A class of modification is proposed for calculating a score for each Player/team in Unbalanced Incomplete paired Comparisons Sports Tournaments. Many papers dealing with Balanced Incomplete Paired Comparison Sports Tournaments with at most one comparison per pair have appeared since 1950. However, little has been written about unbalanced situations in which the player /the team (object) ( j ) plays unequal number of games against the player/the team( m ) in a tournament, and the results of all games can be summarized in a Win-Lose matrix Y = { Yjm } , where Yjm = 1,0,1/2, respectively, according to as the player or the team ( j ) wins, losses or draws against the player or the team (m ). Published papers by Ramanujacharyulu (1964), Cowden, D.J. (1975), and David, H. A.(1988) have concentrated on the problem of converting the results of unbalanced incomplete paired comparison tournaments into rank with little consideration of the main relative ability on each player or team. We suggest (modification) another way of quantifying the outcomes of the games/tournaments, in particular, ratings on a scales, 0 to 5, 1 to 10 .ect. It is important to consider not only the vector Vj(d) or the vectors Sj, in scoring and ranking the k teams in such tournaments, but also the vector Zj, where Zj = Sj + SjRj, to take into account the ratio of the relative ability of each team ( Rj ). The proposed modification helps to introduce these methods for use in comparisons/games (tournaments), where the player/team are quantified on a special scale. e.g. 0-5, 1-10, ..etc. We conclude the following:- The scores stabilized to three decimal places at iteration 2 in Cowden’s method Vj(d) .see table(1.4). The scores stabilized to three decimal places at iteration 2 in David’s method Sj , and it’s modification Zj. The proposed modification (Zj) has the advantage of removing ties from David’s method (Sj), and hence it is the best method.

This paper focuses on the use of principal component analysis technique (PCA) in choosing the best applicant for a job in Cihan University-Erbil. Cihan University has a panel of judges (University staff) to help in choosing the applicants for a job by evaluating or rating each one on different scale of preference and different type of characteristics. This process usually creates complicated multivariate data structure, which consists of 25 applicants for a job rated by a panel of judges on 17 characteristics [25 rows, applicants, and 17 columns, characteristics]. PCA plays a crucial role in conducting impactful research as it offers a potent technique for analyzing multivariate data. Researchers can utilize this method to extract valuable information that aids decision-makers in problem-solving. To ensure the appropriateness of data for PCA, certain testing procedures are necessary. In this study, two tests, namely the Kaiser-Meyer-Olkin (KMO) Measure of Sampling Adequacy and Bartlett's Test of Sphericity, were performed, and their significance is vital. The findings indicate that the data employed in this research are suitable for PCA. Scoring and ranking procedures as extra tools were used to see that applicant No. (1) is the first accepted for a job, applicant No. (17) is the second, applicant No. (12) is the third, and so on.