4? A Publication of The College of Agriculture UNIVERSITY OF CALIFORNIA ^hx^} Relationship of SOLIDS-NOT-FAT to FAT in California Milk E. L. Jack F. H. Abbott E. B. Roessler A. W. Irwin .■ : : ' ■ " ' " -m::mmmwmm; : M;::. Y=» 7.07+ 0.444 X -&) 4 4 4 M CALIFORNIA AGRICULTURAL EXPERIMENT STATION BULLETIN 726 lew comprehensive data are available showing the solids-not- fat content of milks of different fat percentages. What informa- tion we do have is becoming increasingly important because there is no quick, reliable test for determining the solids-not-fat in milk. At the request of the California Bureau of Milk Control, a study was made to obtain data on the relationship between the per- centages of solids-not-fat and fat in California milk. The work was done under the joint supervision of members of the staff of the University of California and the California Department of Agriculture. This bulletin presents the results of the study. Samples of milk — 20,694 in all — were analyzed. These samples were taken from all areas of the state, at all seasons of the year, over a two-year period. Analyses show that while the rela- tionship between percentages of fat and solids-not-fat is not strictly linear, a linear equation seems to fit the data as well as would a more complicated one, and such an equation is offered as a basis for estimating per cent of solids-not-fat. Additional equations have been calculated to allow for variations in milk composition arising from differences in breed. ERRATUM: Table 4, page 9, should be titled "Influence of Breed on the Composition of Milk." September, 1951 THE AUTHORS: Mr. Jack is Professor of Dairy Industry and Dairy Technologist in the Experiment Station, Davis. Mr. Roessler is Professor of Mathematics and Statistician in the Experiment Sta- tion, Davis. Mr. Abbott is Associate Specialist in Dairy Industry, Davis. Mr. Irwin is Assistant Specialist in Dairy Industry, Davis. Relationship of SOLIDS -NOT- FAT to FAT in California Milk E. L. JACK, E. B. ROESSLER, F. H. ABBOTT, AND A. W. IRWIN The increased emphasis on the impor- tance of the nonfat solids of milk, both for their nutritional value and as an aid to proper processing evaluation pro- cedures, has focused attention on the scarcity of comprehensive data that show the solids-not-fat content of milks of dif- ferent fat percentages. Such data are be- coming of greater importance because there is no quick, reliable test for milk solids-not-fat. Numerous studies have been made, but most of them are of limited scope, involving values either from relatively few cows, or for only short periods of time (1,3,4,7, 8, 9, 10, 11, 12). f Among studies of wide scope, Brown and Eckroth (2) compiled data from various sources for over 200,000 samples, but the methods of obtaining the original values are uncertain. Jacob- son (6) analyzed 150,000 samples taken from producers in New England and covering a period of more than a year. These samples were taken at the milk re- ceiving plant, and a regression equation was calculated from the results. Within recent years, the results ob- tained by Jacobson have been generally regarded as the most reliable of those available, and have been in use in Cali- fornia. The relationship between solids- not-fat and fat, as determined by Jacob- son, is: percentage S-N-F = 7.07 + 0A0X (fat percentage). The present study was initiated at the request of the California Bureau of Milk Control to obtain data on the relation- ship between the fat percentage and the percentage of solids-not-fat in California milk. EXPERIMENTAL In order to insure that pertinent fac- tors would not be overlooked, the follow- ing persons met to outline the plan of work and to consider the best method of obtaining appropriate samples. From the University of California: E. L. Jack, Chairman, Division of Dairy Industry; F. H. Abbott and A. W. Irwin, Division of Dairy Industry; David A. Clarke, Giannini Foundation; E. B. Roessler, Chairman, Division of Mathematics; and G. E. Gordon, Agricultural Extension Service. From the California Department of Agriculture: 0. A. Ghiggoile, Chief, Bureau of Dairy Service; W. B. Wood- burn, Chief, Bureau of Milk Control; * Supported in part by funds contributed by the California Bureau of Milk Control. t Italicized figures in parentheses indicate references to "Literature Cited," page 12. and John Marshall, Bureau of Milk Con- trol. In accordance with the plan formu- lated by this group, the state was divided into 10 areas in such a way that the feed, breed of cattle, climatic conditions, and milk sheds supplying the different mar- kets were fairly uniform within each area. The areas were as follows: I. Los Angeles, San Diego, Orange, San Bernardino, and Riverside counties II. Imperial Valley III. South San Joaquin Valley: Bakers- field to Chowchilla IV. North San Joaquin Valley: Chow- chilla to Stockton V. Sacramento Valley: Gait to Red- ding VI. South Coast: Ventura to San Luis Obispo [3 Fig. 1.— Heavy boundary lines show the 10 areas from which milk samples were taken. VII. Salinas Valley VIII. Central Coast: Marin, Napa, Sonoma, interior Mendocino, Alameda, and Santa Clara counties IX. North Coast: Humboldt, Del Norte, coastal Mendocino counties X. Northern and eastern mountain area Figure 1 shows the geographic out- lines of the areas. Arrangements were made for securing samples from cooperating dairy plants in these areas. Shippers from whose plants samples were to be taken were selected following consultation with the company field men or other qualified persons. The plants were chosen so as to represent, in so far as practical, the average dairy practices of the area, the different breeds of cattle in proportion to their numbers in the area, the different feeding regimes, and a proportionate number of manu- facturing-milk and market-milk produc- ers. Samples were taken one day a week (as one-day composites), on the receiv- ing platform, by the plant's licensed weigher and sampler. These were pre- served with formaldehyde and shipped to the Division of Dairy Industry, Uni- versity of California, Davis, either by parcel post or by express. As a result of careful filling, mixing, and packing, sur- prisingly few samples were found unsuit- able for analysis by reason of churning, coagulation, or leakage. After a period of time, it was established that samples taken every two weeks did not show any more variation than those taken every week; consequently, the collection of samples every two weeks was adopted. Table 1 shows the statewide distribution of samples, the cow population repre- sented, and the pounds of milk fat pro- duced in each area. This coverage represents about 3.6 per cent of all commercial dairies in the state — 24,000 — and about 6 per cent of all cows in the state— 800,000. It will be noted that the numbers of cows repre- sented in the samples are greater in the Los Angeles-San Diego, the South Coast, and the Central Coast areas. In these areas there is a predominance of market- milk producers, with correspondingly larger herds. The numbers of shippers sampled, the numbers of cows in the herds, and the total number of samples taken in each area are not necessarily in proportion to the amount of milk pro- duced in the area. It is believed, how- ever, that the samples obtained in each area are truly representative of the milk produced in that area. Collection and analyses of the samples covered approximately a two-year period in most of the areas. The samples were analyzed for fat by the standard Babcock procedure, accord- ing to the regulations in force as part of the California Agricultural Code. The total solids were determined gravimetri- cally, by the official method of the Asso- ciation of Official Agricultural Chemists. [4 RESULTS Statewide analyses. — The data in- volving measurements on 20,694 sam- ples, from all areas of the state, and at all seasons of the year, were analyzed to determine the relationship between milk fat percentage and solids-not-fat content that would be most representative. A regression line was fitted to the 20,- 694 individual samples by the method of least squares. Its equation is y = 7.11+0.436Z where Y = per cent solids-not-fat X = per cent milk fat As indicated in Table 1, the number of samples from each area is not exactly in proportion to the total production of that area. In order to balance inequities that might influence an accurate evalua- tion, a similar equation was calculated in which the values for each area were weighted according to the volume of production of that area as shown in the table. The equation so weighted is Y = 7.07 + 0.444Z As can be seen, it differs only slightly from the unweighted one, substantiating the fact that the samples were taken in correct proportions throughout the state. Similar weighted equations were cal- culated for market milk and manufac- turing milk, separately, throughout the state. These equations are shown in Table 2 along with the Jacobson value for comparison. Figure 2 shows the lines represented by these equations. It is apparent that there is no appreciable difference be- tween the relationship for market milk, manufacturing milk, and the weighted and unweighted composites. Values of solids-not-fat calculated from the Jacob- son relationship are less, by 0.13 per cent for 3 per cent milk fat, 0.18 per cent for 4 per cent, 0.22 per cent for 5 per cent, and 0.26 per cent for 6 per cent milk fat, than those determined from the weighted composite. Figure 3 shows curves for the linear regression for the weighted composite determined from all 20,694 measure- Table 1. — Distribution of Samples from the Different Areas Area Number of shippers sampled Number of cows in sampled herds Per cent of cow pop. of state in the area Number of samples taken 1949 fat producti sn* Market milk Mfg. milk Total 102 16,000 23 3,331 thousands of pounds I 58,900 200 59,100 II 13 750 1 320 650 220 870 m 99 6,275 15 3,594 18,670 14,600 33,270 IV 93 4,200 24 2,861 17,080 32,800 49,880 V 99 2,875 9 2,142 5,900 10,660 16,560 VI 55 5,000 4 2,395 5,320 1,870 7,190 VII 41 2,450 3 1,415 1,610 1,580 3,190 VIII 98 8,000 16 2,507 28,650 6,200 34,850 IX 66 3,075 4 2,094 1,150 8,260 9,410 X 2 40 1 35 980 1,400 2,380 Totals 668 48,665 100 20,694 138,910 77,790 216,700 * California Dairy Information Bulletin Vol. VI. [5] merits, and for the quadratic and cubic relationships of best fit. Although the quadratic and cubic relationships fit the points of high per cent milk fat more closely, their standard errors of estimate for all the data are no smaller than the one for the straight line because of the great predominance of samples testing 3.2 per cent to 5.2 per cent milk fat. It is apparent that the linear relationship fits the data as a whole as well as do the more complicated expressions. Breed differences.— Of the 20,694 samples used in this study, 8,852 came from herds of definite composition as to breed. Table 3 shows the regression co- efficients for the various breeds and the number of samples on which each is based. Overman, Garrett, Wright, and San- mann (10), of Illinois, have studied the influence of breed on the composition of milk. Table 4 shows their results. Comparisons of the Illinois values with those reported here show remarkably good agreement for the Holstein-Frie- sians— Y= 6.7917 + 0.6138* (Illinois) as against Y = 6.60 + 0.554X in California, and for the Jerseys, Y = 8.2340 0.2457Z as against Y = 8.09 + 0.253X. The agree- ment for the Guernseys, the other breed for which comparison is appropriate, is not so close: Y = 7.2763 + 0.4625* as against Y = 7.52 + 0.355Z. Table 2. — Regression Equations for Estimating Per Cent of Solids-not- fat (Y) from Per Cent of Fat (X) for 20,694 Samples of Milk (Y = a + bX) Standard error Coefficient Source and type a b of of estimate correlation Present study: Market milk — weighted 7.00 0.459 0.34 0.610 Mfg. milk — weighted 7.14 0.426 0.40 0.603 Composite — unweighted 7.11 0.436 0.35 0.644 Composite — weighted 7.07 0.444 0.36 0.608 Jacobson study 7.07 0.400 Table 3. — Regression Equations for Estimating Per Cent Solids-not-fat (Y) Per Cent of Fat (X) for Different Breeds (Y = a + bX) Breed * a b Number of samples Mixed 6.52 6.60 7.30 7.52 8.09 0.569 0.554 0.400 0.355 0.253 2,326 3,294 1,083 1,069 1,080 Holstein-Friesian . Colored Guernsey Jersey h«rd« JSX5 «f ™ ? C °^ n ? iSt ° f a PP r ox imat ely half Holstein-Friesians and half Jersey and/or Guernsey. Colored oris J aSSSf, tw £« /i eyS and , Guerns f y s - Th e designated breeds are not necessarily purebreds, but com- prise ammals that present the usual outward characteristics of the breed [6 JACOBSON V = 7.07 0.40X Composite (unweighted) Y = 7.11+0.436X Composite (weighted) Y = 7.07 + 0.444X Market milk y = 7.00 + 0.459X Manufacturing milk y = 7.14 + 0.426X 8.3 1 I I I I I I I I I I I I I I I L_ 3.0 3.4 ,3.8 4.2 4.6 5.0 5.4 5.8 6.2 X— PER CENT MILK FAT Fig. 2.— Relationship between solids-not-fat (Y) and milk fat (X), for market milk, manufacturing milk, and a composite of the two. [7] 9.6 / '* / :/-- 9.5 /rV /// • 9.4 Jr f o // «> 9.3 // O J° ui in ¥ CO ,'r -1 • \/ < 9.2 'Jo tt / O if u. 1- < •? 9.1 / O z / I (ft a 5 9.0 •J o / 111 < tt V 5 89 z Ul o a 8.8 in If a. | '% >- ip 8.7 W if* §0 ft 8.6 / ' Y 7 07 i 111]f 8.5 *M 7l o Y = 6.04 1 + 0.950X - 0.0606X 2 i 7J i X --- Y = 1 0.233 - 1 .947X + 0.5887X 2 - 0.0473X 3 8.4 *- • i 8.3 i 1 1 1 l 1 I 1 1 l 1 1 l 1 1 1 1 3.0 3.4 3.8 4.2 4.6 5.0 5.4 X— PER CENT MILK FAT 5.8 6.2 6.4 Fig. 3.— Various regression curves for per cent solids-not-fat (Y) and per cent fat (X). Black dots are the actual determinations, based on 20,694 samples. [p.] The Illinois data for all samples, as shown in Table 4, are heavily weighted by the Guernsey-Holstein cross, results of which comprise nearly half the sam- ples. If the equation is calculated giving equal weight to each breed rather than to each sample, then the composite equa- tion becomes y = 7.4+0.44Z, which com- pares very closely with the unweighted composite equation for all values in this study— Y = 7.11+ 0.436X. The values for Jersey, Guernsey, and Holstein compare very well with the averages reported by Davis et al. (5). Their average solids-not-fat content for Holstein milk for 207 samples is 8.6 per cent for 3.5 per cent fat. The value com- puted here, from the same fat content, for the breed is 8.54 per cent. Their aver- age for Guernsey milk, from 139 sam- ples, is 9.4 per cent for 4.9 per cent fat. The value computed here, from the same fat content, for the breed is 9.26 per cent. Similarly, for Jersey milk from 160 samples, the Arizona value is 9.5 per cent solids-not-fat, for an average test of Table 4. — Influence of Breed on the Consumption of Milk Breed Number of samples of individual cows a 208 6.7703 428 7.7421 321 7.2763 268 6.7917 199 8.2340 1,002 7.7116 2,426 7.6736 Ayrshire Brown Swiss Guernsey Holstein-Friesian Jersey Guernsey-Holstein cross All samples .5247 .4118 .4625 .6138 .2457 .3849 .3846 From Illinois Exp. Sta. Bui. 457. Table 5. — Regression Equations Constants for Estimating Per Cent of Solids-not-fat (Y) from Per Cent of Fat (X) for Different Areas (Y = a + bX) Area a 6 Standard error of estimate Coefficient of correlation Number of samples I n m IV v VI 6.52 7.13 7.12 7.06 7.21 6.98 6.70 7.31 8.28 8.13 7.11 7.07 0.588 0.443 0.423 0.443 0.408 0.468 0.538 0.387 0.215 0.147 0.436 0.444 0.30 0.22 0.32 0.48 0.24 0.29 0.36 0.32 0.26 0.22 0.35 0.36 0.638 0.641 0.617 0.506 0.760 0.634 0.627 0.545 0.513 0.276 0.644 0.608 3,331 320 3,594 2,861 2,142 2,395 1,415 2,507 2,094 35 20,694 20,694 VII vm IX X Composite Weighted composite [9] 5.1 per cent fat. The like value here is 9.38 per cent solids-not-fat. Area differences. — Table 5 shows, for each of the 10 areas, coefficients of the linear regression equations which best fit the data, and the number of sam- ples from which each is determined. It is interesting to note that, except for Areas I, VII, IX, and X, the regression lines are very close to those of the com- posites. The predominant breeds in Areas I and VII are Mixed and Holsteins, re- spectively, and the area coefficient resem- bles very closely those for these breeds. Jersey is the predominant breed in Areas IX and X, and the regression equations for those areas are very similar to that for the Jersey breed. The samples for this study were taken over a period of approximately two years so that all seasonal effects would be accounted for. Figure 4 shows the monthly variations in the percentages of fat and of solids-not-fat. The usually re- ported relationships, as reviewed recently by Davis et al. (5) , are evident. The data extend through three winter seasons and two summers. Both the fat and the solids- not-fat percentages are higher in the winter months, with the solids-not-fat showing slightly more variability than the fat. The average solids-not-fat range from a high of 9.03 per cent in January, 1949, to a low of 8.76 per cent in July, 1948. The variations in fat average from a high of 4.52 per cent in November, 1947, to a low of 3.72 per cent in May, 1949. Table 6 gives the percentage of solids- not-fat for each % per cent fat percent- age from 3.0 per cent to 7.0 per cent, as calculated from the equation for the weighted composite, Y = 7.07 + 0.444Z. Table 6. — Solids-not-fat Percent- age at Different Fat Percent- ages in California Milk Fat S-N-F per cent per cent 3.0 8.402 3.1 8.446 3.2 8.490 3.3 8.534 3.4 8.578 3.5 8.622 3.6 8.666 3.7 8.710 3.8 8.754 3.9 8.798 4.0 ' 8.842 4.1 8.886 4.2 8.930 4.3 8.974 4.4 9.018 4.5 9.062 4.6 9.106 4.7 9.150 4.8 9.194 4.9 9.238 5.0 9.282 5.1 9.326 5.2 9.370 5.3 9.414 5.4 9.458 5.5 9.502 5.6 9.546 5.7 9.590 5.8 9.634 5.9 9.678 6.0 9.722 6.1 9.766 6.2 9.810 6.3 9.854 6.4 9.898 6.5 9.942 6.6 9.986 6.7 10.030 6.8 10.074 6.9 10.118 7.0 10.162 [10 J 9.1 9.0 O 8.9 Z 8 8.8 Z ui u u £8.7 4.6 4.5 < 4.4 2 4.3 2 4.2 H 5 4.1 u g 4.0 a. 3.9 3.8 3.7 1947 NOV. 48 FEB. >R. JUNE AUG. OCT. DEC. 49 MAR. MAY JULY SEPT. NOV. 1950 JAN. MAR. MAY JULY SEPT. NOV. JAN. FEB. APR. JUNE AUG. OCT. DEC. JAN. Fig. 4.— Monthly milk-fat and solids-not-fat variations from November, 1947, to January, 1950. SUMMARY An analysis of 20,694 samples of milk selected from all areas of the state and at all seasons of the year, and collected as it was delivered to the creameries, in- dicated that the relationship between per cent of solids-not-fat and per cent of milk fat is not strictly linear. However, a linear estimating equation is much easier to use, and it seems to fit the data as well as do more complicated expressions. The per cent of solids-not-fat may be estimated from the per cent of fat by use of the formula Y = 7.07 + 0AUX where Y represents the per cent of solids- not-fat and X represents the per cent of milk fat. The standard error of estimate, 0.36, indicates considerable variability in the data. The per cent of solids-not-fat estimated from this relationship for any particular sample might be expected once in 20 times to deviate from the true value by more than 0.7 per cent. However, in only one weekly composite sample out of 20 would the nonfat solids be expected to deviate from the true value by more than 0.29 per cent, and only once in 20 times, for a monthly period, would the average of estimated values differ from the true value by more than 0.1 per cent. For average or composite tests based on a large number of producers delivering to a single dealer, the relationship would be even more accurate. The equation for the samples from market-milk producers is Y = 7.00 + 0.459Z and for milk from manufacturing-milk producers, Y = 7.14 + 0A26X [11] Each of these conforms closely to the dominating breed or breeds of the area, over-all value. and tends to conform to the composition Similar equations are calculated for of that breed, or combination of breeds, the diiferent breeds in so far as the herds Seasonal variations show higher fat conformed to a definite breed pattern. and solids-not-fat percentages in the The composition of milk for each area, winter months than in the summer. Dis- as shown by similar equations, is in- tinct trends through three winter seasons fluenced, to a great extent, by the pre- and two summers are observed. LITERATURE CITED 1. Bakalor, S. 1948. Investigations on the composition of South African milk. V. The relationship between the various constituents of milk. Dept. of Agr. Bui. 297, Pretoria, S.A. 2. Brown, L. P., and C. V. Eckroth. 1917. Relation of the fat in milk to the solids-not-fat. Ind. Eng. Chem. 9:297-99. 3. Committee on Standardization of Market Milk, American Dairy Science Association. P. F. Sharp, Chairman. 1938. Report to the Annual Meeting. (Unpublished.) 4. Cranfield, H. T., H. D. Griffiths, and E. R. Ling. 1927. The composition of milk. I. Variation in the solids-not-fat, fat, and protein content of cows' milk and their relationship. Jour. Agr. Sci. 17:62-71. 5. Davis, R. N., F. G. Harland, A. B. Caster, and R. H. Kellner. 1947. Variation in the constituents of milk under Arizona conditions. I. Variations of in- dividual cows within breeds by calendar month. Jour. Dairy Sci. 30:415-24. II. Influ- ence of the month of lactation in cows of different breeds. Jour. Dairy Sci. 30:425-33. III. Variation in milk from Jersey, Guernsey, Holstein and mixed breeds. Jour. Dairy Sci. 30:435-42. 6. Jacobson, M. S. 1936. Butterfat and total solids in New England farmers' milk as delivered to processing plants. Jour. Dairy Sci. 19:171-76. 7. Kahlenberg, 0. J., and LeRoy Voris. 1931. The percentage of fat as a basis for estimating the composition of milk. Jour. Agr. Res. 43:749-55. 8. Moore, H. C, and K. S. Morrow. 1940. The inheritance of solids-not-fat percentage in dairy cattle. Jour. Dairy Sci. 23:548-49. 9. Moore, H. C, and H. A. Keener. 1942. Improving the solids-not-fat content of milk by selective breeding. New Hampshire Agr. Exp. Sta. Bui. 351. 10. Overman, O. R., O. F. Garrett, K. E. Wright, and F. P. Sanmann. 1939. Composition of milk of Brown Swiss cows with summary of data on the composition of milk from cows of other dairy breeds. Illinois Agr. Exp. Sta. Bui. 457. 11. Shaw, A. O., and D. L. Fourt. 1936. Preliminary of solids-not-fat content of milk from cows in the Idaho Agricultural Ex- periment Station Holstein and Jersey herds. Proc. 22d Ann. Meeting Western Div. Amer. Dairy Sci. Assn., pp. 70-82. 12. White, G. C, and H. F. Judkins. 1918. Variations in fat, solids-not-fat, and total solids in cows' milk. Connecticut (Storrs) Agr. Exp. Sta. Bui. 94. 80m-9,'51(6397)L.L. [12