which negroes live. 
 
 The above evidence shows that a high value of G tends to indicate 
 unfavorable economic and industrial conditions, resulting in a high 
 adult female death rate and hence that the high AG correlations 
 may be explained in considerable part in terms of correlation 
 between poverty and a high birth rate. This conclusion is in 
 harmony with Heron's findings (10). 
 
 As another possibility it should be noted that the migration rate 
 (as is indicated by analysis of data contained in (9) is probably 
 much higher at the ages 18 to 20 than at the ages 45 and over: 
 hence a community gaining in its female population through 
 migration would tend to have a high G index, while one losing 
 through migration would have a low G. 
 
 To summarize the discussion of the AG correlations, it seems 
 clear that the relationship between fecundity and the age distribu- 
 tion of the women is due, not to differences in the average age of 
 women 21 to 44, but to other factors. Correlation between present 
 
DIFFERENTIAL FECUNDITY IN IOWA 23 
 
 fecundity and fecundity 17 years or so ago is undoubtedly an 
 element. Higher fecundity of migrant than non-migrant stock 
 may be partly responsible, though my study of interstate migration 
 failed to reveal this characteristic among recent migrants (9, p. 50). 
 The most probable explanation appears to lie in the high death rate 
 among women of the poorer classes; the AG correlation is prob- 
 ably a correlation between poverty and fecundity. Analysis of the 
 M and P indices later in this study supports this conclusion. 
 
 7. Iowa's Declining Fecundity. For the analysis of causes 
 related to the decline in fecundity in Iowa only the G and D indices 
 can be readily ascertained for several decades ago. The linear 
 regression equation for predicting fecundity of Iowa Counties in 
 1915 on the basis of G and D is 
 
 A' DG =612±5— (3.33±.15)(D— 16 ±1) -f(.99±.06) 
 (G— 286±3)±37* 
 In 1850 in Iowa, G=790, and D was approximately nine (30). 
 Substituting these values, the fecundity prediction for Iowa in 
 1850 would be 1238±49. The actual fecundity was 1,231. For 
 the United States in 1850, G=527; D=20 (approximately) ; and 
 the predicted fecundity is 938 ±41. The actual fecundity was 927. 
 For whites in the United States in 1910, G=323; D=62.5; and 
 the predicted fecundity is 594±39. The actual fecundity is 644. 
 
 The first two of these predictions are within fractions of the 
 respective probable errors of estimate; the last exceeds the error 
 of estimate by less than one-third. The exact significance of this 
 rather surprising accuracy is, however, difficult to determine. In 
 1850 the age distribution in Iowa was greatly affected by migration, 
 and in those days migrants were more fertile than non-migrants. 
 The average age of the women 21 to 44 was less than a year lower 
 in 1850 than in 1910. 
 
 14. Home-Ownership and Fecundity. All of the AM correla- 
 tions where D is assigned, except one, are negative, and all of the 
 AM correlations where D is not assigned, except one, are positive. 
 The exceptions are within their probable errors of zero. The fact 
 that r A M=+.21±.06 indicates that there is a tendency for counties 
 with large percentages of home owners among the middle-aged 
 to have high fecundities, but the fact that i' A md= — .37 ±.07 indi- 
 cates that, taking urban and rural conditions separately, home 
 
 ♦See footnote on page 16. 
 
24 
 
 IOWA STUDIES IN CHILD WELFARE 
 
 ownership and fecundity are correlated negatively. The inversion 
 is due to the fact that more rural than urban persons own homes 
 (r DM =— .56 ±.05). 
 
 
 TABLE 6 
 
 
 
 AM Correlations 
 
 
 r AM 
 
 +.21±.06 
 
 r AM.DINOP - ^° 0' r AM.JLNOP 
 
 +.11±.07 
 
 r AM.D 
 
 — .37±.06 
 
 rAM.D IP -20±.06 
 
 r AML 
 
 +.26±.06 
 
 r AM.DG 
 
 +.04±.07 
 
 r AM.DJNOP •*■« 07 
 
 r AM.LNOP 
 
 +.41±.06 
 
 r AM.DGI 
 
 — .03±.07 
 
 r AM.DOP .13±.07 
 
 r AM.N 
 
 -j-.21±.06 
 
 r AM.DGIQ 
 
 -.14±.07 
 
 r AM.DNOP .12 — .07 
 
 r AM NOP 
 
 +.40 ±.06 
 
 r AM.DGQ 
 
 — .06±.07 
 
 fAM.G +.55±.05 
 
 r AM.O 
 
 -f.26±.06 
 
 r AM.DI 
 
 —.42 ±.06 
 
 r AM .G. +-47±.06 
 
 r A.M.OP 
 
 +.39 ±.06 
 
 r AM.DIJLNOP 
 
 — .17±.07 
 
 Tam.gi +.42±.06 
 
 r AM.P 
 
 +.37±.06 
 
 r AM.DUNOP 
 
 -.19±.07 
 
 'abli +03±.07 
 r A M.uLNop --02+.07 
 
 r AM.Q 
 
 +.22±.06 
 
 A clearer idea of the significance of these correlations may be 
 gained from the regression equation 
 
 A' DM =612±5— (5.4±.3)(D— 46±1) — (1.0±.2)(M— 143±2)±34. 
 In an urban area, where half of the adults 21 to 44 years of age 
 owned homes, the predicted fecundity would, according to this 
 equation, be — 37 ±72, (or appromimately zero) as compared with 
 463 ±45 in an urban area where no such persons owned homes. In 
 a rural territory where half of the persons 21 to 44 owned homes 
 the predicted fecundity would be 503 ±71 as compared with 
 1003 ±45 in a wholly tenant rural community. Even allowing for 
 the possibility of curvilinear regression, these predictions indicate 
 that, when rural-urban distribution is constant, variations in home 
 ownership are associated inversely with very striking differences 
 in fecundity. 
 
 It seems probable that the relationship between home ownership 
 and fecundity in the city differs from the corresponding relation- 
 ship in rural areas. In the country, of course, home ownership is 
 practically identical with farm ownership. Linear partial regres- 
 sions do not indicate such differences. In order to isolate this 
 problem the correlation between A and M was studied in the 31 
 counties having less than 40 per cent urban population. In these 
 counties r A M= — .67 ±.07, and 
 
 A' M =664±11— (1.7±.2) (M— 157±4) ±30. 
 When M is 500, A' M is 81±77; when M is zero, A' M is 931±45. 
 Although the very low prediction for areas where all homes are 
 
DIFFERENTIAL FECUNDITY IN IOWA 
 
 25 
 
 owned is doubtless an exaggeration, due to curvilinear regression, 
 there can be little doubt that tenant farmers are reproducing much 
 more rapidly than farm owners. If the counties with 40 or more 
 per cent urban are considered, r A M=+-33±.07, but this correlation 
 is probably due to the DM correlation already pointed out. If the 
 11 counties with 70 or more per cent urban are considered 
 r AM =-{-.13±.20, which, of course, is practically zero. It seems 
 evident, then, that home ownership has little or no relationship 
 with fecundity in cities, but a very high relationship with fecundity 
 in rural districts. Probably home ownership, apart from the farm 
 ownership which it implies in rural districts, is not a good index 
 of economic status, since many rather poor workmen in cities buy 
 homes on the installment plan, while many very wealthy people 
 rent their dwellings. The high fecundity of tenant farmers as 
 compared with farm owners has been shown by Kolb (18) and 
 Dunlop (8). 
 
 The relationship between delayed marriage and the low fecundity 
 of farm owners is not evident. Married persons are more likely 
 to own homes than are unmarried persons; ri M =+.39±.06. 
 
 9. Educational Status and Fecundity. Three of the indices 
 used in this study relate to educational status, namely, J, 0, and 
 L. The J index is the number of males 10 to 18 years of age 
 attending school nine months or more, per 1,000 males of these 
 ages. The AJ correlations which have been worked out are shown 
 in Table 7. 
 
 
 
 TABLE 7 
 
 
 
 
 
 AJ Correlations 
 
 
 
 r AJ 
 
 — .52±.05 
 
 r AJ.DMOP 
 
 — .02±.07 
 
 r AJ.LNOP 
 
 — .59±.04 
 
 r AJ.D 
 
 +.07±.07 
 
 r AJ.DNOP 
 
 +.03±.07 
 
 r AJ.M 
 
 — .50±.05 
 
 r AJ.DG 
 
 — .08±.07 
 
 r AJ.DOP 
 
 -f-.Ol— .07 
 
 r AJ.MN 
 
 — .51±.05 
 
 r AJ.DGI 
 
 — .08±.07 
 
 r AJ.G 
 
 — .66±.04 
 
 r AJ.MNOP 
 
 — .48±.05 
 
 r AJ.DGlQ 
 
 — .00±.07 
 
 r AJ.GI 
 
 — .59±.04 
 
 r AJ.MOP 
 
 — .48±.05 
 
 r AJ.DI 
 
 -j-.07±.07 
 
 F AJ.I 
 
 — .42±.06 
 
 r AJ.N 
 
 — .53±.05 
 
 r AJ.DILMNOP 
 
 — .06±.07 
 
 r AJ.ILMNOP 
 
 -.47±.05 
 
 r A J. NOP 
 
 — .59±.05 
 
 r AJ.DIMNOP 
 
 — .07±.07 
 
 r AJ.ILNOP 
 
 — .52±.05 
 
 r AJ.O 
 
 — .54±.05 
 
 r AJ.DINOP 
 
 — .01±.07 
 
 r AJ.IMNOP 
 
 — .47±.05 
 
 r AJ.OP 
 
 — .59±.04 
 
 r AJ.DIOP 
 
 +.01±.07 
 
 r AJ.LMN 
 
 — .54±.05 
 
 r AJ.P 
 
 -58±.05 
 
 r AJ.DLMN 
 
 — .09±.07 
 
 r AJ.LMNOP 
 
 — .48±.05 
 
 r AJ.Q 
 
 — .43±.05 
 
 T AJ.DMNOP 
 
 — .01±.07 
 
 r AJ.LMOP 
 
 — .49±.05 
 
 
 
26 
 
 IOWA STUDIES IN CHILD WELFARE 
 
 For all partials of r A j where D is assigned, the correlations are 
 practically 0. For all partials of r A j where D is not assigned, the 
 values are — .42 ±.06 or higher. It is clear, therefore, that while 
 counties with large percentages of male school attendance for nine 
 months or more per year have decidedly fewer children than 
 counties with lower standards, the difference is wholly due to the 
 fact that urban counties also have the lowest fecundity. 
 
 High School Attendance. Q represents the high school attend- 
 ance per 1,000 persons 10 to 17 years of age. The AQ correlations 
 are shown in Table 10. 
 
 *AQ 
 
 r AQ.D 
 
 r AQ.DG 
 
 r AQ.DGI 
 
 r AQ.DI 
 
 r AQDIL 
 
 -.42±.06 
 .33±.06 
 -.17±.07 
 -.21±.06 
 -.35±.06 
 -.26+.06 
 
 TABLE 8 
 AQ Correlations 
 — .23±.06 
 
 — .21±.06 
 +.32±.06 
 -.35±.06 
 -.45+.07 
 
 'AQ.DIP 
 r AQ.DP 
 
 l AQ.G 
 
 -.28±.06 
 — .39±.06 
 — .43±.06 
 -.42±.06 
 -.41±.06 
 — .38±.06 
 
 Q, although also an educational index, is not influenced by the 
 length of the official school year and the efficiency of attendance 
 officers, which form considerable elements in J. Q shows rather 
 the extent of the desire and ability of parents to secure for their 
 children a high school education. One of the factors conditioning 
 the sending of children through high school is certainly the 
 economic status of the parents. Since therefore both G and Q 
 are to some extent economic indices it is to be expected that partial 
 correlations of either of them with A when the other is assigned 
 will be lower than when the other is not assigned. This proves to 
 be the case. In general, it may be concluded that counties where 
 high school attendance is low have high fecundity, while where 
 high school attendance is high fecundity is low, and that this is 
 true when D is assigned. 
 
 Past Education Reported By Adults. L represents the number 
 per 1,000 persons over school age who were reported as having 
 had eight years or more of schooling. The AL correlations are 
 given in Table 9. 
 
 In considering the significance of the above correlations, it must 
 be remembered that the L index is built upon the unverified verbal 
 statement of a member of the family to a census enumerator, and 
 
DIFFERENTIAL FECUNDITY IN IOWA 
 
 27 
 
 is doubtless subject to systematic errors due to misstatements and 
 exaggerations. It is the opinion of the writer, however, that these 
 errors do not vitiate the results; the correlations are consistent 
 enough to be accepted at least tentatively. 
 
 
 
 TABLE 9 
 
 
 
 
 
 AL Correlations 
 
 
 
 r AL 
 
 — .18±.07 
 
 r AL.DIP 
 
 — .23±.06 
 
 r AL.JMNOP 
 
 — .17±.07 
 
 r AL.D 
 
 — .34±.06 
 
 r AL.DIQ 
 
 — .28±.06 
 
 r AL.M 
 
 — .24±.06 
 
 r ALDG 
 
 — .12±.07 
 
 r AL.DJMNOP 
 
 — .22±.06 
 
 r AL.MN 
 
 — .24±.06 
 
 r AL.DGI 
 
 — .16±.07 
 
 r AL.DJNOP 
 
 — .22±.06 
 
 r AL.MNOP 
 
 — .16±.07 
 
 r AL.DGIQ 
 
 — .11±.07 
 
 r AL.DMNOP 
 
 — .22±.06 
 
 r AL.MOP 
 
 — .15±.07 
 
 r AL.DGQ 
 
 — .08±.07 
 
 r AL.DNOP 
 
 —.22 ±.06 
 
 r AL.N 
 
 — .18±.07 
 
 r ALDI 
 
 — .37±.06 
 
 r AL.DOP 
 
 — .21+.06 
 
 r AL.NOP 
 
 — .12±.07 
 
 r AL.DIJMNOP 
 
 — .21±.06 
 
 r AL.DQ 
 
 — .25±.06 
 
 F AL.O 
 
 — .17±.07 
 
 r AL.DIJNOP 
 
 — .22±.06 
 
 r AL.G 
 
 +.01±.07 
 
 r AL.OP 
 
 -.11±.07 
 
 r AL.DIMNOP 
 
 — .21±.06 
 
 r Ai.I 
 
 -.27±.06 
 
 r AL.P 
 
 -.11±.07 
 
 r AL.DINOP 
 
 — .22±.06 
 
 r AL.IJMNOP 
 
 -.16±.07 
 
 r AL.Q 
 
 — .05±.07 
 
 r AL DIOP 
 
 — .24±.06 
 
 r AL IMNOP 
 
 -.15±.07 
 
 
 
 Although J and Q, the indices of present educational status, are 
 positively correlated with D, indicating that city children are 
 getting better educational advantages than rural, r DL is practically 
 zero. This means that rural adults report themselves as having 
 had eight years or more of schooling just about as often per 
 1,000 as city adults. With L, as in the case of other indices, the 
 assignment of G- greatly reduces the correlation with fecundity. 
 G and L are negatively correlated (r GL = — .36 ±.06). Both G and 
 L appear to be associated with low economic status, one positively, 
 the other negatively. 
 
 The significance of the educational indices Q and L is clearer 
 when studied in regression form. The regression coefficients of 
 fecundity on Q and L respectively when D and I are constant are 
 b A Q.DiL= — .20 ±.05 and b A LDi<i= — .32 ±.08. The error of estimate 
 in predicting A from D, I, L, and Q is ±31. These coefficients 
 mean that, assuming D and I as constant, and neglecting the pos- 
 sibility of curvilinear correlation, a community in which all chil- 
 dren of high school age attended high school, and in which all 
 persons over school age reported having had eight years or more 
 of schooling, fecundity rates would tend to be 420±90 lower than 
 in a community where no children attended high school and no 
 persons over school age reported having had eight, years or more 
 
28 
 
 IOWA STUDIES IN CHILD WELFARE 
 
 of schooling. Of the 420 difference, 320 would be assignable to 
 factors correlated with L, and only 100 to factors correlated with 
 Q, in spite of the fact that the partial correlations r AQD i and 
 ital di are very nearly equal. The data thus indicate clearly that 
 educational status, especially past schooling, is very definitely in- 
 versely correlated with fecundity. 
 
 
 TABLE 10 
 
 
 
 AN Correlations 
 
 
 r AN 
 
 +.01 ±.07 
 
 r AN.DIOP 
 
 +.15±.07 
 
 r AN.JLMOP 
 
 — .03±.07 
 
 r AN.D 
 
 -j-.08±.07 
 
 r AN.DlP 
 
 +.25+.06 
 
 r AN.LMOP 
 
 — .11±.07 
 
 r AN.DG 
 
 — .09±.07 
 
 r AN.DJLMOP 
 
 — .10±.07 
 
 r AN.M 
 
 -f.03±.07 
 
 r AN.DGI 
 
 -f.l3±.07 
 
 r AN.DMOP 
 
 — .08±.07 
 
 r AN.MOP 
 
 — .09±.07 
 
 r AN.DGIQ 
 
 +.11±.07 
 
 r AN.DOP 
 
 — .09±.07 
 
 r AN.O 
 
 — 03±.07 
 
 r AN DGQ 
 
 — .12±.07 
 
 r AN.G 
 
 — .11±.07 
 
 r AN.OP 
 
 — .05±.07 
 
 r AN.DI 
 
 +.24±.06 
 
 r AN.I 
 
 +.34±.06 
 
 r AN.P 
 
 — .03±.07 
 
 r AN.DIJLMNOP~T - l° 07 
 
 r AN.IJLMOP 
 
 +.29±.06 
 
 r AN.Q 
 
 — .06±.07 
 
 10. Religious Indices. Proportion Catholic. The N index, it 
 will be remembered, is the percentage of the population reported 
 as being members of Catholic churches. The AN correlations 
 become appreciably greater than their probable errors only when 
 the proportion married is assigned. The correlation r A N.i=+.34 
 ±.06 is high enough to be definitely significant. The original 
 reports as to church membership may, of course, be in error The 
 statistics of churches appear to have been somewhat care essly 
 handled by the state census office. The total number of church 
 members for Winneshiek County is reported as 177,185, although 
 the sum of the memberships of the various denominations as given 
 for that country is 10,235. Similarly the total given for Wood- 
 bury County is 617,087 instead of 20,087, and for Wright County 
 is 167,304 instead of 5,954. (13, pp. 733-4). It is possible that 
 other errors occurred and were not discovered; if this were true 
 it would probably tend to lower the correlations. Prom the data 
 as they stand with the above corrections, however, it seems probable 
 that the tendency of married Catholics to have more children than 
 married non-Catholics is offset by the fact that Catholics in Iowa 
 tend to marry later than non-Catholics (ri N = — .51±.05). 
 
 Proportion Protestant. The O index — of non-Catholic church 
 members per 1,000 of population — is open to the same doubts as 
 to accuracy as is the N index. The highest AO correlation is 
 
DIFFERENTIAL FECUNDITY IN IOWA 
 
 29 
 
 
 TABLE 11 
 
 
 
 AO Correlations 
 
 
 r A o 
 
 — .09±.07 
 
 r AO.DIJLMNP .13±.07 
 
 r AO.JLMNP 
 
 -.12±.07 
 
 r AO.D 
 
 — .26±.06 
 
 Tao.dip -.2B±.06 
 
 r AO.LMN 
 
 — .20±.06 
 
 r AO.DG 
 
 +03±.07 
 
 r AO.DJLMNP -14±.07 
 
 r AO.M 
 
 — .18±.07 
 
 r AO.DGI 
 
 -.06±.07 
 
 Tao.dlmn -16±.07 
 
 r AO.MN 
 
 — .18±.07 
 
 r AO.DGIQ 
 
 — .00±.07 
 
 r A0G +.14+.07 
 
 r AO.N 
 
 — .09±.07 
 
 r AO.DGQ 
 
 +09±.O7 
 
 r AO.i -.26+06 
 
 r AO.P 
 
 — .03±.07 
 
 r AO.DI 
 
 — .33±.06 
 
 r AO.IJLMNP —.11 — -07 
 r AOJLMN .14±.07 
 
 r AO.Q 
 
 +.05±.07 
 
 rAODi= — .33 ±.06. This negative correlation disappears when G 
 is kept constant, and is quite low when M is constant, indicating 
 that the tendency for Protestants to have fewer children than non- 
 Protestants is due to incidental economic and educational rather 
 than religious differences. 
 
 
 TABLE 12 
 
 
 
 AP Correlations 
 
 
 r AP 
 
 +.21 ±.06 
 
 r AP.DJLMNO 
 
 +.30 ±.06 
 
 r AP.JLMN 
 
 +29±.06 
 
 r AP.D 
 
 -j-.48±.05 
 
 r AP.DLMN 
 
 +.31 ±.06 
 
 r AP.JLMNO 
 
 +.29±.06 
 
 r AP.DG 
 
 -,10±.07 
 
 r AP.DQ 
 
 +.42±.06 
 
 r AP.LMN 
 
 +.33±.06 
 
 r AP.DGI 
 
 +.00±.07 
 
 r AP.G 
 
 — .27±.06 
 
 r AP.M 
 
 +.37±.06 
 
 r AP.DGIQ 
 
 — .03±.07 
 
 r AP.I 
 
 +40±.06 
 
 r AP.MN 
 
 +.37±.06 
 
 r AP.DG<3 
 
 — .13+.07 
 
 r AP.IG 
 
 — .08±.07 
 
 r AP.N 
 
 +.21±.06 
 
 r AP DI 
 
 +.55±.05 
 
 r AP.IJLMNO 
 
 +.38±.06 
 
 r APO 
 
 +.20±.06 
 
 r AP.DIJLMNO 
 
 -j-.38±.06 
 
 r AP.J 
 
 +36±.06 
 
 r AP.Q 
 
 +.12±.07 
 
 r AP.DIQ 
 
 +.50±.05 
 
 
 
 
 
 11. Fecundity of the Foreign-Bom. A positive correlation ap- 
 pears between fecundity and the proportion of foreign-born in 
 every case except where the G index of age distribution is assigned. 
 r AP =+.21±.06, and r A p.Di=+.55±.05. The difference between 
 these two coefficients is due to two factors: first that the slight 
 concentration of the foreign-born in cities tends to cover up their 
 high fecundity as compared with the native-born, and second that 
 the proportion married is negatively correlated with proportion of 
 foreign-born (ri P = — .27±.06). This seems at first in contradic- 
 tion to the well-known fact that foreign-born women marry earlier 
 than native women; see Hart (9, p. 125). The explanation perhaps 
 is that where foreign men are in excess native women have fewer 
 attractive opportunities to marry. 
 
30 
 
 IOWA STUDIES IN CHILD WELFARE 
 
 In terms of a partial regression, b A p.Di=+-62±.06, with an error 
 of estimate of ±30. The whole theoretical range of P (1,000 
 points) therefore corresponds with a difference of 620±61 in fecun- 
 dity. If D and I were at their average values, a wholly foreign- 
 born community would have a fecundity of 1,166 ±62, while a com- 
 munity entirely native-born would have a fecundity of 546±31. 
 This contrast is in harmony with what is known of the relative 
 fecundity of native and foreign mothers. See (11), (19), (37), 
 (38). 
 
 The most striking fact about these AP correlations is that the 
 well known tendency of the foreigner to be prolific disappears en- 
 tirely if the age distribution index G is assigned (r AP . D Qi=+.00± 
 .07). This fact leads to an analysis of the reasons for the high 
 correlation r G p=+.70±.04. For the nine counties having the 
 largest percentages of foreign-born residents in 1915 the values of 
 G were calculated separately for the native-born of native parents, 
 native-born of foreign or mixed parentage, foreign-born, and all 
 persons of foreign parentage. The results are shown in compari- 
 son with similar data for the state as a whole in Table 13. 
 
 As to age distribution the foreign-born of these nine counties 
 are clearly not typical of the foreign-born of the state as a whole, 
 but tend to have markedly younger women. This youthfulness 
 extends also to the other nativity groups in these counties. The 
 explanation for these facts seems to be that foreigners tend de- 
 cidedly to migrate into communities where economic conditions, as 
 reflected by the G index, are unfavorable. Apart from their 
 poverty, as shown by this index, the foreign-born appear to be no 
 more fertile than the native-born. Differential fecundity as 
 
DIFFERENTIAL FECUNDITY IN IOWA 
 
 31 
 
 between nativity groups seems from these partial correlations to 
 be due to economic and educational differences rather than to 
 biological racial differences. 
 
 
 
 TABLE 14 
 
 
 
 
 AI Correlations 
 
 
 r A i 
 
 +.48±.05 
 
 r AI.DOP 
 
 +.41±.06 
 
 r AI.LMN 
 
 +.54±.05 
 
 r AI.D 
 
 +.21±.06 
 
 r AI.DP 
 
 +.37±.06 
 
 r AI.LMNOP 
 
 +.57±.05 
 
 r AI DO 
 
 +.35±.06 
 
 F AI.DPQ 
 
 +.41±.06 
 
 r AJ.LMOP 
 
 +.55±.05 
 
 r AI.DGM 
 
 +.35±.06 
 
 r AI.DQ 
 
 -f.25±.06 
 
 r AI LNOP 
 
 +.64±.04 
 
 r AI.DGQ 
 
 +.37±.06 
 
 r AI.O 
 
 +.57±.05 
 
 r AI.M 
 
 +.44±.05 
 
 r AI.DJLMNOP 
 
 +.44±.05 
 
 r AI.JLMN 
 
 +.54 ±.05 
 
 r AI.MN 
 
 +.53±.05 
 
 r AI.DJLMNO 
 
 +.41±.06 
 
 r AI JLMNO 
 
 +.53±.05 
 
 r AI MNOP 
 
 +.58±.05 
 
 r AI DJLMNP 
 
 4-.47±.05 
 
 r AI.JLMNOP 
 
 +.57±.05 
 
 r AI.MOP 
 
 +.54±.05 
 
 r AI.DJMNOP 
 
 +.45±.06 
 
 r AI JLMNP 
 
 +.58±.05 
 
 r AI.N 
 
 +.56±.05 
 
 r AI.DJNOP 
 
 +.43±.06 
 
 r AI JLMOP 
 
 +.51±.05 
 
 r AI.NOP 
 
 +.64±.04 
 
 r AI DLMN 
 
 +.40±.06 
 
 r AI.JLNOP 
 
 +.58±.05 
 
 r AI.O 
 
 +.52±.05 
 
 r AI DMNOP 
 
 +.44 ±.05 
 
 r AI JMNOP 
 
 +.57±.05 
 
 r AI.P 
 
 +.57±.05 
 
 f AI.DMOP 
 
 +.42±.06 
 
 r A i.j 
 
 +.36±.06 
 
 r AI PQ 
 
 +.56±.05 
 
 r AI DNOP 
 
 +.43±.06 
 
 r AI.L 
 
 +.51±.05 
 
 r AI.Q 
 
 +.50±.05 
 
 12. Fecundity and Proportion Married. The lowest AI corre- 
 lation is +.25 ±.06, so that a positive correlation is, as might have 
 been expected, clearly established. Fecundity tends to be highest, 
 other things being equal, where the largest proportion of the women 
 are married. 
 
 13. General Interpretation of Eecundity Correlations. Im- 
 portant factors conditioning the fecundity of Iowa women may be 
 classified, relative to this investigation, under four heads: 
 
 1. The factors of age distribution, urban or rural residence, 
 percentage married, and percentage of persons of high school 
 age attending high school. 
 
 2. Factors correlated with the indices listed under 1, such 
 as high previous fecundity in the community, high adult 
 female death rate, percentage of population foreign-born, 
 percentage of middle aged persons owning homes, Catholic 
 and Protestant religious affiliations, percentage of male chil- 
 dren of school age attending school nine months or more in 
 preceding year, and percentage of persons over school age -e- 
 ported as having had eight years or more of schooling. 
 
 3. Factors which are independent of the factors listed under 
 1, and which vary markedly as between Iowa comities in 1915. 
 
32 IOWA STUDIES IN CHILD WELFARE 
 
 4. Factors which are independent of the factors listed under 
 1, and which vary, or might vary, markedly as between fam- 
 ilies, but which do not vary greatly as between Iowa counties 
 in 1915. 
 Intelligent appraisal of the results of this study depends to a 
 considerable extent upon the determination of the relative im- 
 portance of these four groups of factors. For this purpose multiple 
 regression equations, predicting A in terms of other variables, are 
 requisite. The most important of these equations are the 
 following :* 
 
 A' DIJLMNOP =612±6-(4.0±.3)(D-46±l) + (.70±.10)(I-746±3) 
 
 — (.03±.04)(J-467±8)-(.13±.04)(I^703±5) 
 
 — (.46±.18)(M— 143±2)+(.11±.05)(N— 80±5) 
 
 — (.09±.04)(O-253±5)+(.42±.07)(P— 106±3)±28. 
 A' DG1Q =612±6-(3.5±.2)(D-46±l)+(.74±.05)(G-286±3) 
 
 +(.38±.07)(I— 746±3) — (.18±.06)(Q-164±3)±23. 
 A' DG i=(l+.000776 i)(.79g+1.34 D— .048 D=+662)±23. 
 A' D0I =( l-j-000775 i)(I+.00241 c) (650+1.7 D-.05D2)±23. 
 
 In the above equations capital letters stand for the original 
 items and small letters for deviations from the respective arithmetic 
 means of the corresponding indices. The last number in each 
 equation is the probable error of estimate. In the last equation 
 a new index C is introduced, consisting in 1,000 times the number 
 of women 18 to 20 years of age, divided by the number 18 to 20 
 plus the number of women over 44 years. If the G index is 
 ^»o_ e , the C index is i™t e . 
 
 f e + I 
 
 The best summary statement of the accuracy with which these 
 various regression equations predict fecundity is the correlation 
 of each series of predictions with the corresponding actual fecun- 
 dities. These may be calculated readily from the errors of estimate 
 of the regression equations and the standard deviation of the 
 fecundities. Between the actual fecundities and the predictions 
 from the D, I, J, L, M, N, O, and P indices the correlation is 
 -4-.86±.02. Between actual fecundities and the predictions from 
 the D, G, I, and Q indices the correlation is 4-.91±.01. The 
 correlations between actual fecundities and predictions from the 
 D, G, and I indices, and between actual fecundities and predictions 
 
 •In these, as in previous, regression equations, the probable errors of the means and 
 of the regression coefficients are given after thier respective quantities, with + signs, 
 and the probable error of estimate is given at the end of each equation with a ± sign 
 before it. 
 
DIFFERENTIAL FECUNDITY IN IOWA 33 
 
 from the D, C, and I series are also 4-.91±.01. The probable errors 
 of these correlations are derived by the usual formula. 
 
 The size of these correlations shows that factors in group 3 on 
 page 31 are practically negligible as compared with factors in 
 groups 1 and 2. 
 
 14. Curvilinear Regressions. Thus far the discussion has been 
 confined to rectilinear regressions. The assumption of rectilinearity 
 is, however, misleading. If, in the equation for predicting A from 
 D, I, J, L, M, N, 0, and P the theoretical extremes of all the 
 variables, corresponding with the lowest fecundity, are substituted, 
 the predicted fecundity becomes —466 ±108, which is of course 
 absurd. Such a prediction should represent the fecundity of a 
 community consisting entirely of unmarried, well educated, home 
 owning, native-born city folks. Such a community would have a 
 certain illegitimate birth rate, and a certain number of adopted 
 children. At the least it could not have less than no children at 
 all. In the equation for predicting A from D, G, I, and Q, while 
 G, strictly speaking has no definite limit, the same possibility of 
 a prediction of negative fecundity appears. 
 
 The reason for this irrationality at the lower extremes seems 
 to be that the effect of the proportion married on fecundity is to 
 be measured by multiplication rather than addition. If the pro- 
 portion married became zero the fecundity would drop approxi- 
 mately to the illegitimate rate, and the absolute effects of other 
 conditions would be very much smaller than in a population where 
 all women of marriageable age were married. The equations pre- 
 dicting A from D, G, and I, and from D, C, and I, attempt to 
 meet this difficulty. It will be noted that, in spite of not using 
 the variable Q, these equations fit the data slightly better than the 
 second equation. Moreover, assuming G and C as being 0, the 
 lowest possible predictions from the equations involving curved 
 regression surfaces are 40 and 63 respectively, as compared with 
 — 127 as the lowest restilinear prediction from D, G, I, and Q. 
 
 The prediction of A from R, I, J, L, M, N, O, and P fits much 
 less closely than the other three equations do. The age index more 
 than takes the place of the religious, economic, educational and 
 nativity indices. The implication seems to be that the age index 
 better reflects the economic and intellectual factors associated with 
 fecundity than do the omitted indices. 
 
34 IOWA STUDIES IN CHILD WELFARE 
 
 While the above argument proves the unimportance of factors 
 which vary markedly from county to county and which are un- 
 correlated with D, G, and I, it is not possible to prove that the 
 correlation of A with D, 6, and I may not be due to some variable 
 not measured in the investigation. The factors still remain which, 
 while they vary little as between Iowa counties, do or might vary 
 greatly as between individual families. Sterility due to venereal 
 disease may, perhaps, be a case in point, though, on the other hand, 
 venereal disease may be correlated with the percentage of urban 
 population, the percentage married, and the age distribution, and 
 so fall into one of the preceding groups of factors. Innumerable 
 other factors, however, such as presence or absence of essential 
 elements in diet, prevalence of sterilization by surgical means, 
 the introduction of new methods of contraception, fluctuations in 
 fashion, the onset and duration of war, biological changes due to 
 selective factors now at work, and so on indefinitely, while they 
 have been proven to exert little independent differential influence 
 on fecundity as between Iowa Counties in 1915, might conceivably 
 have profound influence upon fecundity within counties in 1915, 
 or in Iowa at some other date, or in other localities at any time. 
 
 IV. CONCLUSIONS 
 
 14. Summary. The fecundity of Iowa Counties may be pre- 
 dicted best from three variables among those experimented with : 
 namely, percentage of urban population (D), proportion of women 
 married (I), and steepness of adult female age distribution (G). 
 These three factors, and conditions correlated with them, are 
 responsible for at least five-sixths of the variation between Iowa 
 counties in the number of children under five years per 1,000 
 women 21 to 44 years of age. City people have fewer children 
 than rural, and unmarried women, of course, have fewer than 
 married women. The significance of the G index seems to be as 
 follows: Poor people have high birth rates and high adult female 
 death-rates. The poor in one generation tend to be the parents of 
 the poor in the next generation. There thus arises a more or less 
 continuous poor class with a steep female age distribution, reflected 
 in a high G index. In rural districts poor people are tenant 
 farmers; hence their M index is low. Poor people leave school 
 early, hence their Q and L indices are low. Foreign-born immi- 
 
DIFFERENTIAL FECUNDITY IN IOWA 35 
 
 grants arc mostly poor, and migrate into poor districts; hence 
 indices 6 and P are associated. The fact that the correlations of 
 A with L, M, N, 0, P, and Q are practically negligible when G is 
 constant means that all of these correlations express the same fact, 
 namely that the poor and ill-educated — the unsuccessful in a word 
 — are the highly fecund class. Doubtless also the rearing of chil- 
 dren interferes with economic success. G appears to be the best 
 available summary index of this condition. It might well be called 
 the index of misery. 
 
 The types of individual, then, who are becoming parents most 
 extensively in Iowa are the tenant farmer, the foreigner, and the 
 badly educated. The types most meagerly participating in the 
 bearing and rearing of the next generation are the economically 
 successful, the native-born, the highly educated, and the city 
 dwellers. These differences in fecundity are so radical that they 
 cannot fail to have a profound effect upon the types of children 
 produced, upon the sort of home and community environments pro- 
 vided for them, and hence upon the trend of character of the 
 Iowa population. 
 
 Such conditions, in cooperation with the selective emigration to 
 cities and to other states pointed out in a previous study (9) tend 
 strongly to aggravate the danger of progressive social deterioration 
 in the least favored rural areas of the State. 
 
 15. Recommendations. The first need in connection with this 
 problem is for further research. The counties of the state furnish 
 only 99 itrnis — a number too small for really satisfactory analysis 
 by means of partial correlations. The counties are, moreover, too 
 large, and vary too little among themselves in many respects, to 
 permit safe generalizations about regressions at the extremes of 
 the theoretical ranges, or to determine the nature of the curvilinear 
 regressions which undoubtedly represent the true relationships. 
 
 Research along the following lines is called for: 
 
 1. Securing of accurate detailed social data for several thousand 
 individual families, with a view to analysis of their fecundities 
 in correlation with factors indicative of their success and desir- 
 ability as parents, and as to the conditions which encourage and 
 discourage fecundity. 
 
 2. Analysis of these data with a view to expressing fecundity 
 
36 IOWA STUDIES IN CHILD WELFARE 
 
 in terms of a curvilinear regression equation with an error of 
 estimate approaching zero. 
 
 3. Formulation of definite social policies on the basis of these 
 findings, with a view to counteracting the menace of progressive 
 deterioration in the quality of parenthood. 
 
V. SELECTED REFERENCES 
 
 INVOLVING STATISTICAL DISCUSSION OF DIFFERENTIAL 
 
 FECUNDITY 
 
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 37 
 
38 IOWA STUDIES IN CHILD WELFARE 
 
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 Assn. 1914, (14) 156-174. 
 
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DIFFERENTIA], FECUNDITY IN IOWA 39 
 
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 Washington: Govt. Print. Off. 1905. , 
 
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