Handling and analysis of production data

J.C.M. Trail and J. Durkin

1. Extraction of records and preparation of coding sheets
2. Entry of data into computer file
3. Validation of data
4. Calculation parameters
5. Statistical analyses
6. Interpretation
7. Peripheral studies linking statistical outputs with biological effects

Computer handling and analysis of smallstock productivity data involves a number of basic steps:

1. Extraction of relevant records from field data sheets and preparation of coding sheets

2. Entry of data into computer file

3. Validation of data, necessitating examination and correction

4. Calculation of parameters, construction of logical sub-classes for environmental effects, and preparation of files for analysis

5. Statistical analyses

6. Interpretation

7. Peripheral studies linking statistical outputs with biological effects.

In order to demonstrate these steps, records of birth and weaning weights of 88 lambs on 2 farms were analysed. These lambs were born during a three month lambing season and their individual sires were recorded. This small subset was treated as if it was a large block of legitimate data and all the individual steps in an analysis to determine environmental and genetic parameters were illustrated.

The SPSS package was used to validate the data, into which deliberate errors had been introduced; a simple program was written and used to construct an adjusted weaning weight and a pre-weaning daily liveweight gain; and Harvey's Least-Squares and Maximum Likelihood Program (LSML 76) was used to evaluate all possible environmental influences, and obtain least biased estimates of genetic parameters.

The environmental effects of station, month of birth, dam parity number, sex, and type of birth (single or twin) on the three traits birth weight, weaning weight adjusted to 4 months and daily liveweight gain from birth to weaning, were estimated. In the ease of genetic parameters, the heritabilities of, and the genetic correlations between the three traits could be estimated through a paternal half-sib analysis.

1. Extraction of records and preparation of coding sheets

Table 7 illustrates a typical lambing record sheet with records added daily as lambings occur. Each lamb was assigned a unique number at birth, its dam and sire numbers, sex and type of birth noted, and birth weight was recorded.

Table 7. Field lambing record sheet.

Date of lambing	Ewe No.	Lamb No.	Sire	Sex	Single/ twin	Birth weight (kg)	Comments
2-12-80	243	811	25		T	-	died at birth
2-12-80	243	812	25		T	2· 7
2-12-80	230	813	31		T	2· 7
2-12-80	230	814	31		T	-	died at birth
3-12-80	239	815	25		S	2· 8
3-12-80	240	816	29		S	2· 8
4-12-80	231	817	54		S	2· 4

Table 8 illustrates a weaning weight record sheet, produced once per month in this example, so that all lambs at weaning were between 4 and 5 months of age. The lamb number, its date of birth, sex, dam number, and actual weight were recorded.

Table 8. Weaning weight record sheet.

Lamb No.	Date of birth	sex	Dam No.	Weaning weight (kgs)	Weaning date
812	2/12/80		243	12· 2	1 May 1981
813	2/12/80		230	12· 2	"
815	3/12/80		239	12· 9	"
816	3/12/80		240	12· 9	"
817	4/12/80		231	11· 8	"

Table 9 lays out the coding sheets produced from the two field records, containing the information required for data checking and actual analyses. The station number, sire number, month of birth, type of birth, sex, end parturition number are used in identifying the environmental and genetic classes for the analysis. The date of birth, date of weaning and weaning weight are used in the construction of adjusted weaning weight and daily liveweight gain, which together with birth weight comprise the three traits for analysis.

Table 9. Coding sheet

2. Entry of data into computer file

Data entry would be either through punch cards or directly into core. Table 10 is a listing of the records entered; note from the 12th lamb onwards, lamb numbers and dam numbers have been omitted.

3. Validation of data

For checking and identification of errors, the SPSS package was used to produce relevant frequencies, cross tabulations and breakdowns. Table 11 lays out the basic information required by the SPSS package covering the variable list and labels (e.g. ST station number, LAMB lamb number, etc); the input format (e. g. fixed, field 1 = col 1, field 2 = cols 2 - 5 etc); the value labels (e. g. in sex, 1 = male, 2 = female, etc); and the first task name, frequencies of all relevant parameters (e. g. station, month of birth and year of birth in Table 12 and type of birth, sex and dam parity number in Table 13).

Tables 12 and 13 indicate the outputs from the frequency checks on station number, month and type of birth, sex, and dam parity. Obvious errors are that one lamb appears under a station code 3, one was born in August, one was born in 1979, one has 0 for type of birth, one has 0 for sex and one has 0 for dam parity number.

Table 10. Listing of records entered from coding sheet

1	1	813	230	46 2128022	27	2	0	1	581122
2	1	315	239	2532128011	28	2	0	1	581129
5	1	816	240	29 128011	28	2	0	1	581129
4	1	817	231	54 4088012	24	1	0	1	581118
5	1	818	244	42 5117922	25	1	0	1	481133
6	1	819	241	45 5128031	31	2	0	1	581120
7	1	820	238	54 71280 1	31	1	0	1	581128
8	1	821	242	25 811801	28	2	0	1	481121
9	1	823	252	29 81180119	28	1	0	1	481121
10	1	824	252	42 8108021	24		0	1	381124
11	1	825	237	42 9108012	30	3	0	1	381125
12	1	0	0	4510128012	28	1	0	1	581124
13	1	0	0	2511118012	26	1	0	1	881123
14	1	0	0	2511128021	29	2	0	1	580126
15	1	0	0	2911118012	26	1	0	1	481923
16	1	0	0	3111128021	29	2	0	1	581126
17	1	0	0	5413118022	29	2	0	1	481123
18	1	0	0	2314118011	33	1	0	1	481126
19	1	0	0	2914118011	33	2	0	1	481126
20	1	0	0	5414118011	32	2	0	1	481128
21	1	0	0	2317108022	22	2	0	1	381130
22	1	0	0	2517128012	23	1	0	1	581132
23	1	0	0	2917108022	22	2	0	1	381130
24	1	0	0	3117128012	23	1	0	1	581132
25	1	0	0	4217108011	32	2	0	1	351132
26	1	0	0	4517128011	29	1	0	1	581126
27	1	0	0	4520118012	23	2	0	1	481127
28	1	0	0	4221108012	26	1	0	1	381134
29	1	0	0	5421108022	25	1	0	1	381130
30	1	0	0	2322108011	31	1	0	1	381130
31	1	0	0	2922108011	31	1	0	1	381130
32	1	0	0	2523128011	28	1	0	1	581138
33	1	0	0	3123128011	28	1	0	1	581138
34	1	0	0	5423108021	30	1	0	1	381133
35	1	0	0	2324108012	25	1	0	1	381134
36	1	0	0	2924108012	25	1	0	1	381134
37	1	0	0	4224108011	27	1	0	1	381136
38	1	0	0	2325108011	26	2	0	1	381137
39	1	0	0	2925108011	26	2	0	1	381137
40	1	0	0	4526118021	29	2	0	1	481135
41	1	0	0	5429108011	29	2	0	1	381136
42	2	0	0	95 1128011	33	2	0	1	381136
43	2	3	3	97 1118011	27	1	0	1	381129
44	2	0	0	95 3128012	30	1	0	1	581117
45	2	0	0	87 4118012	28	1	0	1	481121
46	2	0	0	89 6128022	29	2	0	1	581119
47	2	0	0	95 7108011	29	2	0	1	381133
48	2	0	0	89 8128021	31	2	0	1	551122
49	2	0	0	96 8128012	36	1	0	1	581132
50	2	0	0	98 8128011	31	2	0	1	581130
51	2	0	0	87 9118011	22	1	0	1	481124
52	2	0	0	95 9128011	31	1	0	1	581125
53	2	0	0	8711108012	32	1	0	1	381126
54	2	0	0	8911128012	32	2	0	1	581125
55	2	0	0	9611128011	33	1	0	1	581118
56	2	0	0	9811118022	25	1	0	1	481134
57	2	0	0	8914128011	30	1	0	1	581131
58	2	0	0	9514118012	33	2	0	1	481120
59	2	0	0	9714108021	26	1	0	1	381137
60	2	0	0	9814128012	28	1	0	1	581118
61	2	0	0	9515118021	31	2	0	1	481123
62	2	0	0	9915118012	33	2	0	1	481119
63	2	0	0	9816128011	29	1	0	1	581123
64	2	0	0	8717108021	28	2	0	1	381131
65	2	0	0	9617118022	31	2	0	1	481122
66	2	0	0	9917118011	32	2	0	1	481121
67	2	0	0	9518118022	27	1	0	1	481126
68	2	0	0	9618118011	34	2	0	1	481122
69	2	0	0	9720108012	26	1	0	1	381128
70	2	0	0	8721108012	27	2	0	1	381133
71	2	0	0	9921108022	25	1	0	1	381124
72	2	0	0	9522108021	28	1	0	1	381128
73	2	0	0	9622108022	27	1	0	1	381126
74	2	0	0	9722108011	32	2	0	1	381123
75	2	0	0	9822118012	23	2	0	1	481128
76	2	0	0	8923128012	30	1	0	1	581133
77	2	0	0	9623108021	25	1	0	1	381127
78	2	0	0	8724108011	28	1	0	1	381136
79	2	0	0	9924108021	33	1	0	1	381126
80	2	0	0	9525108022	28	2	0	1	381129
81	2	0	0	8927118011	30	2	0	1	481119
82	2	0	0	9727108022	26	2	0	1	381119
83	2	0	0	9927108012	29	2	0	1	381128
84	2	0	0	9528108011	28	1	0	1	381127
85	2	0	0	9828108011	31	2	0	1	381130
86	2	0	0	9828118011	33	2	0	1	481128
87	2	0	0	9530108012	28	1	0	1	381132
88	3	0	0	25 2128022	27	2	0	1	581122

Table 11. Basic information required by SPSS package.

SPSS BATCH SYSTEM

SPSS FOR THE HP/3000 SPRING RELEASE, VERSION 9.1,

DEFAULT SPACE ALLOCATION...	ALLOWS FOR...	32 TRANSFORMATIONS
WORKSPACE	22752 BYTES	130 RECODE VALUES + LAG VARIABLES
TRANSPACE,	324, BYTES	520 IF/COMPUTE OPERATIONS

1 RUN NAME	ILCA 1982 DATA ANALYSIS SMALL RUMINANTS
2 FILE NAME	COURSE
3 INPUT MEDIUM	DISC(*IN)
4 PAGESIZE	NOEJECT
5 VARIABLE LIST	ST, LAMB, DAWN, SIREN, DB, MB, YB, TB, SEX, BWT, PARITY, DW, MW, YW, WWT
6
7 INPUT FORMAT	FIXED (F1.0, 3F4.0, 3F.2.0, 2F1.0, F3.1, F2.0, 4X, 3F2.0, F3.1)
8

ACCORDING TO YOUR INPUT FORMAT, VARIABLES ARE TO BE READ AS FOLLOWS

VARIABLE	FORMAT	RECORD	COLUMNS
ST	F 1.0	1	1-	1
LAMB	F 4.0	1	2-	5
DAMN	F 4.0	1	6-	9
SIREN	F 4. 0	1	10-	13
DB	F 2.0	1	14-	15
MB	F 2.0	1	16-	17
YB	F 2.0	1	18-	19
TB	F 1.0	1	20-	20
SEX	F1.0	1	21-	21
BWT	F 3.1	1	22-	24
PARITY	F 2.0	1	25-	26
DW	F 2.0	1	31-	32
MW	F 2.0	1	33-	34
YW	F 2.0	1	35-	36
WWT	F 3.1	1	37-	39

THE INPUT FORMAT PROVIDES FOR 15 VARIABLES. 15 WILL BE READ
IT PROVIDES FOR 1 RECORDS ("CARDS") PER CASE. MAXIMUM OF 39 "COLUMNS" ARE USED ON A RECORD).

9	VAR LABELS	ST, STATION/
10		LAMB, LAMB NUMBER/
11		DAMN, DAM NUMBER/
12		SIREN, SIRE NUMBER/
13		DB, DAY OF BIRTH/
14		MB, MONTH OF BIRTH/
15		YB, YEAR OF BIRTH/
16		TB, TYPE OF BIRTH/
17		SEX, SEX/
18		BWT, BIRTH WEIGHT/
19		PARITY, DAM PARITY NUMBER/
20		DW, WEANING DAY/
21		MW, WEANING MONTH/
22		YW, WEANING YEAR/
23		WWT, WEANING WEIGHT/
24	VALUE LABELS	SEX (1) MALE (2) FEMALE/
25		TB(1) SINGLE (2) TWIN (3) TRIPLETS/
26		MB, MW (1) JANUARY (2) FEBRUARY (3) MARCH (4) APRIL
27		(5) MAY (6) JUNE (7) JULY (8) AUGUST (9) SEPTEMBER
28		(10) OCTOBER (11) NOVEMBER (12) DECEMBER/
29	TASK NAME	FREQUENCIES ALL RELEVANT PARAMETERS
30	FREQUENCIES	GENERAL = ST, SIREN, DB, MB, YB, TB, SEX, PARITY,
31		DW, MW, YW
GIVEN WORKSPACE ALLOWS FOR 1253 VALUES AND 437 LABELS PER VARIABLE = FOR 'FREQUENCIES'
AFTER READING		88 CASES FROM SUBFILE COURSE	END OF DATA WAS ENCOUNTERED ON LOGICAL UNIT # 8

Table 12. SPSS frequencies for station, month of birth and year of birth.

ILCA 1982 DATA ANALYSIS SMALL RUMINANTS
FREQUENCIES ALL RELEVANT PARAMETERS
FILE COURSE (CREATION DATE = 12/13/82)
ST	STATION
CATEGORY LABEL	CODE	ABSOLUTE FREQ (PCT)	RELATIVE FREQ (PCT)	ADJUSTED FREQ (PCT)	CUM FREQ (PCT)
	1.	41	46.6	46.6	46.6
	2.	46	52.3	52.3	98.9
	3.	1	1.1	1.1	100.0
	TOTAL	88	100.0	100.0
VALID CASES	88	MISSING CASES		0
MB	MONTH OF BIRTH
CATEGORY LABEL	CODE	ABSOLUTE FREQ	(RELATIVE FREQ PCT)	ADJUSTED FREQ (PCT)	CUM FREQ (PCT)
AUGUST	8.	1	1.1	1.1	1.1
OCTOBER	10.	35	39.8	39.8	40.9
NOVEMBER	11.	25	28.4	28.4	69.3
DECEMBER	12.	27	30.7	30.7	100.0
TOTAL	88	100.0	100.0
VALID CASES	88	MISSING CASES		0
YB	YEAR OF BIRTH
CATEGORY LABEL	CODE	ABSOLUTE FREQ	RELATIVE FREQ (PCT)	ADJUSTED FREQ (PCT)	CUM FREQ (PCT)
	79.	1	1.1	1.1	1.1
	80.	87	98.9	98.9	100.0
	TOTAL	88	100.0	100.0
VALID CASES	88	MISSING CASES		0

Table 13. SPSS frequencies for type of birth, sex and dam parity number.

ILCA 1982 DATA ANALYSIS SMALL RUMINANTS
FREQUENCIES ALL RELEVANT PARAMETERS
FILE COURSE (CREATION DATE = 12/13/82)
TB	TYPE OF BIRTH
CATEGORY LABEL	CODE	ABSOLUTE FREQ	RELATIVE FREQ (PCT)	ADJUSTED FREQ (PCT)	CUM FREQ (PCT)
	0.	1	1.1	1.1	1.1
SINGLE	1.	59	67.0	67.0	68.2
TWIN	2.	27	30.7	30.7	98.9
TRIPLETS	3.	1	1.1	1.1	100.0
	TOTAL	88	100.0	100.0
VALID CASES	88	MISSING CASES		0
SEX	SEX
CATEGORY LABEL	CODE	ABSOLUTE FREQ	RELATIVE FREQ (PCT)	ADJUSTED FREQ (PCT)	CUM FREQ (PCT)
	0.	1	1.1	1.1	1.1
MALE	1.	47	53.4	53.4	54.5
FEMALE	2.	40	45.5	45.5	100.0
	TOTAL	88	100.0	100.0
VALID CASES	88	MISSING CASES		0
PARITY	DAM PARITY NUMBER
CATEGORY LABEL	CODE	ABSOLUTE FREQ	RELATIVE FREQ (PCT)	ADJUSTED FREQ (PCT)	CUM FREQ (PCT)
	0.	1	1.1	1.1	1.1
	1.	45	51.1	51.1	52.3
	2.	41	46.6	46.6	98.9
	3.	1	1.1	1.1	100.0
	TOTAL	.88	100.0	100.0
VALID CASES	88	MISSING CASES		0

The programme lists the identification numbers of the anomolous types, for reference back to the coding sheets and correction. Acceptable ranges for parameters can also be indicated, so that, for example, lambs with birth weights below 1 kg and over 5 kg might be listed.

Table 14 lists a crosstabulation requested between sire number and month of birth of lamb. In all genetic analysis it is vital to cheek that there is no confounding of time with use of individual sires, or apparent genetic effects may actually be time period effects. E interaction effects are to be estimated it is essential to identify any subcells with missing values before commencing the main analyses, and crosstabulations are a useful method.

Table 15 lists an example of a breakdown, in this ease birth weight by sire number, both to give an indication of the possible importance of sire effects and pinpoint any gross data errors (e. g. sire 29).

After adjustment of all errors, a rerun of SPSS confirms that all corrections have actually been carried out. Table 16 indicates the corrected picture of station frequencies from Table 12.

Table 16. SPSS frequencies for station, after data correction.

ILCA 1982 DATA ANALYSIS SMALL RUMINANTS
	FREQUENCIES ALL RELEVANT PARAMETERS
FILE COURSE (CREATION DATE = 12/13/82)
ST		STATION
CATEGORY LABEL		CODE	ABSOLUTE FREQ	RELATIVE FREQ (PCT)	ADJUSTED FREQ (PCT)	CUM FREQ(PCT)
		1.	42	47.7	47.7	47.7
		2.	46	52.3	52.3	100.0
		TOTAL	88	100.0	100.0
VALID CASES		88	MISSING CASES		0

Table 17 is a listing of the corrected records and should be compared with the original listing in Table 10.

Sorting of a file is very often required before analyses, and Table 18 lists the records after use of a standard sort program to arrange their sequence on sire number within station. Thus the order is progeny of sires 23 to 54 within station 1, followed by progeny of sires 87 to 99 within station 2.

Table 14. SPSS crosstabulation between month of birth and sire number.

Table 15. SPSS breakdown of birth weight by sire number.

40 *SELECT IF	(BWT NE 0)
41 TASK NAME	AVERAGE BWT WITHIN SIRES
42 BREAKDOWN	TABLES = BWT BY SIREN/

DESCRIPTION OF SUBPOPULATION
CRITERION VARIABLE BWT				BIRTH WEIGHT
	BROKEN DOWN BY SIREN			SIRE NUMBER
VARIABLE		CODE	VALUE LABEL	SUM	MEAN	STD DEV	VARIANCE	N
FOR ENTIRE POPULATION				340.4000	3.8682	9.5942	92.0484	(88)
SIREN		23.		13.7000	2.7400	.4506	.2030	(5)
SIREN		25.		18.9000	2.7000	.2000	.0400	(7)
SIREN		29.		111.9000	13.9875	31.8469	1014.2270	(8)
SIREN		31.		8.0000	2.6667	.3215	.1033	(3)
SIREN		42.		16.4000	2.7333	.3077	.0947	(6)
SIREN		45.		14.0000	2.8000	.3000	.0900	(5)
SIREN		46.		2.7000	2.7000	.0000	.0000	(1)
SIREN		54.		20.0000	2.8571	.2992	.0395	(7)
SIREN		87.		16.5000	2.7500	.3209	.1030	(6)
SIREN		89.		18.2000	3.0333	.1033	.0107	(6)
SIREN		95.		32.6000	2.9636	.2111	.0445	(11)
SIREN		96.		21.7000	3.1000	.5873	.1500	(7)
SIREN		97.		13.7000	2.7400	.2608	.0680	(5)
SIREN		98.		16.9000	2.8167	.3710	.1377	(6)
SIREN		99.		15.2000	3.0400	.3435	.1180	(5)
	TOTAL CASES = 88
ILCA 1982 DATA ANALYSIS SMALL RUMINANTS					MON, DEC 13, 1982, 1:50 PM PAGE 27
	AVERAGE BWT WITHIN SIRES
TRANSPACE REQUIRED.. 100 BYTES
	1 TRANSFORMATIONS
	0 RECODE VALUES + LAG VARIABLES
	3 IF/COMPUTE OPERATIONS
CPU TIME REQUIRED 2.57 SECONDS

Table 17. Listing of corrected records.

1	1	0	0	25 2128022	27	2	0	1	581122
2	1	0	0	31 2128022	27	2	0	1	581122
3	1	0	0	25 3128011	28	2	0	1	581129
4	1	0	0	29 3128011	28	2	0	1	581129
5	1	0	0	54 4128012	24	1	0	1	581118
6	1	0	0	42 5118022	25	1	0	1	481133
7	1	0	0	45 5128011	31	2	0	1	581120
8	1	0	0	54 7128011	31	1	0	1	581128
9	1	0	0	25 8118011	28	2	0	1	481121
10	1	0	0	29 8118011	28	1	0	1	481121
11	1	0	0	42 8108021	24	1	0	1	381124
12	1	0	0	42 9108012	30	2	0	1	381125
13	1	0	0	4510128012	28	1	0	1	581124
14	1	0	0	2511118012	26	1	0	1	481123
15	1	0	0	2511128021	29	2	0	1	581126
16	1	0	0	2911118012	26	1	0	1	481123
17	1	0	0	3111128021	29	2	0	1	581126
18	1	0	0	5413118022	29	2	0	1	481125
19	1	0	0	2314118011	33	1	0	1	481126
20	1	0	0	2914118011	33	2	0	1	481126
21	1	0	0	5414118011	32	2	0	1	481128
22	1	0	0	2317108022	22	2	0	1	381130
23	1	0	0	2517128012	23	1	0	1	581132
24	1	0	0	2917108022	22	2	0	1	381130
25	1	0	0	3117128012	23	1	0	1	581132
26	1	0	0	4217108011	32	2	0	1	381132
27	1	0	0	4517128011	29	1	0	1	581126
28	1	0	0	4520118012	23	2	0	1	481127
29	1	0	0	4221108012	26	1	0	1	381134
30	1	0	0	5421108022	25	1	0	1	381130
31	1	0	0	2322108011	31	1	0	1	381130
32	1	0	0	2922108011	31	1	0	1	381130
33	1	0	0	2523128011	28	1	0	1	581138
34	1	0	0	3123128011	28	1	0	1	581138
35	1	0	0	5423108021	30	1	0	1	381133
36	1	0	0	2324108012	25	1	0	1	381134
37	1	0	0	2924108012	25	1	0	1	381134
38	1	0	0	4224108011	27	1	0	1	381136
39	1	0	0	2325108011	26	2	0	1	381137
40	1	0	0	2925108011	26	2	0	1	381137
41	1	0	0	4526118021	29	2	0	1	481135
42	1	0	0	5429108011	29	2	0	1	381136
43	2	0	0	95 1128011	33	2	0	1	581133
44	2	0	0	97 1118011	27	1	0	1	381129
45	2	0	0	95 3128012	30	1	0	1	581117
46	2	0	0	87 4118012	28	1	0	1	481121
47	2	0	0	89 6128022	29	2	0	1	581119
48	2	0	0	95 7108011	29	2	0	1	381133
49	2	0	0	89 8128021	31	2	0	1	581122
50	2	0	0	96 8128012	36	1	0	1	581132
51	2	0	0	98 8128011	31	2	0	1	581130
52	2	0	0	87 9118011	22	1	0	1	481124
53	2	0	0	95 9128011	31	1	0	1	581125
54	2	0	0	8711108012	32	1	0	1	381126
55	2	0	0	8911128012	32	2	0	1	581128
56	2	0	0	9611128011	33	1	0	1	581118
57	2	0	0	9811118022	25	1	0	1	481134
58	2	0	0	8914128011	30	1	0	1	581131
59	2	0	0	9514118012	33	2	0	1	481120
60	2	0	0	9714108021	26	1	0	1	381137
61	2	0	0	9814128012	28	1	0	1	581118
62	2	0	0	9515118021	31	2	0	1	481123
63	2	0	0	9915118012	33	2	0	1	481119
64	2	0	0	9816128011	29	1	0	1	581123
65	2	0	0	8717108021	28	2	0	1	381131
66	2	0	0	9617118022	31	2	0	1	481122
67	2	0	0	9917118011	32	2	0	1	481121
68	2	0	0	9518118022	27	1	0	1	481126
69	2	0	0	9618118011	34	2	0	1	481122
70	2	0	0	9720108012	26	1	0	1	381128
71	2	0	0	8721108012	27	2	0	1	381133
72	2	0	0	9921108022	25	1	0	1	381124
73	2	0	0	9522108021	28	1	0	1	381128
74	2	0	0	9622108022	27	1	0	1	381126
75	2	0	0	9722108011	32	2	0	1	381123
76	2	0	0	9822118012	23	2	0	1	481128
77	2	0	0	8923128012	30	1	0	1	581133
78	2	0	0	9623108021	25	1	0	1	381127
79	2	0	0	8724108011	28	1	0	1	381136
80	2	0	0	9924108021	33	1	0	1	381126
81	2	0	0	9525108022	28	2	0	1	381129
82	2	0	0	8927118011	30	2	0	1	481119
83	2	0	0	9727108022	26	2	0	1	381119
84	2	0	0	9927108012	29	2	0	1	381128
85	2	0	0	9528108011	28	1	0	1	381127
86	2	0	0	9628108011	31	2	0	1	381130
87	2	0	0	9028118011	33	2	0	1	481128
88	2	0	0	9530108012	28	1	0	1	381132

Table 18. Listing of corrected records sorted by sire number within station.

1	1	0	0	2325108011	26	2	0	1	381137
2	1	0	0	2324108012	25	1	0	1	381134
3	1	0	0	2322108011	31	1	0	1	381130
4	1	0	0	2317108022	22	2	0	1	381130
5	1	0	0	2314118011	33	1	0	1	481126
6	1	0	0	2511118012	26	1	0	1	481123
7	1	0	0	25 8118011	28	2	0	1	481121
8	1	0	0	25 3128011	28	2	0	1	581129
9	1	0	0	2523128011	28	1	0	1	581138
10	1	0	0	2517128012	23	1	0	1	581132
11	1	0	0	2511128021	29	2	0	1	581126
12	1	0	0	25 2128022	27	2	0	1	581122
13	1	0	0	2925108011	26	2	0	1	381137
14	1	0	0	2924108012	25	1	0	1	381134
15	1	0	0	2922108011	31	1	0	1	381130
16	1	0	0	2917108022	22	2	0	1	381130
17	1	0	0	2914118011	33	2	0	1	481126
18	1	0	0	2911118012	26	1	0	1	481123
19	1	0	0	29 8118011	28	1	0	1	481121
20	1	0	0	29 3128011	28	2	0	1	581129
21	1	0	0	3123128011	28	1	0	1	581138
22	1	0	0	3117128012	23	1	0	1	581132
23	1	0	0	3111128021	29	2	0	1	581126
24	1	0	0	31 2128022	27	2	0	1	581122
25	1	0	0	4224108011	27	1	0	1	381136
26	1	0	0	4221108012	26	1	0	1	381134
27	1	0	0	4217108011	32	2	0	1	381132
28	1	0	0	42 9108012	30	2	0	1	381126
29	1	0	0	42 8108021	24	1	0	1	381124
30	1	0	0	42 5118022	25	1	0	1	481133
31	1	0	0	4526118021	29	2	0	1	481135
32	1	0	0	4520118012	23	2	0	1	481127
33	1	0	0	4517128011	29	1	0	1	581126
34	1	0	0	4510128012	28	1	0	1	581124
35	1	0	0	45 5128011	31	2	0	1	581120
36	1	0	0	5429108011	29	2	0	1	381136
37	1	0	0	5423108021	30	1	0	1	381133
38	1	0	0	5421108022	25	1	0	1	381130
39	1	0	0	5414118011	32	2	0	1	481128
40	1	0	0	5413118022	29	2	0	1	481123
41	1	0	0	54 7128011	31	1	0	1	581128
42	1	0	0	54 4128012	24	1	0	1	581118
43	2	0	0	8724108011	28	1	0	1	381136
44	2	0	0	8721108012	27	2	0	1	381133
45	2	0	0	8717108021	28	2	0	1	381131
46	2	0	0	8711108012	32	1	0	1	381126
47	2	0	0	87 9118011	22	1	0	1	481124
48	2	0	0	87 4118012	28	1	0	1	481121
49	2	0	0	8927118011	30	2	0	1	481119
50	2	0	0	8923128012	30	1	0	1	581133
51	2	0	0	8914128011	30	1	0	1	581131
52	2	0	0	8911128012	32	2	0	1	581128
53	2	0	0	89 8128021	31	2	0	1	581122
54	2	0	0	89 6128022	29	2	0	1	581119
55	2	0	0	95 7108011	29	2	0	1	381133
56	2	0	0	9530108012	28	1	0	1	381132
57	2	0	0	9528108011	28	1	0	1	381127
58	2	0	0	9525108022	28	2	0	1	381129
59	2	0	0	9522108021	28	1	0	1	381128
60	2	0	0	9518118022	27	1	0	1	481126
61	2	0	0	9515118021	31	2	0	1	481123
62	2	0	0	9514118012	33	2	0	1	481120
63	2	0	0	95 9128011	31	1	0	1	581125
64	2	0	0	95 3128012	30	1	0	1	581117
65	2	0	0	95 1128011	33	2	0	1	581133
66	2	0	0	9628108011	31	2	0	1	381130
67	2	0	0	9623108021	25	1	0	1	381127
68	2	0	0	9622108022	27	1	0	1	381126
69	2	0	0	9618118011	34	2	0	1	481122
70	2	0	0	9617118022	31	2	0	1	481122
71	2	0	0	9611128011	33	1	0	1	581118
72	2	0	0	96 8128012	36	1	0	1	581132
73	2	0	0	97 1118011	27	1	0	1	381129
74	2	0	0	9720108012	26	1	0	1	381128
75	2	0	0	9722108011	32	2	0	1	381123
76	2	0	0	9727108022	26	2	0	1	381119
77	2	0	0	9714108021	26	1	0	1	381137
78	2	0	0	9811118022	25	1	0	1	481134
79	2	0	0	9828118011	33	2	0	1	481128
80	2	0	0	9822118012	23	2	0	1	481128
81	2	0	0	9816128011	29	1	0	1	581123
82	2	0	0	9814128012	28	1	0	1	581118
83	2	0	0	98 8128011	31	2	0	1	581130
84	2	0	0	9927108012	29	2	0	1	381128
85	2	0	0	9924108021	33	1	0	1	381126
86	2	0	0	9921108022	25	1	0	1	381124
87	2	0	0	9917118011	32	2	0	1	481121
88	2	0	0	9915118012	33	2	0	1	481119

4. Calculation parameters

Table 19 lays out a simple program to calculate for each lamb the weaning weight adjusted to 120 days and the daily liveweight gain from birth to weaning. Lines 19 to 29 of Table 19 show the use of a function NDAY to calculate the number of days between the lamb's birth date and weaning date; the subtraction of birth weight from weaning weight to give total growth; division by the number of days to give the daily liveweight gain; conversion to grams; and multiplication of daily liveweight gain by 120 and addition of birth weight to give adjusted 4 month weaning weight.

Table 20 is a listing of the sorted records with the adjusted weaning weight and daily liveweight gain indicated in the last two fields, each of 3 digits (e. g. the first lamb has an adjusted weaning weight of 130 kg x 10 and a daily liveweight gain of 87 am).

5. Statistical analyses

The general model these data fit is-:

where

is the station set of fixed effects
are the sire set of random nested effects
are all the other fixed sets of effects and their interactions (month, parity, sex, birth type, station × month). Interactions of random and fixed effects are assumed to be unimportant.

Table 21 indicates the parameter cards required for the analysis (Harvey, 1977).

The distribution of classes and subclass numbers and the overall means and standard deviations for the three traits are listed by the program (Table 22), and the combined least-squares analyses of variance are laid out (Table 23).

6. Interpretation

Taking birthweight as an example, Table 23 indicates that parity of dam and sex (P <. 01) and station, month and birth type (P <. 05) had statistically significant effects, while sires within station and station x month interaction had no significant effects.

Table 24 lists the constants, least squares means and standard errors. Taking birthweight as the example, lambs from station 2 were 0.20 kg or 7% heavier than those from station 1; lambs born in December were 0.24 or 9% heavier than those born in October, etc. The environmental effects on the three traits can thus be quantified and compared.

Table 19. Program to calculate adjusted weaning weight and daily liveweight gain.

1			$CONTROL USLINIT, FILE=1-8
2			$INTEGER *4
3				PROGRAM ADDWWT
4	C
5	C		TO CALCULATE ADJUSTED WEANING WEIGHT (120 DAYS)
6	C		AND DAILY GROWTH (GRAMS) BIRTH TO WEANING
7	C
8			COMMON IN(20), ID1 (3), ID2(3)
9	1		FORMAT (I1, 3I4, 3I2, 2I1, I3, 12, I4, 3I2, I3, 3I2, I3)
10			INUM=0
11		18	CONTINUE
12			READ (2, 1, END=999) (IN(K),K=1,20)
13			DO 13 K=1,3
14			L=K+4
15			M=K+12
16			ID1 (K)=IN(L)
17			ID2 (K)=IN(M)
18	13		CONTINUE
19			IDS=NDAY (ID1, ID2)
20			A=IDS
21			B=IN(10)
22			C=IN(16)
23			D=(C-B)/A
24			G=100*D
25			IN (18)=IFIX (G)
26			E=D*120
27			E=E + B
28			IN (17)=IFIX (E)
29			WRITE (1,2) (IN(K),K=1,18)
30	2		FORMAT (I1, 3I4, 3I2, 2I1, I3, I2, I4, 3I2, I3, 2I3, 2I2, 2I3)
31			GO TO 18
32	999		CONTINUE
33			STOP
34			END
35			INTEGER FUNCTION NDAY (A,B)
36			INTEGER A(3), NOD (13), ANS, Y1, Y2, B(3)
37			DATA NOD/365, 334, 306, 275, 245, 214, 184, 153, 122, 92, 61,31, 0/
38			IF (A(2). GE. 1. AND. A(2). LE. 12. AND. 8(2). GE. 1. AND. B(2). LE. 12.
39		1	AND. A(1).GT. 0. AND. B(l). GT. 0) GO TO 1
40	100		CONTINUE
41			NDAY= -NOD(1)
42			RETURN
43			1 CONTINUE
44			Y1=A (3)
45			Y2=B (3)
46			IF (Y1. LT. 100. AND. Y2. LT. 100) GO TO) 101
47			IF (Y1. GE. 100. AND. Y2. GE. 100) GO TO 102
48			IF (Y1. GE. 100) GO TO 103
49			Y1=(Y2/100)*100+Y1
50			GO TO 102
51	103		CONTINUE
52			Y2=(Y1/100)*100+Y2
53			GO TO 102
54	101		CONTINUE
55			Y1=Y1+1900
56			Y2=Y2+1900
57	102		CONTINUE
58			M1=A(2)
59			M2=B(2)
60			LEAP1=0
61			LEAP2=0
62			IF (M1. LE. 2. AND. ((MOD(Y1,4). EQ.0. AND. MOD (Y1,100). NE.0)
63		1	OR. MOD (Y1, 400). EQ. 0)) LEAP 1=1
64			IF (M2. LE. 2. AND. ((MOD (Y2, 4).EQ. 0. AND. MOD (Y2,100). NE.0)
65		1	OR. MOD (Y2,400). EQ.0)) LEAP 2=1
66	C
67	C
68	C
69			IT1=NOD (M1)-NOD (M1+1)
70			IT2= IT1+LEAP1
71			JT1=NOD (M2) -NOD (M2+1)
72			JT2=JT1+LEAP2
73			IF ((A(1). GT. IT1. AND. M1. NE.2). OR. (A(1). GT. IT2. AND. M1. EQ.2)
74		1	OR. (B(1). GT. 0T1. AND. M2. NE. 2). OR. (B(1). GT. JT2. AND. M2. EQ. 2)
75		2	GO TO 100
76	C
77			ANS=NOD (M1) - A(1) -NOD(M2)+B(1)+LEAP1 - LEAP2
78			IF (Y1. LE. Y2) GO TO 2
79			ANS=-ANS
80			M1=Y1
81			Y1=Y2
82			Y2=M1
83	2		CONTINUE
84			Y1=Y1+1
85			IF (Y1. GT. Y2) GO TO 4
86			DO 3 M1=Y1, Y2
87			ANS=ANS+365
88			IF(MOD (M1, 400). EQ. 0. OR. (MOD(M1,4).EQ. 0. AND. MOD(M1,100).
89		1	NE. 0)) ANS=ANS+1
90	3		CONTINUE
91	4		CONTINUE
92			NDAY=IABS (ANS)
93			RETURN
94			END