Aspects of Diversity in Multiple Comparisons: A Case Study of Selected Hybrid and Local Cows in Gezira State, Sudan (19692000)
Bushara MO A and Ibrahim F S
Published on: 20191122
Abstract
Livestock is an important branch of economic in Sudan. The main objective of this study is to give an overview of post hoc multiple comparisons to discuss the difference between the hybrid and local cows on Calving Interval and Total Milk. Secondary data source of 162 cows collected from ElNishishiba and ElBashair Dairy Farm are used. The study’s results are that: the factors: farm and type of cow have significant effect on tow traits. Parity and interaction between age group*parity have significant effect on Calving Interval but no effects on Total milk. The factor type*age group has significant effect on Total Milk while no effects on Calving Interval. The factors, age group, type*farm, and type*parity have nonsignificant effect on tow traits. LSD test is the best one to discuss the difference between local and hybrid cows. Kenana and Butana are the same on tow traits. The hybrid 50% cow is differing from Kenana, Butana and hybrid 75% but it same with hybrid 62.5% and hybrid 87.5%, no difference between hybrid 62.5% and hybrid 87.5% on tow traits. Parity seven, eight and nine are same on two traits. This finding supports that to keep the contented of cow’s herd to be between local cow and exotic blood 50% and keep cow until parity six.
Keywords
Cow breed; Post HOC tests; Calving interval; Milk yield; SudanIntroduction
Livestock is an important branch of economics in Sudan. Sudan has 30 million cows, which distributed among states and middle states have 30% of cows. Statistics play an important role in knowledge of the difference between the hybrid and local cows. Analysis of Variance and post hoc tests are the better statistical techniques to study the difference between the hybrid and local cows. Analysis of Variance (ANOVA) is common statistical analysis to know if there is difference between more than two groups. ANOVA tells that groups are different but does not tell which group is giving significant difference from the other groups; then more tests needed to know where the difference is from. For some research purposes, this might be sufficient. Post hoc tests have been designed for analysing and understanding the situation of null hypothesis rejection that all groups are same, they are usually done after the collection of data and ANOVA F test of hypothesis that all groups' means are equal is not significant thus, the null hypothesis is rejected. Rejection of null hypothesis required more tests to distinguish between groups in the study, which are the same, and which are different also, the differences between the groups are significant or not. Post hoc procedures give vulnerable to statistical decision when they are used in wrong way. If there are Multiple Comparisons, there is warring about type I error and how can control error rate while keeping the test has high power? There were many studies on hybrid cow but the data did not satisfy the assumptions of ANOVA table, researchers were located in using alpha in wrong way in multiple comparisons and the result statistically were wrong.
Problem
Since the cows are important in the economy of the Sudan and there were many studies on hybrid cow but the data did not satisfy the assumptions of post hoc procedures to measuring statistical significant differences between local and hybrid cows based on Calving Interval, Total Milk. Post Hoc Procedures may be the right way to examine this case. It’s appropriate to carry this study to correct the situation.
Research Questions
 Whether post hoc procedure has controlled the error rate and high power test at the same time?
 Whether post hoc procedure has good confidence interval?
 Whether the best post hoc procedure is powerful to describe the difference between hybrid and local cows?
 Whether all hybrid breeds are being same in Calving Interval and Total Milk?
 Are hybrid cows best than local cows in Calving Interval and Total Milk?
Objective
To test whether post hoc procedures can be used in a right way to help non statistical researchers to choose the best post hoc procedure to support their ANOVA’s results throw actual data.
Specific objective
 To give new approach to common post hoc procedures.
 To control disadvantages of post hoc procedures.
 To find the ways of differences between post hoc and the interpreted differences statistically.
 To build scientific information about hybrid cows under condition of environment of Gezira state.
 To explain the calving interval and total milk yield for hybrid and local cows and which of them is the best?
Justification
 Posthoc analyses are required when a significant relationship has been found between the dependent variable and independent variables on the study which have more than two levels. This allows researchers to ascertain to which levels, the significance can be ascribed too.
 Most of the researchers are thinking that the pvalue in ANOVA enough to give information that the groups are different, if they are testing multiple hypotheses of single sample of data, then they made inflate of type I error.
 Researchers must have knowledge about how to use post hoc procedures correctly in simple way to support their result of ANOVA, and they must get help about how to get an optimum of post hoc procedure through controlling advantages and disadvantages of post hoc procedure.
Literature Review
Sudan is one of agricultural country that contributes to national income by 30.6% about 90% of the Livestock come from traditional sector where Livestock have great social economic importance. Sudan is considered one of the richest Arab and African countries with its animal wealth. Livestock (cows, goats….e.t.c?) are estimated with about 103 million heads and 30 millions cows. Animal wealth contribute to the Sudanese economy, providing food security and contributing to income. Sudanese cows belong to the Asian Zebu cattle and are mixed with some African breeds in addition to the imported pure breeds and its special facets, the Friesian with the Butana and the Kenana, explained [12]. In Sudan, the rural communities own 80% of the livestock and the nomadic tribes own 90% of the rural holdings with livestock playing a central role in their livelihoods. Attempts to infuse exotic improved blood into Sudanese dairy cattle population led in some cases to the extinction or nearextinction of the best local types of cattle (Butana and Kenana) in some areas of the country. Through experience, many herdsmen have come to understand that the best results are obtained by crossing the best local cattle (usually Butana and Kenana) with the exotic breeds (usually Friesian). This has led to widespread concern over the fate of Butana and Kenana types and to efforts for conservation of these strains for both present and future use. This concern is motivated by the fact that the genotypes of the improved indigenous breeds may be required to upgrade or replace low producing cattle in harsh nomadic environments where exotic cattle cannot survive. Another cause for concern is the fact that the directions of future demand cannot be predicted with any certainty.
A Kenana cattle is considered as one of the most important dairy cattle breeds in the Sudan. They represent about 83% of the total cattle in Sudan spread in western bank of Blue Nile on the region from Sennar in the north to A’lli Nile States in South they have dual purposes milk and beef on the first milk production about 6.6 to 7.9 kg per day and lactation length 244273 days, age at first calving 38.443.4 month on high 51 months, calving interval is 368432 days and pregnancy length is 283 days.
Butana cattle are found in the Butana plain in the central Sudan, between the Blue Nile and Atbara Rivers. The breed is known as good milk producer in a rather harsh climate. They represent about 8.7% of the total of cattle in Sudan in tringle bounded by in East Atbara River, in western Blue Nile, Nile River and south of the line 14^{?} north. The location of this breed called Sahel el Butana. Milk yield 5.5 to 7.4 kg per day and lactation length 267 days, age at first calving 50.3 months to high 51 months. Analysis of Variance: The Analysis of Variance (ANOVA) is general statistical technique. It is appropriate procedure for testing the equality of several means. The ANOVA approach is partitioning and analyzing the variation in continuous response variable (study variable) into unexplained (experimental error) and explained (treatments) by one or more categorical predicators called factors. ANOVA is probably the most useful technique in the field of statistical inference. However; the analysis of variance has a much wider application. Explained [34]. The categories of each factor are groups or experimental treatments or levels and the focus is often comparing response variable means between groups. Generally, the main aims of Anova:
 To examine the relative contribution of different sources of variation to the total amount of variability in the response variable.
 To test the null hypothesis H_{0} that population groups or treatments means are equal.
The assumptions of ANOVA for estimating parameters and testing hypotheses depended on
 The sample must be chosen randomly.
 The data has normality distribution this made reliability of estimators and decision based on tests hypotheses.
There are two tests to diagnosis normality
 KolomogorovSimanov test for small samples.
 Shapiro and Wilk that is comparatively quite sensitive to wide range departures from normality such as skewed kurtosis of the distribution.
 Barrlett’s test.
3Ahomogeneityofvariance test that is less dependent on the assumption of normality than most tests. The variance must be homogeneity or equal for all groups and tested with many procedures to test homogeneity like:
 Hartley’s involving the ration of largest to the smallest of the variance within groups.
 Cochran’s test involving the ration of largest to the sum of the variances.
 Leveno test: checks for homogeneityof variances and the null hypothesis is that all variances are equal.
To solve the heterogeneity is to use the transformation of data and find suitable form. The number of the factors that contain in the experiment determine the classification of ANOVA model, if the experiment contain one factor it called one –way and if it have two factors it called twoway ANOVA and so on.
Multiple Comparisons: Multiple comparison procedures go against this basic philosophy in that they appear to formulate and test hypotheses in the same study simultaneously. In fact, the multiple comparison controversy is resolved if the procedures are thought of as hypothesis generators rather than as methods for simultaneous generation and test in [5]. Statistical testing of comparisons among a number of groups remains a common occurrence in behavioral science. However researchers do not provide calculated test values where appropriate, but simply give Pvalue [6]. Thus for pairwise comparison and to test
H_{0}: µ_{i} = µ_{j }i, j=1… a
It become
Where:
t_{diff}: test statistic for the difference of two groups.
: The mean of the i th group.
: The mean of the j th group.
MSE: the estimation of sample variance.
Ci: the confection of the i th group's mean in the comparison.
n_{i}: the sample size of the i th group.
For equal sample size
If there is more than one comparison t must be referred to appropriate critical value for the Multiple Comparisons Procedures. The selection of Multiple Comparisons Procedures will depend upon the choice of error rate.
Bonferroni procedure
The most widely applicable familywise control procedure for small families is the Bonferroni correction. One of the fundamental and historically utilized adjustments for type I error is the Bonferroni correction. The Bonferroni correction adjusts the alpha level at which a statistical test considered to be significant based on the total number of analyses being conducted. It is most common procedure to adjusting significant level to control Type I error rate in multiple testing situations. Specifically, the utilized alpha level is quantified as being the original alpha level divided by the number of comparisons being made. Implicitly, the Bonferroni adjustment assumes that these test statistics are independent. So each comparison is tested at α/c where:
α: significant level.
c: is number of comparison in family.
It provides great control over Type I error but conservative when there are lots of comparisons. The advantage is that can be applied to many situations where there is a family of tests [7].
DunnSidak procedure
It modification of the Bonferroni procedure which improved power for each comparison which test by α= (1(1 α)^{ 1/c}). The ŠidàkBonferonni approach becomes very conservative when the number of comparisons becomes large and the tests are not independent.
Sequential Bonferroni Holm
An equivalently more powerful statistical procedure is the Holm–Bonferroni technique. The HolmBonferroni technique is a successively rejective adaptation of the simpler Bonferroni adjustment for multiple analyses and strongly controls the alpha level. The HolmBonferroni adjustment ranks all of the observed pvalues in order. It is major improvement on Bonferroni procedure where the c number test statistics (F, t) or pvalues are ranked from largest to smallest (smallest to largest) p value is tested at α/c. if the first pvalue is greater than or equal to α/c procedure is halted and the null hypothesis is accepted. If the first pvalue is found to be significant the second pvalue is compared to the α/c1. Testing stops when nonsignificant result occurs. This procedure provides more power for individual test and it is recommended for any situation in which Bonferroni adjustment is applicable. Hochberg described similar procedure that worked inverse. The largest p is tested at α rejecting all other tests if this one is significant. If it is not significant the next largest at α/2 and soon. Shaffer stated that Hochberg’s procedure is slightly more powerful than Holm’s. The sequentially rejection Bonferroni test is an easily applied, versatile statistical tool that enables researchers to make simultaneous inferences from their data without risking an unacceptably high overall type I error rate [8].
Table 1: The normality measurements due to calving interval and total milk.
Trait 
Calving Interval (month) 
Total Milk (kg) 
N 
Valid 954 
699 
Missing 0 
0 

Mean 
17.3029 
2459.5784 
Std. Deviation 
9.0161 
3108.80370 
Variance 
81.29 
9664660.443 
skewness 
2.202 
12.482 
Std. Error of Skewness 
.079 
0.092 
Kurtosis 
6.158 
195.910 
Std. Error of Kurtosis 
0.158 
0.185 
Tukey (Honestly Significant Difference) HSD Procedure
Tukey`s Honestly Significant Difference(HSD) is most popular simple, easy and reliable comparison test which compares each group mean with every group mean in pair wise manner and control Type I error rate to no more than nominal level. The logic of Tukey’s HSD:
 Using t test and calculate the stander error for the difference between two means.
Using harmonic mean of the sample sizes when the groups have unequal simple size this is some time called Tukey –Kramer modification and reduced to 1/n in equal sample size.

 Compare HSD with t_{diff}:
If t_{diff}> HSD then rejected H_{0 }that in the respective population means are not equal. Otherwise, accept H_{0}. Repeat this for all pairs of means.
The power of the test may be low for less than all pairwise comparisons it prefer for all pairwise comparisons [9].
Scheffe Procedure
The Scheffe multiple: comparison has constant critical value for all comparisons on all group mean and it is appropriate for all possible comparison not just for pairwise comparison. Scheffe procedure controlling of p (at least one Type I error) at α using ERFW will do pairwise, nonpairwise comparison, orthogonal polynomial and so on. Scheffe procedure is very conservative test based on Fratio statistic. The comparison suggested by the data.
Reject H_{0} if:
Otherwise, accept H_{0}. The Scheffe procedure conserves the power of test unless there are large number of comparisons then it a good for large number.
Fisher’s protected t test LSD
This test is often called the Least Significant Difference (LSD), and it is popular multiple comparisons and usually attributed to Fisher. It is protected t test because it is compute usual t after only if the overall F ANOVA test is significant, Least Significant Difference is due to that α level t critical value that t statistic must exceed in order to be significant when only a single comparison is considered. Unfortunate because it controls p (at least Type I error) at α using ERFW for full null hypothesis. To make decision rule by two steps first: Test overall H_{0} with ANOVA F if F test is significant then second step else if F test is not significant then fail to reject H_{0 }for all comparisons. Second is to reject H_{0} for a comparison if
Otherwise, fail to reject H_{0}. LSD does not require equal sample sizes.
The power of test calculated as:
Where
ES: effect size.
α: significant level.
n: sample size.
σ: the standard division of population
Data and Methodology
The study carried in the Gezira State from two farms El Nisheishiba Dairy Farm of Gezira University and Bashaier Dairy Farm in ElShuckaba in South of Gezira State also, the tow farms have the same environment and managements
Data Source
Cow’s records from two farms are 162 cows. All cows have more than or equal three calving. The records for Calving interval are 954 and for Total Milk, Yield are 699.
Data Variables
The independent variables are type of cow (Kenana, Butane, hybrid cows50%, hybrid cows 62.5%, hybrid cows 75%and hybrid cows 87.5%), age at first calving, parity number and type of farm. Dependent variables are calving interval and total milk.
The Methodology
Completely Randomize Design (CRD) model constructed to show the relationship between dependent variable and independent variables.
The data had been checked to satisfying all the assumption of ANOVA.
ANOVA F test was used to enable the rejection of null hypothesis.
Then post hoc tests (Benoforrni, DunnSidak, LSD, Tukey, Scheffe ,Gabrial, Hochberg) were carried . The data was analyzed by SPSS 20.0 software.
The Model
Y_{ijklm}: the study trait calving interval or total milk yield.
µ: the general mean.
τ_{i}: type of cow (1: Kenana, 2: Butana,3: 50% ,4: 62.5% ,5: 75% ,6: 87.5%)
β_{j}: type of dairy farm(1=nishishiba,2=bashaier).
γ_{k: }age group (1=12,2=23,3=34,4=45,5=56) year.
δ_{l}: parity) 1=1,2=2ed,3=3,4=4^{th},5=5^{th} ,6= 6^{th} ,7=7^{th},8=8^{th},9=9^{th}).
(τβ)_{ij}: interaction between ith type of cow and jth type of dairy farm.
(τγ)_{ik}: interaction between ith type of cow and kth age group
(τδ)_{il}: interaction between ith type of cow and lth parity number.
(γδ)_{kl}: interaction between kth age group and lth parity number.
ε_{ijklm}: the error term which satisfy constrain that ε_{ijklm}~NIID (0, σ^{2})
The Data preparation
The important assumptions of ANOVA must be check before using the multiple comparison as following:
1The normalityof the data by using skewness and kurtosis tests.
2 Homogeneity of variance by using Levene test. Levenetested that the group’s variances are equal.
(Table 2) shewed the results of Levene test due to total milk and calving interval.
The result of two tests that the data not satisfy the assumptions. Then log10 was taken to transform the data.
Table 2: The results of Levene test due to total milk and calving interval.
Traits 
Fvalue 
Degrees of freedom 1 
Degrees of freedom 2 
Sig. 
Calving Interval 
1.691 
154 
862 
0.00 
Total Milk 
4.810 
150 
548 
0.00 
ANOVA Tables
(Table 3) shows analysis of variance table the dependent variable is Calving Interval. The less than 0.05. The factors explained 51.7 % of the variation on Calving Interval. The factors farm, type, parity, type*farm and age group*parity have significant effect pvalue is less than 0.05. The factors age group, type*age group and age group*parity have nonsignificant effect p value is greater than 0.05. R Squared = .517 (Adjusted R Squared = .465) Source: SPSS of study data. (Table 4) shows the analysis of variance table the dependent variable is Total Milk yield (kg). The model that used to interpret the Total Milk data is corrected because p value (sig) is less than 0.05. The factors explained 52.8 % of the variation on Total Milk. The factors type, farm, and interaction type*age group have significant effect on Total Milk pvalue is less than 0.05. The factors, age group, parity, the interaction type*farm, age group*parity and type*parity have nonsignificant effect p value is greater than 0.05. Results (Table 5) shows the means and standard deviation (std) for two traits Calving Interval (month) and Total Milk (kg) overall the study due to the type of cow. (Table 6) was showed the mean and standard deviation (std) for two traits Calving Interval (month) and Total Milk (kg) overall the study due to parity. After the ANOVA tells that there are differences then post hoc tests was done. Post hoc tests tested the hypothesis:
H_{0}: µ_{a}= µ_{b}
H_{a}: µ_{a}≠ µ_{b}
As pairwise comparisons. The post hoc tests that can be made confidence interval are be used in this study. (Table 7) shows the post hoc tests compared value and the power of test.
Table 3: The ANOVA due to calving interval transformed data.
Source 
Type III Sum of Squares 
df 
Mean Square 
F 
Sig. 
Partial Eta Squared 
Corrected Model 
17.302^{a} 
93 
.186 
9.903 
.000 
.517 
Intercept 
153.338 
1 
153.338 
8161.882 
.000 
.905 
farm 
.228 
1 
.228 
12.158 
.001 
.014 
type 
.288 
5 
.058 
3.067 
.009 
.018 
age group 
.096 
4 
.024 
1.283 
.275 
.006 
parity 
2.912 
8 
.364 
19.377 
.000 
.153 
farm * type 
.179 
3 
.060 
3.180 
.023 
.011 
type * age group 
.247 
8 
.031 
1.640 
.109 
.015 
type * parity 
.489 
32 
.015 
.813 
.760 
.029 
age group * parity 
1.637 
32 
.051 
2.722 
.000 
.092 
Error 
16.157 
860 
.019 



Total 
1394.031 
954 




Corrected Total 
33.459 
953 




Table 4: ANOVA table due to total milk yield (kg) the transformed data.
Source 
Type III Sum of Squares 
df 
Mean Square 
F 
Sig. 
Partial Eta Squared 
Corrected Model 
32.179^{a} 
83 
.388 
8.304 
.000 
.528 
Intercept 
539.414 
1 
539.414 
11553.561 
.000 
.949 
type 
2.470 
5 
.494 
10.580 
.000 
.079 
farm 
.405 
1 
.405 
8.675 
.003 
.014 
age group 
.349 
4 
.087 
1.868 
.114 
.012 
parity 
.298 
8 
.037 
.797 
.605 
.010 
farm * type 
.110 
3 
.037 
.788 
.501 
.004 
type * age group 
1.037 
8 
.130 
2.777 
.005 
.035 
type * parity 
1.604 
27 
.059 
1.273 
.163 
.053 
age group * parity 
.918 
27 
.034 
.728 
.842 
.031 
Error 
28.713 
615 
.047 



Total 
7589.484 
699 




Corrected Total 
60.893 
698 




Table 5: Calving interval and total milk means due to type of cow breeding. [i]
Trait Type 
Calving Interval(month) Mean ± Std 
Total Milk(kg) Mean ± Std 
Kenana 
1.223 ± 0.0180 
3.170 ± 0.029 
Butana 
1.272 ± 0.039. 
3.189 ± 0.067 
Hybrid 50% 
1.161 ± 0.0110 
3.395 ± 0.028 
Hybrid 62.5% 
1.132 ± 0.0260 
3.472 ± 0.050 
Hybrid 75% 
1.214 ± 0.0260 
3.468 ± 087 
Hybrid 87.5% 
1.122 ± 0.0430 
3.058 ± 0.075 
Table 6: Calving interval and total milk means due to parity.
Trait parity 
Calving Interval Mean ± Std 
Total Milk Mean ± Std 
first 
1.545 ± 0.022 
3.227 ± 0.026 
second 
1.192 ± 0.016 
3.260 ± 0.026 
third 
1.167 ± 0.016 
3.327 ± 0.028 
fourth 
1.173 ± 0.017 
3.312 ± 0.033 
fifth 
1.150 ± 0.020 
3.358 ± 0.054 
sixth 
1.145 ± 0.034 
3.336 ± 0.051 
seventh 
1.096 ± 0.026 
3.246 ± 0.068 
eighth 
1.139 ± 0.038 
3.369 ± 0.085 
ninth 
1.145 ± 0.046 
3.257 ± 0.125 
Table 7: post hoc tests ' comparedvalue and power.
procedure 
traits 
Tab value 
power 
α 
Tukey HSD 
Calving Interval 
2.8496 
0.2017 
0.05 
Total Milk 
3.1042 
0.0609 
0.05 

Scheffe 
Calving Interval 
0.2017 
0.05 

Total Milk 
3.9395 
0.0609 
0.05 

LSD 
Calving interval 
1.645 
0.2017 
0.05 
Total Milk 
1.645 
0.0609 
0.05 

Bonferroni 
Calving interval 
2.947 
0.0133 
0.0033 
Total Milk 
2.704 
0.0017 
0.0014 

Sidak 
Calving interval 
2.94 
0.0137 
0.0034 
Total Milk 
2.704 
0.0017 
0.0014 

Gabriel 
Calving interval 
2.649 
0.4856 
0.1204 
Total Milk 
2.542 
0.0543 
0.0445 
Discussion
The study’s means due to calving interval for Kenana and Butana greater than 15.20±0.04 and 12.60±0.06 respectively. Butana total milk mean also less than and Kenana total milk means was greater than but study’s mean of hybrid 50% is less than 14.80±0.12 [1012]. Found that the blood group had reversed effects on calving interval. study found that there is no significant differencebetween: 1Kenana and Butana breed(local cows)on two traits (Calving Interval and Total Milk). (Table 8) shows that there is no difference between Kenana breed and Butana breed cows. Also, Bonferroni, Sidak and Hochberg had the same length confidence interval except LSD has narrow one and Scheffe had wider one on two traits (Calving Interval and Total Milk). Hybrid cow 50% and (62.5, 75 ,87.5) % in Calving Interval but they have significant differences in Total Milk. (Table 9) shows that there is no difference between Hybrid cow 50% and Hybrid cow 62.5% when HSD, Scheffe, LSD, Bonferroni Sidak, Gabriel and Hochberg are used on Calving Interval. Also (Tables 1011) shows that there is no difference between Hybrid cow 50% and Hybrid cow 62.5% when HSD, Scheffe, Bonferroni Sidak, Gabriel and Hochberg are used but LSD shows there is difference between Hybrid cow 50% and Hybrid cow 62.5% on Total Milk and LSD had a narrow Confidence Interval in two traits (Calving Interval and Total Milk). In the same way the differences between 50 and 75, 50 and 87.5. 3Hybrid cow cows 62.5 %and (75, 87.5) %. 4Hybrid 75% and 87.5% in Calving Interval but they have significant differences on Total Milk. However, there are significant differences between: 1Hybrid cow (50, 62.5,75 , 87.5) % and local cow Kenana. (Table10) showed that there was different between Kenana breed and Hybrid cow 50%. Also, all pairwise comparisons approximately have the same confidence interval except LSD has narrow one on two traits (Calving Interval and Total Milk0. 2Local cow Butana and Hybrid cow (50, 62.5 , 75 , 87.5) %. (Table 11) shows that there is difference between Butana and Hybrid cow 50% when HSD, Scheffe, LSD, Bonferroni, Sidak, Gabriel and Hochberg ware used but Scheffe had wider interval and LSD has a narrow length of Confidence Interval. The Hybrid 50% has better reproduction traits than the other Hybrid cow which agree with. Also, the study shows that there are no differences on two traits (Calving Interval and Total Milk) between: parity one and parity four, parity one and parity six, parity two and parity three, parity two and parity five, parity three and parity four, parity four and parity five, parity five and parity eight, parity six and parity seven, parity six and parity eight, parity six and parity nine, parity seven and parity eight, parity seven and parity nine. Parity eight and parity nine. Otherwise, there are significant differences between the other parities on two traits (Calving Interval and Total Milk).
Also, the tables from 7 to 11, showed that:
1α decreased as the number of comparisons increased.
 Bonferroni is good for 6 comparisons or less.
 All post hoc procedures have approximately the same tabulated value if the data are balanced.
 Scheffe has the longest confidence interval.
 LSD is the best for balanced and unbalanced data and has the shortest confidence interval.
In practice, an applied statistician cannot afford to recommend an inconsistent procedure, so the unrestricted LSD procedure is the only procedure that can be safely recommended to researchers. In addition to its consistency, the unrestricted LSD procedure has many practical advantages over the alternative procedures because it is simple, provides a natural extension to the twopopulation case, flexible enough to cater easily for unequal replication or heterogeneity of variance and also because LSD is consistency, simplicity, flexibility in calculations and Type I error rate is constant, maximum Power. This explanation is compatible with the results obtained by this study.
Table 8: The comparisons between Kenana and Butana on Calving Interval and Total Milk.
Comparison

Traits 
sig 
95%confidence interval 
Length of confidence 

Lower bound 
Upper bound 

Tukey HSD 
Calving Interval 
0.793 
0.0380 
0.1002 
0.1382 
Total Milk 
0.413 
0.1934 
0.0397 
0.2331 

Scheffe 
Calving Interval 
0.895 
0.0496 
0.1118 
0.1614 
Total Milk 
0.616 
0.2130 
0.0593 
0.2723 

LSD 
Calving Interval 
0.199 
0.0164 
0.0786 
0.0950 
Total Milk 
0.060 
0.1569 
0.0033 
0.1602 

Bonferroni 
Calving Interval 
1.000 
0.0401 
0.1023 
0.1424 
Total Milk 
0.900 
0.1970 
0.0433 
0.2400 

Sidak 
Calving Interval 
0.964 
0.0399 
0.1021 
0.1420 
Total Milk 
0.605 
0.1967 
0.0430 
0.2397 

Gabriel 
Calving Interval 
0.916 
0.0327 
0.0949 
0.1276 
Total Milk 
0.446 
0.0322 
0.1859 
0.2181 

Hochberg 
Calving Interval 
0.963 
0.0399 
0.1021 
0.1420 
Total Milk 
0.602 
0.0430 
0.1967 
0.2397 
Table 9: Hybrid 50% and Hybrid 62.5% cow comparisons on calving interval and total milk.
Comparisons 
Traits 
sig 
95%confidence interval 
Length 

Lower bound 
Upper bound 

Tukey HSD 
Calving Interval 
1.000 
0.0698 
0.0573 
0.1271 
Total Milk 
0.159 
0.01740 
0.1984 
0.2158 

Scheffe 
Calving Interval 
1.000 
0.0804 
0.0680 
0.1484 
Total Milk 
0.333 
0.2165 
0.0355 
0.2520 

LSD 
Calving Interval 
0.779 
0.0499 
0.0374 
0.0873 
Total Milk 
0.017 
0.2017 
0.0163 
0.2180 

Bonferroni 
Calving Interval 
1.000 
0.0717 
0.0593 
0.1310 
Total Milk 
0.252 
0.2017 
0.0208 
0.2225 

Sidak 
Calving Interval 
1.000 
0.0716 
0.0591 
0.1307 
Total Milk 
0.225 
0.2014 
0.0205 
0.2219 

Gabriel 
Calving Interval 
1.000 
0.0632 
0.0507 
0.1139 
Total Milk 
0.100 
0.1888 
0.0078 
0.1966 

Hochberg 
Calving Interval 
1.000 
0.0715 
0.0591 
0.1306 
Total Milk 
0.224 
0.2014 
0.0204 
0.2218 
Table 10: Kenana and Hybrid cow 50% comparisons on calving interval and total milk.
Comparison

Traits 
significant 
95%confidence interval 
Length of confidence 

Lower bound 
Upper bound 

Tukey HSD 
Calving Interval 
000 
0.0885 
0.1451 
0.2336 
Total Milk 
000 
0.3928 
0.2887 
0.1041 

Scheffe 
Calving Interval 
000 
0.0838 
0.1498 
0.2336 
Total Milk 
000 
0.4015 
0.2800 
0.1215 

LSD 
Calving Interval 
000 
0.0974 
0.1363 
0.11103 
Total Milk 
000 
0.3765 
0.3050 
0.0715 

Bonferroni 
Calving Interval 
000 
0.0877 
0.1460 
0.2337 
Total Milk 
000 
0.3944 
0.2871 
0.1073 

Sidak 
Calving Interval 
000 
0.0878 
0.1459 
0.2337 
Total Milk 
000 
0.3943 
0.2872 
0.1067 

Gabriel 
Calving Interval 
000 
0.0880 
0.1456 
0.2336 

Total Milk 
000 
0.3939 
0.2876 
0.1063 
Hochberg 
Calving Interval 
000 
0.0878 
0.1459 
0.2337 
Total Milk 
000 
0.3943 
0.2873 
0.1070 
Table 11: Butana and Hybrid cow 50% comparisons on calving interval and total milk.
Comparison

Traits 
significant 
95%confidence interval 
Length


Lower bound 
Upper bound 

Tukey HSD 
Calving Interval 
0.004 
0.0182 
0.1532 
0.1350 
Total Milk 
000 
0.3778 
0.1501 
0.2277 

Scheffe 
Calving Interval 
0.023 
0.0069 
0.1646 
0.1577 
Total Milk 
000 
0.3969 
0.1310 
0.2659 

LSD 
Calving Interval 
0000 
0.0393 
0.1321 
0.0928 
Total Milk 
000 
0.3421 
0.1857 
0.1564 

Bonferroni 
Calving Interval 
0.005 
0.0162 
0.1553 
0.1391 
Total Milk 
000 
0.3813 
0.1465 
0.2348 

Sidak 
Calving Interval 
0.005 
0.0162 
0.1551 
0.1389 
Total Milk 
000 
0.3810 
0.1468 
0.2342 

Gabriel 
Calving Interval 
0000 
0.0258 
0.1456 
0.1198 
Total Milk 
000 
0.3668 
0.1611 
0.2057 

Hochberg 
Calving Interval 
0.005 
0.0163 
0.1551 
0.1388 
Total Milk 
000 
0.3810 
0.1469 
.2341 
Conclusion
After ensuring that the data satisfied the conditions of the analysis of variance then at significant level 0.05: LSD has a narrow interval. Scheffe is good for pair wise and nonpairwise but has wide interval. Bonferroni is good for small comparisons. Kenana and Butana have the same reproductive traits. Hybrid 50% cow has good reproductive traits than other Hybrid cows. The cow can be stay at the herd until parity six. There are differences between tow farms on tow traits.
Recommendations
From this study, it could finally recommended that: LSD is the best post hoc procedure to study the difference between groups. It has been established that dairy cattle managers at ElNishishiba and El Bashaier dairy farms, may be advised to keep crossbred dairy cows of the intermediate exotic blood (50%Friesian inheritance) for higher production and reproduction traits. The cow may be culled after parity six. More work in evaluation crosses with the intermediate blood level with large number of records and for longer period was so needed at the two farms. The tow farms must be established scientific data sets for each cow. For future research development of software of statistical analysis that first checks the data that satisfy the assumption of any statistical techniques before it is used is may be place.
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