Completely Random Design and Least Significant Differences for Breast Cancer in Al-Najaf City ( )

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1 International Research Journal of Applied and Basic Sciences. Vol., 3 (6), , 2012 Available online at www. irjabs.com ISSN X 2012 Completely Random Design and Least Significant Differences for Breast Cancer in Al-Najaf City ( ) *Hadeel Salim Alkutubi 1, Ebtesam Najim Al-Bistenchy 1 and Hasan Ali Al-Azzam 2 1- Informatics Center for Research & Rehabilitation, Kufa University, Iraq 2- Al-Sader Medical City, Najaf, Iraq Corresponding Author hadeelkutubi@live.com Abstract In this study, we evaluate breast cancer in Al-Najaf city in Iraq for the period The data is analyzed using completely random design to explain the significant difference between all variables: age, tumors level, occupation, marital status and education. And least significant differences to find all differences between the pairs of treatments. The differences greater than or equal to the least significant difference are significant. In the results, ANOVA Table explain there is a significant different between age groups, levels of Tumor, occupation groups, marital status groups, and finally education groups. LSD values explain there is a significant different between three age groups only, that is (21-30), (31-40), (41-50). But, we can see a significant different for one group only of level of tumor that is level 4. Also, there exists one significant different group for occupation that is unemployed group. But, we can see one significant different group that is married group. And, there are three significant different groups for education that is ittiteracy, primary, and secondary group. Keywords: ANOVA Table, Breast cancer ( ), completely random design, degress of freedom, least significant differences. Introduction We have taken 900 cases from Al-Sader medical city in Al-Najaf in Iraq for the period This data contain breast cancer divided between age groups, Levels of Tumor, Occupation, Marital Status and Education. The main aim of this study are presentation and description all cases of breast cancer and find the significant difference between all years and groups depend on all variables age groups, levels of tumor, occupation, marital status and education using ANOVA table for completely random design and least significant differences test. In completely random design, there is a simply chosen at random from the population to which inferences to be made. Also the total sample is randomly divided into groups and the different treatments are then applied to the groups, one treatment or condition to a group. If the treatments differ from each other then the various treatment groups will have different mean values at the end of the experiment. The general method for the completely random design is the analysis of variance. The process of using the ANOVA (analysis of variance) (Table 1).( Alkutubi H S, Yaseen N K 2009) Each experimental unit in completely randomized design has an equal and independent chance of receiving any one of the treatments. The basic assumption underlying this design is that the observed values in any one group represent a random sample of all possible values of all experimental units under that particular treatment. We assume that the responses are normally distributed about the treatment mean and that the variation among observations treated alike is identical for all treatments.( Mood A M, Graybill FA 1974, Taylor J K Cihon C 2004) In the least significant differences, we found all the differences between the pairs of treatments. The differences greater than or equal to the least significant difference are significant.

2 Materials and Methods Completely Random Design In this part of study we present the theoretical method of completely random design. We depend on CHAP (Bland Martin 2000, Chap T LE 2003, Montgomery D C 1997) to explain the method of completely random design as follow. We have continuous measurements X' s from k independent samples. In that combined sample of size the variation in X is measured in terms of the deviations, the total variation denoted by SST, is the sum of squared deviations:. The first term reflects the variation within the ith sample is called the within sum of squares, denoted by: SSB The difference between the two sums of squares is called the between sum of square. Denoted by SSB represents the variation or differences between the sample means. Corresponding to the partitioning of the total sum of squares SST, there is partitioning of the associated degrees of freedom (df). We have n-1 degrees of freedom associated with SST. SSB has k-1 degrees of freedom representing the differences between k groups. The remaining degrees of freedom are associated with SSW. These results lead to the usual presentation of the ANOVA process: 1. The within mean square, denoted by 2. The between mean square, denoted by, represent the average variation (or differences) between the k sample means. 3. The breakdowns of the total sum of an analysis of variance table (Table 1) the test statistic F for the one-way analysis of variance above compares MSB (the average variation or differences between the k sample means) and MSE (the average variation within the k samples ). A value near 1 supports the null hypothesis of no differences between the k population means. Decisions are made by referring the observed value of the test statistic F to the F table with (k-1, n-k) degress of freedom. Table 1. ANOVA Table Source of variation SS df MS F statistic P value Between sample SSB k-1 MSB MSB/ MSW p Within sample SSW n-k MSW Total SST n-1 Least Significant Differences We can get LSD using the following calculate (Alkutubi H S, Yaseen N K 2005, Alkutubi H S, 2009, Alkutubi H S, Yaseen N K 2009 ) 2MSE LSD = t, where n is the number of replications. After that found all the differences α, df MSE n between the pairs of treatments. The differences greater than or equal to the least significant difference are significant. Results and Discussion In this part of study, we will used the theoretical method of completely random design (section 2.1) and method of least significant differences (section 2.2) to get the following Tables

3 Table 2. Number of People with Breast Cancer Broken Down by Age Groups. Age Groups Years Table 3. ANOVA for Age Groups Source Df SS MS F Treatment Error Total We can see in this table F value equal to 8.073, that is greater than F table (F 0.01(7,32) =4.30), then we can get a significant different between Age group. Table 4. Mean value for Age Groups Age Mean When we compare LSD value with mean value for age group, we find a significant different between three groups only, that is (21-30), (31-40), (41-50). Table 5. Number of People living with Breast Cancer Broken Down by Levels of Tumor. Years Table 6. ANOVA for Levels of Tumor Treatment Error Total In this table, F value equal to 6.078, that is greater than F table (F 0.01 (3, 16) =4.34), then we can get a significant different between levels of tumor. Table 7. Mean value for Levels of Tumor Tumor Mean We compare LSD value with mean value for levels of tumor, we find a significant different between one group only, that is level 4.

4 Table 8. Number of People living with Breast Cancer Broken Down by Occupation Years Unemployed Employed Table 9. ANOVA for Occupation Treatment Error Total In this table, F value equal to , that is greater than F table (F 0.01(1,8) =11.259), then we can get a significant different between occupation groups. Table 10. Mean value for Occupation Occupation unemployed Employed Mean We compare LSD value with mean value for occupation, we find a significant different between one group only, that is unemployed group. Table 11. Number of People living with Breast Cancer Broken Down by Marital Status Years Single Married Widow Divorced Table 12. ANOVA for Marital Status Treatment Error Total In this table, F value equal to , that is greater than F table (F 0.01(3,16) =5.2922), then we can get a significant different between marital status. Table 13. Mean value for Marital Status Marital Status Single Married Widow Divorced Mean We compare LSD value with mean value for marital status, we find a significant different between one group only, that is married group. Table 14. Number of People living with Breast Cancer Broken Down by education Years Ittiteracy Primary Secondary Diploma University further

5 Table 15. ANOVA for Education Source Df SS MS F Treatment Error Total In this table, F value equal to 7.695, that is greater than F table (F 0.01(5,24) =3.8951), then we can get a significant different between education. Table 16. Mean value for Education Education Ittiteracy Primary Secondary Diploma University further Mean We compare LSD value with mean value for education group, we find a significant different between three groups only, that is ittiteracy, primary, and secondary group. Conclusion ANOVA Table explain there is a significant different between age groups in Table 3, levels of Tumor in Table 6, occupation groups in Table 9, marital status groups in Table 12, and finally education groups in Table 15. LSD values explain there is a significant different between three age groups only, that is (21-30), (31-40), (41-50) in Table 4. But in Table 7, we can see a significant different for one group of level of tumor that is level 4. Also, there exists one significant different group for occupation that is unemployed group in Table 10. But in Table 13, we can see one significant different group that is married group. And from Table 16, there is three significant different groups for education, that is ittiteracy, primary, and secondary group. References Alkutubi HS, Yaseen NK, Evaluation of cancer disease for the period ( ) in Tikrit teaching hospital, Tikrit journal of pharmaceutical science, Iraq, 1(2). Alkutubi HS, Experimental design of HIV patients. European journal of scientific research. Euro journal publishing, Inc. 35(1): Alkutubi HS, Yaseen NK, On Completely Random Design of Cancer Tumors in Tikrit Teaching Hospital. European journal of scientific research. Euro journal publishing, Inc. 35(4): Bland M, An introduction to medical statistics, 3 th ed, Oxford University Press, Inc., New York. Chap TLE, Introductory biostatistics. A john wiley & sons publication. New Jersey. Montgomery DC, Design and analysis of experiments.5 th ed. John Wiley & Sons, Inc. Mood AM, Graybill FA, Introduction to the theory of statistics, 3 th ed. MCGraw- Hill kogakusha, Lth. Taylor JK Cihon C, Statistical Techniques for data analysis. 2 nd ed.chapman & Hall / CRC.