:1 T] ) LU a q ‘14 C) .1) f1 1) ‘L‘ '11 )1 a U C) P ‘ E 1‘: H \ M‘ H H ‘i ‘ M j ‘ 1 “ "l‘ { ‘I H! \U “i ‘! ‘ 1I ‘. W , I M j H } “I“ ‘1‘ I“ ’ 1‘ ‘ 1 . l1 1 ‘ I‘ ‘U | \ I l l M i w 1‘ I 3‘ i [w l A t V l I «I —‘ 1833 l (Duh- STATiSTQCAL STUDEEfi 0? $151. TECHNIQUES 0N HYQRm CORN ‘E’EJZLALS fixesis {w 336 Degree of M. Sc MECE‘flGAN S?A‘F’E CGLiE—GE 239mm J7. Ragabaam 3958 M3195 Date This is to certifg that the thesis entitled presented bg has been accepted towards fulfillment of the requirements for fin ___-.- ;_____degree in_;‘ I _ ___.' __ . ,.(__,,,_ e .f‘___._ Major professor STATISTICAL STUDIES OF FIELD TECHNIQUES ON HYBRID CORN TRIALS BY GEORGE J. HOGABOAM A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Farm Crops 19h8 ’1 nLSIS STATISTICAL STUDIES OF FIELD TECHNIQUES ON HYBRID CORN TRIALS 5301404. The writer wishes to acknowledge his indebtedness to Dr. E. E. Down for his guidance and aid in making this study. Gratitude is also expressed to Dr. Leo Katz and to Mr. H. M. Brown for their willing cooperation and helpful advice and criticism. TABLE OF CONTENTS IntrOdUCtion 00000000000.0000000000000000ooooooooooooooooooooo... Review Of previous literature 0.00.0000000000000000000000.0.0...5 methOdS Of experimentation 0.000....0.0.0...OOOOOOOOOOOOOOOOOOO.. Data 0.0.0....O...0.0.0.0....OOOOOOIOOOOOOOOOOOOOO...000...... HethOds Of analySis used .00....0.00000000000000000I00.0.00... Illustration Illustration Illustration Illustration Illustration Illustration Illustration Illustration of of of of of of of of Methods of ranking Illustration Illustration Illustration Illustration Illustration of of of of of field data ................................ method one ................................ method two ................................ checks and standards data ................. method four ............................... method five a . xmflmdfflmt>n.u.g.u.u.u.n.n.n.u methods six a and six b ................... used ...................................... method.A .................................. method B .................................. method C .................................. method D .................................. methOd E I0.0000000000COOOOOOOOOOOO0.00.... iethods of comparing planting and harvesting techniques ...... Presentation of data and discussion ............................. MethOdS Of analySis OOOOOOOOOOOOOOCOOOOOOOOO0.0.0....0......O. Illustration of results obtained by different analyses .... HethOdS Of ranking OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO. Comparison of planting and harvesting techniques ............. summary O...0.0...OOOOOOOOOOOOOOOOOOOOOOO0.0.0....IOOOOOOOO00.... Literature Cited OOCOOOOOOOOOOOOOO00.0.0.0...OOOOOIOOOOOOOOOOOOO. Page CO Kl U1 5:" P‘ M 10 10 11 12 12 13 1b 15 16 17 18 19 20 20 22 23 2h 27 28 INTRODUCTI ON Members of the Farm Crops Department are constantly searching for a better method of analysis and comparison of agronomic data with field crops. An expanded program of corn breeding in l9h2 lead to a study of corn results in 19h3 and l9hh by Frey (2). Because of Frey's studies and similar studies made by Farm Crops staff members, the method of planting and harvesting of corn was slightly changed in 1916. Frey's work indicated a need for further study on the methods of analysis and methods of comparing corn hybrids in the overstate corn trials. Such a study, when compared to Frey's data, would also give an indication of the value of the different'methods of planting and harvesting. It is with these prdblems in mind that this investigation is conducted. -2- REVIEW OF PREVIOUS LITERATURE Frey (2) used four different methods of analysis for standard error in each trial of the l9hh data. These methods are as follows: "Method one or 'individual squares average' method, is the method where each square of a trial is analyzed individually, giving a standard error for each. From these, an average of the standard errors of all the individual squares is obtained and this average is used as the error for the whole experiment............ Method two or 'as a randomized experiment' is illustrated....... In this design, the rows of the Latin squares become the replications, so all row A's in the squares are included in replication one, B's in replication two, etc., thus making the replications continuous across the field. The randomized design formed is very special in that each variety occurs within a width of six.plots for all replications. Method three treats the whole experiment as one unit, but the squares making up the trial retain their individuality. Method four (checks and standards) errors are calculated fran the assembled data of checks and standards, with each being considered as a variety, so that between x's (varieties) and 'between replications' sums of squares can be extracted from the total.” Frey (2) concludes that "No significant differences were found between any two of the methods of analysis within the same trial, but in several cases, the differences approach significance". Down, et al. (1) in wheat investigations consider the error of the checks to be that of the varieties when testing for significance between varieties. Frey (2) describes three methods of ranking of varieties as follows: Add and subtract method. The mean.yields of the checks on either side of the square and the mean yield of the standard within that square are averaged. The amount that this average is above or below the average yield of all checks and standards in the trial is added to or subtracted from the mean of each variety within this particular square. The method proceeds for all squares in like manner. Actual yield method. This method consists of letting each variety stand as it yielded with no corrections. g/s method. This method calls for dividing the mean yield of each variety in a square by the mean yield of the standard within that square. 4,- METHODS OF EXPERIMENTATION Data: A county yield trial is made up of a series of 6 x 6 Latin squares. These squares are placed side by side across the field. six varieties are planted in each square one of which is common to all squares to serve as a standard variety. A row of this standard variety is planted between each square to serve as a check. This row also tends to eliminate the border effect which would give unequal competition between squares if the squares were placed next to each other. The check and standard is a variety that is average in maturity and yield for the locality in which the trial is conducted. Frey's data came frcm plots one row wide and 12 hills long and thinned to three stalks. The two least desirable hills were discarded at harvest time. Harvested hills might consist of one, two, or three stalks. The yield.was corrected on the basis of a regression line to a.perfect stand of three stalks. The 19h5 and l9h6 data.came from.plots two rows wide and seven hills long. This allows for a choice to be made at harvest time. Only the first ten three-stalk hills are harvested. In case ten three-stalk hills cannot be found, eight are harvested and the yield proportionally increased. Three trials from each years data were selected for the investigation. For 19115 they were Ingham County trials with three squares, Saginaw County trials with three squares, and Monroe County trials with seven squares. For l9h6 they were Ingham County trials with three squares, Saginaw County trials with five squares, and Monroe County trials with nine squares. Only the squares whiCh had no more than one missing plot were selected from the trials for investigation. Yields per acre were calculated on the basis of fifteen and.one half percent moisture. This allowed the comparison of all varieties on a dry weight basis regardless of the date ofxnaturity. The formula used for calculation considered 70 pounds per'buShel because the weights were taken on ear corn. Methods of analysis used: The standard deviations (standard errors) for the l9hh data were worked by Frey by the four methods outlined in the review of previous literature. The standard deviations for the l9h5 and l9h6 data were worked by five different methods of analyses for each trial. Method one or "individual squares average" is the same as was outlined by Frey except that the remainder mean squares of each square were averaged to give an average remainder mean square for the trial from which the standard deviation for the trial was Obtained. The standard deviation obtained in this manner is the same as that -6- Obtained by the method three outlined by Frey, hence method three is omitted from these analyses. Analysis by method one is illustrated in table 3. Method two or "as a randomized experiment" is the same as was outlined by Frey. This method of analysis is illustrated in table 1.. Method four (checks and standards) is the same as was outlined by Frey. This method of analysis is illustrated in table 5. Method five is an analysis of the checks and standards where the squares remain as a unit. Since there is a check on either side of a square there are two different ways of grouping the checks and standards for analysis. The standard can be paired with the check on the left of the square (same square number) or with the check on the right of the square (different square number). The standard deviation for the trial is obtained from the average remainder mean square as in method one. This method of analysis is illustrated in table 5. Method six is an analysis of the checks and standards where the squares are not retained as a unit and the trial is considered as a ”randomized experiment". In this method the data are paired by the two different methods used in method five so that the only difference between the analyses by method five and method six is the manner in which squares are considered. This method of analysis is illustrated in table 5. Table l. -7- Yields of corn in buShels per acre, 15.5% moisture, for squares 30, 60, and 70 and their adjacent checks for the 1985, Ingham County trial. Column Ck. 30 l 2 s . 30 3 q 8 5 6 Total Ck. 8o Ck. 60 l 2 s . 60 3 q 8 5 6 Total Ck. 70 1 2 s . 0 3 q 7 8 5 6 Total Ck. 80 Note: Table 2. Column O‘WP‘WNH “'Standard variety occupies no. 1 position in each square 7‘ 65.1 68.0 61.8 67.2 70.7 60.2 67.3 390.8 68.5 76.6 76.3 67.1 71.6 82.9 73.0 71.3 882.2 81.1 77.5 67.8 75.5 71.7 71.8 71.6 835.5 76.2 * O‘V'IITWNH b B 71.5 67.8 58.0 62.3 66.6 68.8 65.6 388.3 67.7 76.8 73.8 81.6 79.8 75.8 80.7 71.8 862.3 68.8 71.1 75.0 69.5 88.7 67.3 77.6 885.2 76.3 HNULP'UIO‘ w *- Row C 69.8 73.7 70.2 67.5 78.0 76.6 72.9 838.9 77.1 75.6 88.5 79.1 71808 72.5 77.3 81.3 869.5 77.9 63.6 88.5 77.3 71.8 7501 73.5 885.8 80.2 Row C t'O\naunkdu: as indicated by the asterisk D 70.3 63.3 61.2 69.5 62.5 73.3 63.7 393.5 67.8 78.6 78.8 70.1 58.5 78.8 73.8 83.5 882.3 73.7 73.7 82.9 73.3 79.5 80.7 72.0 862.1 78.1 WPU'II'OO‘JT' U E 68.0 59.9 61.7 58.2 53.1 63.0 71.0 366.9 60.6 72.8 $01 73.6 71.0 67.9 66.8 78.7 818.1 62.8 76.8 78.5 69.8 76.8 79.0 76.7 856.8 78.3 {:11 VIM) Chi-JPN Included are column and row totals for each square. Data are in field order and not varietal order. H 71.0 72.2 63.9 63.8 60.6 61.0 67.8 388.5 68.6 69.0 76.7 66.8 81.2 79.8 78.3 70.3 888.3 69.9 78.3 72.2 71.2 79.3 80.3 78.7 856.0 75.6 Nth-'O‘an :13 Total 811.7 800.5 376.8 388.1 391.5 802.3 807.9 2366.9 802.3 885.8 889.8 837.9 836.9 856.5 885.5 856.5 2682.7 833.8 836.6 860.5 836.2 863.0 hflnz 850.1 2700.6 868.7 squares are numbered 00, 10, 20, 30, etc. across the field. Key to determine varietal yields from field order -3- Table 3. Analysis of squares 30, 60, and 70 Ingham County, 1985 by mEthOd 1 0 Square 30 Source d.f. SS HS SD Total 35 156,703.99 - ct 8 1,086.89 Column 5 155,726.62 - ct 8 109.52 Row 5 156,087.88 - ct = 870.38 Variety 5 155,881.56 -.ct = 268.86 52.89 Remainder 20 282.53 12.13 3.88 Ct = 155,617.10 Square 60 Source d.f. SS MS SD Total 35 201,256.59 - ct = 1,383.28 Column 5 199,975.52 - ct = 62.21 Row 5 200,183.70 - ct - 270.39 Variety 5 200,836.36 - ct - 523.05 108.61 Remainder 20 887.63 28.38 8.98 Gt 3 1995913031 Square 70 Source d.f. SS HS SD Total 35 203,811.86 - ct = 821.85 Row 5 202,669.68 - ct = 79.63 variety 5 202,963.30 - ct = 373.29 78.66 Remainder 20 257.39 12.87 3.59 Ct : 202,590.01 Average Remainder ( average of Remainder MS of squares 30, 60, and 70 ) us so (12.13 + 28.38 + 12.87)/ 3 : 16.86 8.06 -9- Table 8. Analysis of squares 30, 60, and 70, Ingham County, 1985 by method 2. SStotal 2 (156,703.99 4 201,256.59 + 203,811.86) - ct 2 5,209.08 Sum.row-A : 390.8 + 882.2 + 835.5 : 1,268.5 SSrow : (sum row'A)2 + (sum rou'B)2 + .... + (sum row'H)2 - ct = 556,550.81 - ct : 387.85 SSvariety = (sum variety32)2 4 .... 4 (sum variety36)2 6 + (sum variety 62)2 + .... (sum.variety 76)2 + 67 (sum standards 31 4 61 e 71)2 - ct = 558,578.75 - ct 18 : 2,811.79 SSwithin standards : d.f. SStotal = 98,922.38 - ct = 773.27 17 SSra' : 98,161.37 - Gt 3 12.30 S SSwithin standards = 760.97 12 Ct = 98,189.07 Ct : (2366.9 + 2682.7 + 2700.6)2 /108 = 556,162.96 Source d.f. 83 MS SD Total 107 5,209.08 ROW 5 387085 W.Standard 12 760.97 63.81 va 75 1,688.87 21.98 (RXV)+'W.Standard = pooled remainder 87 2,809.88 27.69 5.26 Table 50 their analyses Column Ck. 30 St. 31 Ck. 80 Ck. 60 St. 61 Ck. 70 St. 71 Ck. 80 Method 8: both sides Source Total Column Row Remainder A 65.1 68.0 68.5 76.6 76.3 81.1 77.5 76.2 B 71.5 65.6 67.7 76.8 71.8 68.8 77.6 76.3 -10- C 69.8 67.5 77.1 75.6 78.8 77.9 77.3 80.2 Rows D 70.3 62.5 67.8 78.6 78.8 73.7 79.5 78.1 E 68.0 61.7 60.6 72.8 73.6 62.8 78.5 78.3 H 71.0 61.0 68.6 69.0 78.3 69.9 80.3 75.6 Checks and Standards Data used in Methods 8, 5, and 6 and Total 811.7 382.3 802.3 885.8 888.8 833.8 870.7 868.7 Using standards in the squares concerned and the checks on of those squares. Ct : 289,365.09 251,057.75 - Ct 250,h97052 - Ct 289,537.29 - ct 1,692.66 1,132.83 172.20 388.03 d.f. 87 7 5 35 us 4 11.09 SD 3.33 -11- Table 5 continued. Method 5: Squares remain as units a) Using standards and the checks with same square number (nearest, on the left of the standard) Columns 30 and 31 Source 55 total SS net d.f. MS SD Total 52,691.18 - ct = 158.81 11 Column 52,608.36 - ct = 72.03 1 Row 52,587.82 - ct : 51.09 5 Remainder : 31.69 5 6.38 Ct = 52,536.33 Columns 60 and 61 Total 66,705.86 - ct = 73.06 11 Column 66,633.77 - ct = .97 1 Row 66,669.33 - ct = 36.53 5 Remainder : 35.56 5 7.11 Ct : 66,632.80 Columns 70 and 71 Total 68,528.81 - ct = 387.72 11 Column 68,290.16 - ct : 113.87 1 Row 68,278.52 - ct : 101.83 5 Remainder 2 132.82 5 26.88 Ct 2 68,176.69 Average error for trial Total Remainder = 199.67 15 13.31 3.65 Table 5 continued. Method 5 continued: b) Using standards and the checks with different square number (nearest, on the right of the standard) Columns 31 and 80 Columns 61 and 70 Columns 71 and 80 Average error for trial 55 net d.f. MS SD Total Remainder : 135.58 15 9.08 3.01 Method 6: Squares not retained as units, i.e. a randomized experiment a) Using same standards and checks as in Method 5a SS d.f. MS Error Total 187,921.81 - ct 2 1,196.60 35 Column 187,532.28 - ct 2 807.87 5 Row 186,832.32 - ct = 107.51 5 Remainder : 281.62 25 11.26 Ct : 186,728.81 b) Using same standards and checks as in Method 5b Total 189,689.20 - ct : 1,895.68 35 Column 189,188.51 - ct : 1,030.99 5 Row 188,315.08 - ct : 161.56 5 Remainder = 303.13 25 12.12 Ct : 188,153.52 Methods of ranking used: The 1985 and 1986 data were ranked by five different methods as follows: Method A, the ranking of varieties according to their uncorrected average yields. Method B, the ranking of variety yield after correction by the add and subtract method using checks and standards as outlined by Frey. Method C, the ranking of varieties yields as a percentage of their standard (P/S). Method D, the ranking of varieties according to the difference between their yield and the yield of their respective standard. The comparative yields are obtained by applying these differences to the mean yield of the trial standard. Method E, the ranking of varieties according to the corrected difference between their yield and the yield of their respective standards. The differences within each square are corrected according to the relation between the individual square's standard deviation and the trial's standard deviation. The standard deviation of the square is divided into the standard deviation for the trial to Obtain a correction factor. The differences in yield are multiplied by this correction factor to obtain the corrected difference. The comparative yields are obtained by applying these differences to the mean yield of the trial standard. -18- Table 6. Varieties of Saginaw, 1986 trial ranked according to Method A, uncorrected average yield. ** Square Rank*** Yield 00 10 20 30 50 Var. Yield 75 ‘45:“ 16 72.2 02 71.8 78 08 71.8 _ -71" 26 6809 73 7 13 68.7 16* 35 68.0 72 .2 3,4,, 52 67.7 71 0'2 08 457—- 7,, 53 67.6 * ;8““;8““"7'““"““‘" ' '"”" " m*‘"‘"—"”"“ ” “““ 18 67.2 70 110-2.. w 1 O3 6509 ml) " "“ 12 65.1 69 _,uu_ 7. —- '.f' 38 6501 A ‘7! 72:1 05 65.0 68 st 13 26 “35 23 68.8- 4.2____.. .7 e9 .0 at 613.3 67 . 187 1.1:;1. 527 53 15 63.9 .2 g ,_ .7 .6 28 63.5 66 St- 55 6305 ,1 25 . 63.3 65 03 05 12 38 58 63.0 09 00 01 .1 33 1 6208 — -v3—— r~—.8 _._1__- — - ~r-—u- ' 22 62.2 63 15’ 28 25 58 55 06 61.5 ,__5g .9 7 .5 .3 .0 .5 36 61.0 62 1111;. 22 *33 56 32 60.5 .2 .8 .8111 1 61 06 sill__o st ’36 *"’“*‘ .569 £2 .6 .5 .6 60 3; 7__riL 59 - __,_ 58 ‘553; 51,1. 1 1 1 22 56 55 ._____ 58 7,57811 53 _§37 For footnotes see table 10. -15- Table 7. Varieties of Saginaw, 1986 trial ranked according to Method B, add and subtract. - Square Rank“ Yield“ 00 10 20 30 50 Var. Yield 72 _ZL'E.. 16 71.8 21 163‘“ 7H 26 69.3 ' , LIL 02 68.9 70 ll 08 68.9 .70g 13 67.9 $0 25. -.-. “Eu" 71:573..“(3: 35 67.8 w 8 73m— 31‘ 636 02 0 2 . 6 13 7 ‘3... 3511;- 38 68.9 7 .9 7' . 23 68.8 66 18 12 68.3 3’4 St 61103 65 st 752 53 28 63.9 it— 96 OS _ 25 6307 68 32 23 38 st 15 63.1 .3 .8 .9 .0 Us? 03 63.0 63 03 st 15 28 25 22 62.6 .0 .5 .1, ,9 .L 33 62.6 62 05 st 22 33 05 62.1 .1 ”2,9:‘6 .6 55 61.14 61 st 55 58 60.9 .03— 0 ' 36 6008 60 32 36 58 56 56 60.7 #:1‘_ 03 .8 09.17297 32 6003 SLW _ - u g; 06 58°6 06 - -;._,:__ 7. 58 @580 {a 3 57 in; _ 523 56 "‘” SS __£iL_ 53 J21 CL 52 For footnotes see table 10. -16- Table 8. Varieties of Saginaw, l9h6 trial ranked according to Hethod C, P/S. of Square Rank*** §.,e* oo 10 20 3o 50 Var. Yield 112 1639 .28 gas: :29? 16 72.2 -; _:§§ --1*a1_ 35 71.1 i;fl. eEZ;;‘ 3h 68.0 , _:,, Oh 67.7 108 . JL=““—- , .23 67.2 ._1 -—-~;-fl1::5:_- , , 1— 18 67.2 107 11,: 2h 66.3 106 g3 ;- a- 52 65.9 2 L - 8 3h 53 65.8 105 O O 8: 33 65.7 .28 .28 lb 23 ' ’ 12 65.1 10h 22 68.9 151 05h st 6h03 103 21g 15 63 09 ~25 33 5 36 63.8 2 3 2 6 . 102 .76 .11 .62 .27 33 63,; 101 .63 55 61.8 100 .7 _ g: 21.3 *t1‘* °‘~* ~* .__1.__1..1. 1.1 99 .35 _j{g 06 57.9 32 98 .37 97 03 55 96 .63 .07 05 Sh 56 95 .31 .31 .01 9h 93 . I-.- 1:. 92 3 4~~5 . 91"* " ‘"” fit 90 ‘ '08 r 1.4-. L i A 89 31:19 _. -- M 1.. 88 8&1: 8777 For footnotes see table 10. -17- Table 9. Varieties of Saginaw, l9h6 trial ranked according to Method D, difference. Square Differ- ;; Rank*** ence**' OO 10 20 SO‘L 50 Var. Yield +7 16*: 26 -¥Li-* 39 ‘73;£- " 7L 12 72oz r 35' "2 71. +6 5'“ .5; 35 70.8 5 ,. ., .1— 13 68.7 iii” H- “€;T:: i_u.i___i"ifif “— ,_ ‘_"WL; 02 67.9 h {3“ 0h 67.9 + oh .. .’---.___. 314 6709 +3 02 on 3D 1h 67.2 06 .6 .6 23 6701 ’ 1h 23 2h 66.2 *2 . .9 .8 '~ 25 66.0 1 2h 4257 33 52 53 52 65.9 * .9 .7 - .3 .6 .5 . 53 65.8 +0 12 ’22 33 65.6 .8 .6 ~. 12 65.1 _,. 15 ‘36 *— 22 614.9 5’ . .h .5 st 6h.3 1 32 15 63.9 " .o 36 63.8 _2 03 3'5 32 63.3 .3 .6 03 62.0 _3- 05 5h 56 55 61.7 .2 .i.;.3 5h 61.2 h 05 61.1 - ’ A i.e.”: 52 61.2 ;§——‘ .4ii__ -fi-_-fi. _' 0 S7. -6 05 25.: 07 ’7’ -7 -:Zj-- -:1£L- _8 ‘flii For footnotes see table 10. -13- Table 10. Varieties of Saginaw, l9h6 trial ranked according to Method E, corrected difference. Diff er— Square Rank*** ence** 00 10 20 30 50 Var.'Yie1d 16F 8 .6 16 72.9 26 26 71.8 7 .1 35 69.8 13 69.1 6 02 67.8 5 35 Oh 67.8 h 3 2 ..‘-—-——-—"-- awV-“ — 7‘ ”him. if v .5, i . 1h 67.5 it? 38 67.3 .8 23 66.0 02 08 *IL 3h 52 66.3 .5 .5 .2 .0 53 66.2 23 '52* 26 66.1 .7 .0 25 66.0 1 1 2a 25 33 53 33 65.8 .8 .7 .1 .9 12 65.2 ‘12 22* 22 68.9 0 .9 .6 r‘fi st 68.3 _0 15 32 36 "" 15 63.9 - .h .8 .h 36 63.9 1 32 63.5 ‘ 03 62.1 03 05 61.2 '2 .2 55 61.1 05 SE’ 55" 5h 60.5 ‘3 .1 .8 .2 56 60.2 h 56 06 57.8 - 01 -.'* _.l_.,,__,.__...- _ .. -6 06 .5 ‘7J w v-—.—._-—..—_.-.oa~—— .I1‘-.‘I- ... .-.—. ~u----- I Footnotes for tables 6 to 10 inclusive Yield of standard 5% level of significance from the standard 1% level of significance from the standard “Ill Variety numbers Yields in even units (bushels, tables 6 & 7; percentage, table 8; and difference in bushels, tables 9 & 10) are shown in the left hand column and the decimal units are under the variety numbers *** Ranked according to decreasing yield, except in table 6 all rank yields are relative -19- Methods of comparing planting and harvesting techniques: Yield trial remainder mean squares for l9hh data were obtained by squaring standard errors (Method three) reported by Frey. Their corresponding degrees of freedom were determined by multiplying the number of squares in each trial by 20, which is the degrees of freedom of the remainder mean squares on a per block basis. Yield trial remainder mean squares for the 19h5 and l9h6 data obtained by method one analyses are used to compare with the 19bh remainder mean squares to indicate differences due to planting and harvest techniques. These comparisons are made by a direct F test between.the two remainder mean squares. Yield trial remainder mean squares of the l9h5 and l9h6 data are compared to give an indication of differences due to years. -20- PRESENTATION OF DATA AND DISCUSSION Methods of analysis: Table 11 shows that method 1 consistently gave lower remainder mean squares than did method 2. In three of the six county trials this difference was significant; these were Monroe 19h5, Monroe l9h6 and Ingham 19h5. Comparing methods 1 and h it will be noted that neither method is consistently lower; however method one is significantly lower in the Monroe 19h5, Monroe 1966, and Saginaw 19h6 trials. Comparing methods 1 and S will show that the remainder mean squares are very similar with no significant differences within any one trial. Comparing methods 1 and 6 gives the same results as comparing method 1 and h. This is to be expected as method h and 6 are the same except that the data used is slightly different. Comparing methods 2 and h shows that the remainder mean squares are nearly the same except in the Ingham l9h5 trial where method h is significantly lower. These methods are nearly the same, the difference being that method 2 deals with all varieties whereas method h deals only with the check-standard variety. Comparing methods 2 and 5 shows that with one exception, Ingham l9h6, method 5b, the remainder mean squares of method 5 were consistently lower than method 2. In three cases method 5 was significantly lower, these being Monroe l9h5, Monroe l9h6 and Ingham 19h5. It should be noted that comparing methods 2 and 5 gives the A - (1— same results as comparing methods 1 and 2. Comparing methods 2 and 6 gives the same results as comparing methods 2 and h. Since methods h and 6 are so nearly alike, methods 5 and 6 are compared. Methods 5a and 6a were calculated from the same data and methods Sb and 6b were calculated from the same data. Comparing methods 5a and Sb shows that there is no significant difference in the manner in which the checks and standards are paired for this method of analysis. Comparing methods 5a and 6a shows that method 5a gives significantly lower remainder mean squares in the Monroe l9h5 and Monroe l9h6 trials. These trials contain 7 and 9 squares respectively. A comparison of methods Sb and 6b gives the same results as 5a and 6a except that in the Hmroe 19115 trial the difference only approaches significance. When there are less than 7 squares in a trial, there is no apparent difference in the results of the two methods. Comparing methods 6a and 6b again shows there is no significant difference in the way the checks and standards are paired for analysis. Method 1 appears better than methods 2, h, and 6 which shows that in analyzing a trial, the difference in rows should be taken out by squares rather than taken out across the entire trial. There was no significant difference between methods 1 and S which indicates that it makes no difference whether all varieties are analyzed or just the check-standard variety is analyzed. -22. .mpmb mmmwpcmnm new mxoono means Amy Locomocm op Mademooom bovommmoo axon xoonu m Bong mcflmmwe poam oco * mm mm ma ma on em on no muospme pmopommwv on» ma pomflwpno Beboohm mo moopmoo gamma can mmnmsom some hopmflmaom mama oo.mw mm ma.mm mm wa.mm ma om.mm ma mm.bm mm mm.mm um. Hm.wH 00 mfi Mb ammme MH.NH a~.HH no.m Hm.ma ao.aa mo.em on.oH mfl mama as me new mm ea 5 OOH up mama mm.mm #:m mm.wm mm mm.om *JH aa.mm ma mm.mm *mm mm.mm pm ww.wH 00 mm mm ammawwm mw.oa m.ba 50.0N Hm.m Hw.ma wm.mm Om.ma m2 mama mm mm me me mm new one we ww.mm -.:m mH.om am.mm m~.mm 4w.mm mq.am m2 mama as me as am a: Ham 0.: MU monsofi mo.sm oe.mm .N.mm oo.mm am.:m Hw.om No.oN m2 mama be no mm mfimhdwnm mo mponpoz .nnmmm one madam» hp momhawcw .HH manna -23- Methods of ranking: Varieties which are grown in the same latin square can be compared with each other directly. This direct method of comparison is lost when comparing a variety grown in one square with a variety grown in another square. Such a comparison can be made only by comparing the two varieties to a third (standard) variety which is common to both squares. If a variety is significantly better than the standard in its square, it should remain significantly better than the standard when the varieties of the trial are ranked. When ranking the varieties by actual yield, table 6, it will be noted that although variety 16 remains significantly better varieties 26 and 35 are not shown as significantly better than.the standard when the entire trial is considered. Note that the standards in the different squares do not have comparable yields. When ranking the varieties by the add and subtract method, table 7, it will be noted that when considering the entire trial varieties l6 and 26 are significantly better than the standard. However, variety 35 is still considerably below the 5% significance level. This method has brought the square standard yields closer to the average standard yield for the trial. The low yield of the standard in square 30 has seriously penalized the position of variety 35. When ranking varieties by the P/S method, table 8, it will be noted.that this method places all the standards on the same line; however, the significance levels are still variable between squares. -gh- It would still be possible for a variety in square 50 to be significantly better than the standard and not show up significantly better in the trial; likewise it would be possible for a variety in square 30 to show up as significantly better in the trial yet not be significantly better than the standard in its square. ‘When ranking varieties by the difference in yield from the. standard variety, table 9, it will be found this method is subject to the same criticism as the P/S method. When ranking varieties by the corrected difference in yield from the standard variety, table 10, it will be noted that the standards of all squares have the same yield and that the significance levels of all squares are the same. This allows the investigator to say with the certainty of the significance level that any variety in the trial which is above this significance level is better in yield than the standard. When each square has the sane standard variety yield and the same significance levels, the varieties of the trial can be ranked without fear of false significance showing up or of true significance being concealed. Comparison of planting and harvesting techniques: The Ingham County trials are the only trials which are common to the three years l9hh, l9h5, and l9h6. The following are the remainder mean squares for Ingham County trials: 19th 19h5 19h6 MS df MS df MS df 81.36 160 16.b6 60 18.91 60 An F test of the above mean squares gives the following results: 25 -5- Years F value F value for significance 5% level 1% level 1988 a 1985 8.98 1.86 1.71 1988 a 1986 8.30 1.86 1.71 1985 a 1986 1.15 1.58 1.87 Considering the pooled remainder mean squares of the trials in the southern half of the state to be an estimate of the remainder mean square of the southern half of the state, the following pooled remainder mean squares may be compared to give an indication of the value of the different method of planting and harvesting. 1988 1985 1986 ms df us or as df 77.69 500 18.56 260 22.97 338 An F test of the pooled mean squares gives the following results: Years F value F value for significance 5% level 1% level 1988 a 1985 8.19 1.21 1.32 1988 a 1986 3.38 1.19 .28 1985 a 1986 1.23 1.28 1.35 The l9hh remainder mean squares are significantly higher than the l9h5 or l9h6 remainder mean squares. This shows that there was much more control on the yield trials in 1985 and 1986 than there was in l9hh. Since the method of planting and harvest was changed in l9h5 and continued in l9h6, there is a good indication that this change in technique has exercised more control on the yield trials enabling smaller differences in yield to be measured. This interpretation of the test of field technique is not clear out however, since it is confounded with years. Such things as different weather conditions from one year to the next, different fields for the trial from year to year, -26- difference due to possible disease epidemics, and different hired labor from year to year may have had some effect on the experimental control from year to year. The smaller F values between the l9h5 and 1986 mean squares than between the l9hh and l9h5 and the l9hh and l9h6 mean squares leads one to believe that the difference due to improved planting and harvest technique is real. -27- For this investigation there were available data from three hybrid corn trials grown in l9h5 and from three hybrid corn trials grown in l9h6. Data from six hybrid corn trials grown in l9hh were obtained from.Frey's (2) thesis. The investigation was carried on to find the method of analysis giving the lowest valid standard deviation for analyzing a series of 6 x 6 latin squares, to find a better method of ranking varieties in a yield trial, and to get an indication of the value of the method of planting and harvest used in l9h5 and l9h6 over the method used in l9hh. From the data presented in this paper, the following conclusions may be drawn: Method one, which analyzes the squares individually to Obtain an average mean square from which the trial standard deviation is extracted, in most cases gives a smaller standard deviation than the other methods of analysis except for method five. Method five is the same as method one except that it is an analysis of the check—standard variety whereas method one analyzes all the varieties in the squares. The standard deviations of methods one and five are very similar. Ranking varieties by a corrected difference from the yield of their standard allows the investigator to say, with the certainty of the significance level chosen, that all varieties with mean yields beyond the difference required for significance from the standard.by the trial standard deviation are significantly better. -28- The results indicate that the method of planting and harvesting put into use in l9h5 gives more experimental control than the method of planting and harvesting used in l9hh. -29- LITERATURE CITED (l) Down, E.E. Brown, H.M. Patten, A.J. Winter, O.B. and Coons, G.H., Investigations on Winter Wheats in Michigan. Mich. State College Tech. Bul. No. 88. 1928. (2) Frey, Kenneth J., A Comparison of Some Statistical Studies of Hybrid Corn Trials. Thesis for the Degree of M.S. Mich. State College. 1985. (3) Snedecor, George W., Statistical Methods. The Collegiate Press, Inc. 1986. IGAN STATE UNIVERSITY LIBR I AR es 1 49 MICH 3 1193 03085 4