Categorical data analysis with Practical Application

The main purpose of this study is to find out vectors that can be inserted to the statistical analysis of certain groups of variables which are formed as a result of a certain condition depending on categorical data (i.e. Qualitative variable ). Many statistical models have been discussed to deal with this condition in order to have a discriminate function or to have variables by which we can specify the condition gradually. Depending on the importance of the inserted variable in that condition, a theorem form of this sensitive variable has been derived . Some applications have been also used in this paper.


Introduction
This paper will try to explain samples (models) of vector expectations versus models for every response or order pairs individually or multiply . The discrimination between one another is known as linear logarithm models (see Mahalanobios (1936), Hand (1981), Fisher (1950) and Anderson (1957) [2]. The discriminate studies concerning the sensitive data or qualitative data are limited and Fisher (1950) disregarded and them . This case was treated by random specific values where two common approximates of the prospects equations are compared and which are relates to the assumed statistic knowledge and as follows: First : Concerning all the knowledge at one point then the estimation of the regression knowledge by statistically .
Secondly : The estimation of the regression and the united statistical knowledge is done at one time .
What we are doing ,in particular, is discriminating the independence of each response for the other illustrative variables or describing the union among responses (i.e Qualitative variables).
In general ,our style (method) of response analysis depends on applying the formula of each option , response or class of variables as value for each item with two basic ideas of the discriminate analysis of the quantitative data and of the discriminate analysis of the paired data .It is possible first to determine the classes characteristics transfer from quantitative data into qualitative data and then to be used in the discriminate analysis in order to find out the variables and their importance for a case like the quantitative data . The work of Tielschetal (1989) is considered as an example for this , He conducted a theoretical analysis for the specific data of the vision power that was taken from a survey mode on 5000 persons at age of 40 . This sample was tested as it represent the total population from which it had been randomly taken.
This work is to determine the quantitative data that affect the eye power then observing it until the examination result . Its importance will be according to the examination result and it will be distinguished in the same way as the power of the level of education, taking medicine and its quantity , … etc in which the versus regression model clarifies the importance of the middle versus through the variables .
weighted sum of squares [4]; The identity matrix is a special case of a diagonal matrix . This matrix arises in a number of situation .we minimize a weighted sum of squares The OLS estimator of β is found by minimizing the sum of squares The vector of partial derivatives of the sum of squares with respect to β may be expressed as When we equate this expression to zero and solve , it yields the OLS estimator The variance -covariance matrix of b is obtained by multiplying the mean square error , , 2 σ ε or its estimate ,by the inverse of the sum of squares and cross-products matrix , , ' x x as follows : This operation results in a square matrix with ) var( bk along the diagonal and

Binary variables :
The scientists kuder and Richardson at (1933) [5] represent the first way which used the alternative variables which is called by (binary scores ) .Which is the responses mean which depends on one another , when we ask about a specific phenomenon the respond will be yes or no .which win give it a specific value like (1 , 0) and there is a hard difficulty for reaching to the like values which reduces the dissimilarity inside the units (between the testing ) At 1935 (Horst) [6] mentioned that the selection will adjust to give the greatest discriminate value between it, and he depended on the deaf-variables , , , , 33  3  32  2  31  1  22  2  21  1  13  3  12  2  11 1 By using Lacherange multiplier [1] and statistics and athematics processes the researchers have all the detail about it in getting the matrix .
The variable which carries highest value is the best for the discriminate process.
Following the variable carries the lowest value ,and follow for any variables .

Practical Application:
One of the factories announced its requirement for a huge number of personnel, and that which carries different degrees to work at that factory ,which had been carried out by one of the architecture companies .and the difficult that faced this factory was that the number of personnel that applied for a job were above the factory's requirement .
Also it was hard to determine the personnel's skill and capability for the job and statistics features had been putting in the effect in which the stipulation of age and testimony had been putting aside ,and been settled previously the statistics authorities noticed by many questionnaires the following . These things were the causing that were influencing the work path and acceptance of the project works .
So ,we want to apply these variable s to distinguish the state for every worker before his acceptance in this factory .and the binary discriminate data were the excellent directions here .
And for simple analysis ,male and female have been analyzed one by one .And a100 item has been taken from each sex as random sample , representation the total population to obtain discriminate variable to get benefit from them in the new acceptance ,and for easiness the last two tests have been mixed and formed that In the case when any male advances to work at this factory it is enough to give him this list to fill it and then we can expect if he will be a good works or not hence we will give the superior checker a recommendation to decide the acceptance or the refusal .
As for females , the results were as following :

Conclusion and recommendation
We conclude from what we displayed that there is a statistical method which had been neglected by many statistics application studies, and it is the ability of getting benefit from the qualitative data and classification . Then distinguish its importance in affecting a specific phenomenon . We advise for increasing the statistics researches and then using them on the real life for getting benefit from it as we showed in our research .We derive and take a specific method for treating with qualitative data by depending on various resources.